Abstract: This case discusses about the export of spices from India. It begins with the definition of trade and types of trade and further discusses about the reason of trading. Further it's about India as a permier destination of organic spices, which includes the varieties of spices offered, by India, organic farming, Indian Spice Board initiative, Promotion of spices. Apart from this case discusses about cultivation of various spices in India and then the major Export destinations for spices. It further includes key markets for spices of India, various exporting companies, shipping details for exporting and the logistic method used for exporting spices. The report ends up with conclusion and a news article on export of spices.
Keywords: Destinations, Organic farming, Organic spices, Spices Board, Weather.
Abstract: In this competitive era creating and sustaining the quality of service to meet the expectation of customers is of utmost importance. Understanding the zone of tolerance of consumers and taking innovative measures can certainly enhance the business opportunities and increase market share.
Service quality and customer satisfaction are the vital aspects which companies must understand in order to gain a competitive advantage. Therefore it is has become imperative for companies to know how to improve the moments of truth in a positive way in the mind of customers, measure and analyze the consumer trends and preferences. Service quality is of utmost importance as it leads to higher customer satisfaction, customer loyalty and retention. Further a it also helps to garner higher profit margins through cross selling and up selling.
The purpose of this paper is to study the customer expectations of the customers about the quality of service offerings by Panthanivas in Bhubaneswar and measure the customer satisfaction on various services offered using SERVEQUAL Model.
Keywords: zone of tolerance, moments of truth, Service quality, customer expectations, customer satisfaction, SERVEQUAL Model.
Abstract: To succeed in the modern global economy, it is critical to build a Logistics network that is information-rich, highly flexible, cost effective, and defined by both customer needs and internal corporate strategy. Organizations must constantly reinvent the Logistics network to allow business growth and change. Yet, the superiority in Logistics operations is anything but enough to achieve competitive advantage. The proper handling of Reverse Logistics is currently perceived as the leading distinction edge among organizations. From another perspective, high operational efficiency is dependent on quick, accurate, and continuous exchange of information within an organization. Such ability is achieved through the use of modern Information Technology and computer automation. As organizations cannot move into the highly competitive environment by adapting old management methods, Process Reengineering might be the solution. In this research, the concepts of Reverse Logistics, Information Technology, and Process Reengineering are spotlighted. A reengineering of the current maintenance process of a major Egyptian Healthcare Medical Equipment Provider is proposed in order to enhance the Customer Service Quality and the Operational Efficiency. Computer simulation modeling is used to evaluate the proposed model.
Keywords:Business Process Reengineering, Computer Simulation, Customer Service Quality, Cycle Time, Healthcare, Operational Efficiency, Reverse Logistics.
Abstract: The Youth Enterprises have to survive in the global economic environment through defining the areas in which they can achieve the superior results and on them base their complete business. This article discusses the back ground information regarding youth enterprises in relation to vision 2030 and the global trends on SMES competitiveness as well as regional trends on SMES competitiveness. The research objectives are the effects of collaborative networks, innovation, product diversification and entrepreneurial skills on competitive advantage of youth enterprises. Conceptual framework focuses on both independent and dependent variables, independent variables namely; collaborative networks, innovation, product diversification and entrepreneurial skills; dependent variable namely competitive advantage. The purpose of this article is: to unite and to expand the existing cognitions about the concept of collaborative networks, innovativeness, product diversification, and entrepreneurial skills; propose the universal model for the process of transformation of implementing these concept and to point on the guidelines which should follow these concepts.
Keywords: Collaborative networks, Competitive advantage, Product diversification and Entrepreneurial Skills.
Abstract: Modern Marketing Philosophy advocates the concept of customer relationship marketing that creates customer delight. In the banking field a unique relationship exists between the customers and the bank. Due to various reasons like financial burdens, risk of failure, marketing inertia etc., many banks are still following the traditional ways of marketing and only few banks are making attempts to adapt customer relationship marketing. The role of custom er relationship marketing is very vital in leading the banks towards high level and volume of profits. So there is a need to study the role of customer relationship marketing in development and promotion of banking sector through the side-lines of the practices, problems and impact of CRM on banking sector all the time.
Keywords: customer relationship marketing in development, promotion of banking sector, CRM.
Abstract: Commercial Surrogacy, which is the act of selling a woman's ability to give birth to a child with another man strictly for business purposes, is a rapidly growing industry in today's societies that permit it. It is also an issue that has many moral and ethical implications. It compromises many moral principles and values and therefore raises many questions to consider whether or not commercial surrogacy is moral. Examples of these moral implications include questions such as whether or not it is ethical to put monetary value on the creation of life, how does commercial surrogacy affect women's rights in countries such as India where we see a particular vast growth in this industry, where women may not necessarily be fully protected by law and may be forced by their families who live in poverty to perform this act for financial necessity. Due to the fact that this is a very modern, as well as rapidly growing issue, it is very important to discuss and raise awareness that it is a very real issue that creates a lot of moral dilemma so that it can be changed and perhaps banned in countries that currently allow it, if deemed immoral. To examine this issue, the situation of commercial surrogacy in India, which has grown into a multibillion dollar industry and is therefore, deemed the worldwide capital of surrogacy. The statistics such as the projected net worth of commercial surrogacy as an industry in 2012 will be analysed as well as different things such as families in India who have experienced commercial surrogacy. The Law Commission of India has submitted the 228th Report on "Need for Legislation to Regulate Assisted Reproductive Technology Clinics as Well as Rights and Obligations of Parties to a Surrogacy."
Keywords: Surrogacy, gestational surrogacy, traditional surrogacy, Commercial surrogacy, constitution, law commission, process, Destinations.
Abstract: The purpose of the study was to examine the effect of strategic planning on the performance in Secondary Schools in Trans-Nzoia West Sub-County. The objective of this study was to assess the influence that resources have on performance of secondary schools. The target population was 370 numbers of stakeholders in public secondary school in Trans-Nzoia West sub-county. Purposive and random sampling technique was used to sample the schools and the sample size was 30% of the target population. Data collection instruments were questionnaires, interviews and observation. Data was processed by use of percentages. The key recommendations were as follows: - i) The Ministry of Education should ensure that all schools have strategic plans in place to guide in the allocation of school's resources for efficiency and effectiveness. ii) The government through Ministry of Education together with the County Government should increase funding of infrastructure in the schools in order to ensure that all schools have the necessary basic physical facilities to be able to compete favourably with others that are endowed with adequate facilities. iii) The government through the Ministry of Education should regularly visit schools to monitor and evaluate the implementation of the objectives in the strategic plan and take remedial measures to address failures in areas that need help.
Keywords: Strategic planning and performance.
Abstract: This paper sought to examine financial factors affecting the operational efficiency of water companies in Kenya. It was driven specifically by the fact that despite great improvement in the sector, water companies have not yet achieved operational efficiency. It was guided by four objectives: To assess the Effect of Firm's profitability on the Operation Efficiency of Water Companies in Kenya, to assess effect of revenue collection efficiency on Operation Efficiency of Water Companies in Kenya, to evaluate the effect of size of the firm on Operation Efficiency of Water Companies in Kenya and to evaluate the effect of Operation and Maintenance cost on Operation Efficiency of Water Companies in Kenya. A descriptive survey design was employed where stratified sampling was used to select a sample of 52 respondents. Interview schedules and the questionnaire were administered as the main tools for data collection. The Data collected was analysed using both descriptive and inferential statistics aided by SPSS software. From the findings Revenue Collection Efficiency and Operation and Maintenance Cost Coverage were found to be positively correlated with the Cash Conversion Cycle. Thus the above should be considered as key determinant enhancing operational efficiency in water service provision.
Keywords: Working capital management, Operational Efficiency, Cash Conversion Cycle, Operation and Maintenance cost, Revenue Collection Efficiency, Profitability.
Abstract: Supply chains as one of the governance aspect are complex systems with different structures and power proportions between partners. Managers would be in a better position to meet the challenges of global supply chain processes if they understand the implementation issues and their roles on supply chain effectiveness. The main purpose of the study is to investigate the effect of supply chain management competencies on organizational performance and specifically the effect of innovation Orientation on organizational performance. Explanatory research design was used. The population of study comprised 244 employees from selected Parastatals in Nairobi City County. Questionnaires were used to collect data and data was analyzed using descriptive statistics like means, frequencies, and percentages, and inferential statistics, Pearson correlation and multiple regressions. Results indicated that innovation orientation has significant and positive effect on organizational performance. This concludes that firms whose managers have innovation orientation improve performance. It is recommended that there should be further research and development on innovative and leading organizational practices in order to enhance performance and need for supply chain management policies and procedures that follow an appropriate sequence and structure.
Keywords: Governance, Management competencies, Organizational performance, Parastatals, Supply chains.
Abstract: Retention possesses an essential spot and position inside the entire administration process. This component is utilized productively for swaying staff to make positive commitment for accomplishing organizational goals. Retention is vital, as individual temperament needs some kind of prompting, consolation or motivation to give higher execution. Over the past 5yrs, the rate of nursing staff leaving their jobs has been 40% annually and this has continued to be a problem affecting the delivery of health services. Motivation of employee's therefore, offers numerous edges to the Organization and also to the staff. Hence this study sought to establish the factors affecting retention of health workers in the health sector and especially nurses in the health department of Transnzoia County Government. The study was guided by the following objectives; - to determine the factors that affect nurse retention in the Health sector of Transnzoia County Government, to find out the effects of job satisfaction on nurse retention in the Health sector of Transnzoia County Government and to establish the effect of retention programs in the health sector of Transnzoia County Government. The design used for this study is the descriptive method. The targeted sample for this study comprised of senior management nurses as well as junior management nurses at the hospitals, health centers and dispensaries within Transnzoia County. The total population of nurses currently stands at three hundred and twenty. A sample size of one seventy five members was selected by using random sampling method. Both primary and secondary sources of data were used during the study. The procedures for collection of data for this study were basically questionnaires and interviews. Data collected using the questionnaires was edited for clarity and then frequency tables drawn to show the final results using Pearson product-Moment Coefficient correlation and Statistical Package for Social Science (SPSS) software. The SPSS was used to analyze the information gathered which was used in development of charts and graphs. It is therefore important to understand personal premises and key retention factors anchored on contemporary nursing management practices with identifiable indicators.
Keywords: Retention possesses an essential spot and position Statistical Package for Social Science (SPSS) software.
Abstract: Employee commitment always plays a very key role in improving the academic performance. Distinguished performing companies perceive that employee commitment is a premier contributing factor toward maintaining continual success and composing value. A committed employee is participative and energized about their work and performs in an aspect that will progress the organization's interest. The purpose of this study was to determine the effects of employee commitment on academic performance of secondary schools in Elgeyo- Marakwet County. The objectives of the study were: to determine the effect of emotional commitment of the headteacher on school's academic performance, to establish the effect of normative commitment of the headteacher on school's academic performance, to examine the effect of continual commitment of the headteacher on school's academic performance. The study adopted a census case design that entailed having all the headteachers of all the secondary schools in Elgeyo-Marakwet County as the respondents. The three constructs of employee commitment i.e. the normative, emotional and continuous commitment were treated as the independent variable while academic performance was the dependent variable. Data was analyzed using SPSS and both descriptive and inferential statistics was used. Regression was used to construct models that were used to determine the nature of the relationships between the variables of interest. All the hypothesized relationships developed were found to be statistically significant at level p < 0.05 i.e. emotional commitment (r = 0.401, p < 0.000), continual commitment (r = 0.410, p < 0.000), normative commitment (r = 0.273, p < 0.000) were correlated to academic performance significantly and positively. all the organizational commitment constructs of emotional commitment, continual commitment, and normative commitment have significant positive relationship with academic performance (emotional commitment: β=.258, p-value= 0.000; continual commitment: β= .137, p-value= 0.020; normative commitment: β= .056, p-value= 0.044). The results of this study will form the framework for policy making on the issue of organizational commitment and academic performance.
Keywords: Employee commitment, organizational commitment and academic performance.
Abstract: Medical tourism is a growing phenomenon with policy implications for health systems, particularly of destination countries. Private actors and governments in Southeast Asia are promoting the medical tourist industry. This article presents a conceptual framework that outlines the policy implications of medical tourism's growth for health systems, drawing on the cases of Thailand, Singapore and Malaysia and other hubs for medical tourism. Variables for further analysis of the potential impact of medical tourism on health systems are also identified. The framework can provide a basis for empirical, in country studies weighing the benefits and disadvantages of medical tourism for health systems. The policy implications described are of particular relevance for policymakers and industry practitioners in other Southeast Asian countries with similar health systems where governments have expressed interest in facilitating the growth of the medical tourist industry. This article calls for a universal definition of medical tourism and medical tourists to be enunciated, as well as concerted data collection efforts, to be undertaken prior to any meaningful empirical analysis of medical tourism's impact on health systems.
Keywords: Medical Tourism, Health care, Medication Cost, Medical treatments, Destinations.
Abstract: India, a country which is known for its textile manufacturing and handlooms, since the early times; and this is revealed by literary and archaeological evidences. India's textiles manufacturing sector is one of the pillar of the national economy. Government of India has taken many steps to create a brand of Indian textile in the global arena. All the exporters are been provided with various different promotion council to promote their items. For each item there is an export council and for textile it is TEXPROCIL (The Cotton Textiles Export Promotion Council). " By not just pulling away the protectionist measures, but also by enhancing business sector access, avoiding policies which distort competition & also to agree on reforms to world trade regulations; with the help of these council there can be boost in trade and also seize the opportunities that it offers for everyone, in the years to come". Undoubtedly the coin has two phases similarly, the councils has some failing points also. The drawbacks of the council have leaded the exports to battle with various problems in promoting their products. The problems are been stated below.
Keywords: Export, Handlooms & Manufacturing, Problems, Textile sector, TEXPROCIL.
Abstract: Japanese 5S was selected as the quality improvement tool in this study as 5S is the stepping stone for many quality improvement concepts and its roots date back to 16th century. When successfully implemented, 5S gives many benefits to the organization as well as its stakeholders. Though 5S itself has a tool to sustain, most of the organizations find it difficult to sustain the 5S practice over the time. Therefore the objective of this study was to find out the effect of the organizational culture on the sustainability of quality improvement in Government Healthcare institutions in Sri Lanka. This study was a descriptive cross sectional study with two components. First component was to identify the degree of 5S sustainability in each healthcare institution by validated evaluation sheet. Second component was to determine the effect of the organizational culture on the sustainability of 5S programmes in selected study setting which were government hospitals in RDHS area Kurunegala. Self-administrated questionnaire was used for this purpose. Total study population was 543 employees of all the categories of hospital staff. Calculated sample size was 422 and 375 were responded to the questionnaire giving response rate of 88.9%. The study revealed that organizational culture has great impact on sustainability of quality improvement while value of the organization is the major contributing factors.
Keywords: Organizational culture, Quality Improvement, 5S, RDHS area Kurunegala.
Abstract: This study sought to establish the challenges in managing Non Motorized Transport system in Kenya with Eldoret town as a case study. Drastic increases in the number of vehicles have strained urban road networks in Kenya, resulting in traffic congestion for most of the day. The high proportion of all motor vehicles in Eldoret town are private cars, where more than 70% only carry one passenger and the use of bicycles is very limited. The road infrastructure within CBD is majorly designed for Motorized Transport giving little attention to Non Motorized Traffic. Non Motorized Transport passengers generate no air pollution, no greenhouse gases, and little noise and air pollution; they are efficient and environmentally sustainable means of making short trips within urban centers. The study was guided by the following research objectives: To; examine how Project governance challenges affect management of NMT, evaluate how Project financial management challenges affect management of NMT, and assess how Project management practices challenges affect management of NMT. Descriptive survey design was explained fully to answer research objectives outlined. It includes quantitative data using self-administered structured questionnaires and qualitative data using interview schedules was collected. Participatory transect walks for two weeks was undertaken to observe and document the modes of NMT system. Photographs were taken to document the existing challenges on the mobility facing the Eldoret town residents. To strengthen illustrations, visual aids such as maps and sketches were used to propose the physical infrastructural intervention that can promote the NMT within Eldoret town. Secondary data were collected from the review of published and unpublished materials, government reports, print media and the internet. A Population of 520 non motorized road users on Nairobi-Malaba Highway, Kapsabet and Iten Roads were targeted. Targeted also are 5 Government officials of Kenya Urban Roads Authority-North Rift Region, Kenya National Highways Authority-North Rift Region and NEMA as well as 10 senior employees in the Department of Physical Planning, County Roads and Transport and County Enforcement unit. Both simple and stratified random sampling technique was employed to collect data from respondents. Pearson's correlation and multiple regression methods will be applied to analyze the data. This study sought to establish the management of NMT (cycling and walking) as a factor in the reduction of traffic congestion and air pollution. The study found that there was a significant relationship between the effects of project control measures on project quality and the effects of project control measures on project budgets (p=0.000). It concluded that accomplishment of objectives is very important in the project delivery schedules. This is mainly because a project that meets its intended objectives qualifies it to control systems that are expected to deliver ever-higher levels of effectiveness. The study recommended that the management of the NMT systems and other projects should ensure timely accomplishment of the project objectives through careful monitoring and evaluation of the projects against the set targets and orientation.
Keywords: Non Motorized Transport system, Non Motorized Traffic, Eldoret town, Kenya.


Welcome to St. James United Methodist Church!
We want to share some of our ministries with you so that we can get to know you better. Whether you have been a long-time Christian and church member somewhere or whether you are just starting out to grow in faith, there is a place for you here.
They are meant for you.


This medication is used to treat or avoid specific urinary tract infections.
This medication is an antibiotic that actually works by stopping the growth of bacteria. It will perhaps not work for viral infections (age.g., common cold, flu). Unnecessary overuse or use of any antibiotic can result in its decreased effectiveness.
Nitrofurantoin shouldn't be used in children not as much as one month of age as a result of danger of a particular bloodstream problem (hemolytic anemia).
Take this medication by lips, with milk or food, as directed by your doctor. This medication is usually taken four times daily to treat an infection or once daily at bedtime to prevent infections. Swallow the medication whole. Avoid magnesium that is using antacids while using this medication. Magnesium trisilicate-containing antacids bind with nitrofurantoin, preventing its full consumption.
Dosage and duration is founded on your medical condition and response to treatment. For children, the dosage is also based on weight.
Antibiotics work most useful if the amount of medicine within your body is kept at a level that is constant. Therefore, take this medication at evenly spaced intervals.
When using this medication to stop infection, take it exactly as directed by your doctor. Do not skip doses or stop taking it without your doctor's approval. Inform your doctor while you are urinating) if you notice signs of a new urinary tract infection (e.g., pain.
If you should be taking this medication to deal with an infection, continue to simply take this medicine until the amount that is full-prescribed completed, even in the event signs disappear after a couple of days. Stopping the medication too early may allow bacteria to keep to develop, which may result in a relapse of the infection. Inform your physician if your condition persists or worsens.
Exactly what conditions does nitrofurantoin treat that is macrocrystal?
Nausea, vomiting, loss of appetite, or headache may occur. Take this medication with food to help minimize nausea. If any of these effects persist or worsen, notify your doctor or pharmacist quickly.
This medication may cause your urine to turn dark yellow or brown in color. This impact is harmless and can fade away when the medicine is stopped.
Understand that your doctor has prescribed this medication she has judged that the benefit to you is greater than the risk of adverse effects because he or. Many people using this medication do not have serious adverse effects.
This medication may cause very serious rarely (possibly fatal) lung problems. Lung problems may occur within the month that is first of or after long-lasting use of nitrofurantoin (generally for a few months or longer). Get medical help immediately in the event that you develop signs of lung problems, including: persistent coughing, chest pain, shortness of breath/trouble breathing, joint/muscle pain, bluish/purplish skin.
Tell your doctor straight away if any of these rare but very serious side effects occur: brand new indications of disease (age.g., fever, persistent sore throat), easy bruising/bleeding, mental/mood changes, persistent or severe headaches, vision changes.
This drug may rarely possibly cause serious fatal) liver disease, blood or nerve problems. Tell your doctor right away if you notice any of the following rare but very side that is serious: persistent nausea/vomiting, dark urine, yellowing of eyes/skin, unusual/persistent fatigue, fast/pounding heartbeat, numbness/tingling of the arms/legs, muscle weakness.
This medication may rarely cause a severe intestinal condition (Clostridium difficile-associated diarrhea) due to a type of resistant bacteria. This condition may occur during treatment or weeks to months after treatment has stopped. Do not use anti-diarrhea products or narcotic pain medicines them worse if you have any of the following symptoms because these products may make. Tell your physician right away in the event that you develop: persistent diarrhea, abdominal or stomach pain/cramping, blood/mucus within your stool.
Usage with this medication for prolonged or repeated periods may end in oral thrush or a new vaginal candida albicans (e.g., oral or vaginal fungal illness). Contact your doctor if you notice white spots in your mouth, a big change in vaginal discharge, or other new symptoms.
A tremendously serious reaction that is allergic this drug is rare. However, get help that is medical away if you notice any symptoms of a serious allergic attack, including: rash, itching/swelling (especially of the face/tongue/throat), severe dizziness, difficulty breathing.
Call your doctor for medical advice about side-effects. You may possibly report adverse effects to FDA at 1-800-FDA-1088 or at www.fda.gov/medwatch.
In Canada - Call your medical professional for medical advice about adverse results. You may possibly report side effects to Health Canada at 1-866-234-2345.
List nitrofurantoin adverse that is macrocrystal by likelihood and severity.
Before taking nitrofurantoin, tell your medical professional or pharmacist if you are allergic to it; or if you have any other allergies. This product may contain inactive ingredients, which can cause allergic reactions or other problems. Confer with your pharmacist for more information.
This medication shouldn't be used when you yourself have specific conditions that are medical. Before utilizing this medicine, check with your doctor or pharmacist if you have: little or no urine output (oliguria or anuria), serious renal disease, certain genetic conditions (glucose-6-phosphate dehydrogenase deficiency), a history of liver problems due to nitrofurantoin use in the past.
Before applying this medication, tell your doctor or pharmacist your medical background, particularly of: certain bloodstream disorders (e.g., anemia), renal or liver problems, lung diseases, certain neurological problems (peripheral neuropathy), certain eye conditions (optic neuritis), diabetes, untreated mineral imbalance, vitamin B deficiency.
Kidney function declines while you grow older. The kidneys remove this medication. Therefore, older adults may be at a greater risk for side effects while using this drug, especially nerve, liver or lung problems (see negative effects section).
This medication should be used only when demonstrably needed during maternity. This medication should not be taken if you are at term (weeks 38-42 of pregnancy), near or during the time of distribution due to feasible harm to the newborn, such as a certain bloodstream issue (hemolytic anemia). Discuss the risks and benefits with your physician.
This medication passes into breast milk and may also have undesirable effects on nursing infants less than one month old and infants with a certain hereditary condition (G-6-PD deficiency). Consult with your medical practitioner before breast-feeding.
What should I understand pregnancy that is regarding nursing and administering nitrofurantoin macrocrystal to children or older people?


Apple has joined "Made in India" initiative and started production in its first facility in India. The newly "Designed by Apple in California, Assembled in India" iPhone SE has started hitting the market.
India being the fastest growing smartphone market in world, it has been a special focus for Apple but Apple is yet to make a significant dent in the Indian price sensitive market.
iPhone SE was Apple's effort to penetrate the market with affordable offering but it didn't worked well. Apple cheapest offering in the Indian market is iPhone 5S which is selling around 15000/-.
iPhone SE was launched in India with the starting price of 39000/- which was very close to iPhone 6 in the market at that time.
iPhone models usually attracts the import tax which doesn't allow them to reduce the cost as they were build in China. That makes it very hard sell on the Indian market.
With the production started in India, iPhone can get rid of that import tax and afford to reduct the cost.
Apple has revised the iPhone SE price to start with 27200/-, which will get you 32GB unit and 128GB unit will be offered in 37200/-. The phone gets sold in US for $399 and $499 respectively.
This brings the iPhone SE price to very close to what you get in US market, though on the higher end you are shelling out little bit more money as Apple decided to keep the difference of 10000/-.
There are some discounts offered on Amazon after this reduced price, which can bring the cost further down to 24000/-. So if you are looking to buy the phone, check here once.
India has been a huge market for mid-low segment and looks like with this move Apple is trying to make some impact in mid-segment.
Currently it looks like the production has started on the limited basis and only some units have reached the market with the expansion being planned. Currently the only model being built in Indian facility is iPhone SE.
I would expect iPhone 5S and iPhone 6 to be in the mix which will bring their price down and will help Apple to make some impact in the market. There are many phone available in the mid-segment but no one can match Apple on service or product support, so it should be a great battle.
Manufacturing units was also a prime requirement for opening Apple's own store in India. With the facility functioning, Apple would look to start having their own stores in India also.
iPhone SE matches iPhone 6S in terms of hardware except few things like screen. But its a vary capable handset in that price point and with Apple unparalleled support, it should run good for another few years.


text:
North America has lost nearly 3 billion birds since 1970
By Sophie Lewis
September 19, 2019 / 5:54 PM / CBS News
"Staggering" decline in America's bird population
"Staggering" decline in America's bird popula... 01:52
Over the last 50 years, the U.S. and Canada have slowly but surely lost 29% of their bird populations — amounting to nearly 3 billion birds. The shocking loss could be a sign of an ecological crisis, scientists said Thursday.
According to a new study published in the journal Science by top ornithologists and government agencies, even common birds such as sparrows and blackbirds have faced declines in North America since 1970.
"It's staggering," said lead author Ken Rosenberg, a conservation scientist at the Cornell University Laboratory of Ornithology.
Researchers studied 529 bird species over the last half-century to compile the most comprehensive study ever done on North American birds, the journal said. Thanks to the decades of monitoring by researchers and bird enthusiasts across the continent — as well as weather radars — scientists had a huge amount of data to work with.
3 Billion Birds Lost by American Bird Conservancy on YouTube
What they found was unexpected. While scientists believed rarer species would be declining, they assumed more common species would be on the rise due to their resilience as well as conservation efforts. But the declines have far outweighed the gains.
"We expected to see continuing declines of threatened species," Rosenberg said. "But for the first time, the results also showed pervasive losses among common birds across all habitats, including backyard birds."
Grassland birds such as meadowlarks and northern bobwhites have declined by 53% since 1970 — a loss of 700 million adults in the 31 species studied. Shorebirds such as sanderlings and plovers are down by about one-third, according to the study.
"There's an erosion of the numbers of common birds," Rosenberg said. Indeed, 19 common species have lost more than 50 million birds in the last 50 years. Birds such as sparrows, warblers, finches and blackbirds have been hit particularly hard, the study found.
North America has lost nearly 3 billion birds since 1970. Cornell Lab of Ornithology
"When you lose a common species, the impact will be much more massive on the ecosystem and ecosystem services," said Gerardo Ceballos, an ecologist and conservation biologist at the National Autonomous University of Mexico in Mexico City. "It's showing the magnitude of the problem."
Between 2007 and 2017, the mass of birds migrating in the spring has dropped 13%, with the greatest decline in birds migrating up the eastern United States. "We want this to be the real wake-up call," Rosenberg said.
While not all of the factors for the mass decline have been pinpointed, researchers say habitat loss is a major concern. Pesticide use, climate change and predators could also be contributing to the decline.
"This is being caused entirely by humans. Habitat loss, which is the primary driver here, is a human-caused issue," said the study's co-author Peter Marra, director of the Georgetown Environment Initiative.
Seven ways to help save birds. Cornell Lab of Ornithology
Birds are indicator species, acting as a measurement for overall environmental health. Scientists fear the decline signals a major crisis, since birds play a part in controlling the spread of plants and insects.
"It's imperative to address immediate and ongoing threats, both because the domino effects can lead to the decay of ecosystems that humans depend on for our own health and livelihoods — and because people all over the world cherish birds in their own right," Marra said. "Can you imagine a world without birdsong?"
The western meadowlark is the state bird of six states: Montana, Kansas, Nebraska, North Dakota, Oregon, and Wyoming. Matthew Pendleton, Macaulay Library at Cornell Lab of Ornithology
According to a comprehensive U.N. report published in May, one million species of plants and animals are currently at risk of extinction. More than half a million species on land "have insufficient habitat for long-term survival" and are likely to go extinct, many within decades, unless their habitats are restored.
Fighting climate change and saving species are equally important, the report said.
The new study did find a few species of birds that have rebounded from decline and started to thrive. Waterfowl such as ducks, geese and swans and raptors such as bald eagles have made significant recoveries thanks to government funding and protection efforts.
If nothing else, scientists hope the concerning statistics will encourage people to pay more attention to birds. "It might stir needed action in light of the public interest in our feathered friends," Stanford University ecologist Paul Ehrlich said.
Extinction risk due to humans: U.N. report 03:24
According to the American Bird Conservancy, strengthening protections for birds at the government level may be the best way to protect them. Defending and strengthening the Migratory Bird Treaty Act, increasing funding for programs to protect habitats, enacting the Recovering America's Wildlife Act and advancing climate solutions may help reverse the decline.
"The story is not over," said co-author Michael Parr, president of American Bird Conservancy. "There are so many ways to help save birds. Some require policy decisions such as strengthening the Migratory Bird Treaty Act. We can also work to ban harmful pesticides and properly fund effective bird conservation programs. Each of us can make a difference with everyday actions that together can save the lives of millions of birds — actions like making windows safer for birds, keeping cats indoors, and protecting habitat."
First published on September 19, 2019 / 5:54 PM
Sophie Lewis
Sophie Lewis is a social media producer and trending writer for CBS News, focusing on space and climate change.
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redpajama_set_name: RedPajamaCommonCrawl


text:
/**
 *
 */
package rocks.bottery.connector;

import com.pengrad.telegrambot.model.Chat;

import rocks.bottery.bot.IConversation;

/**
 * A telegram conversation (or chat)
 *
 * @author Harald Kuhn
 *
 */
public class TelegramConversation implements IConversation {

	private Chat chat;

	TelegramConversation(Chat chat) {
		this.chat = chat;
	}

	/*
	 * (non-Javadoc)
	 *
	 * @see org.sylvani.bot.IConversation#getId()
	 */
	@Override
	public String getId() {
		return String.valueOf(chat.id());
	}

	/*
	 * (non-Javadoc)
	 *
	 * @see org.sylvani.bot.IConversation#getChannel()
	 */
	@Override
	public String getChannel() {
		return "telegram";
	}

	/*
	 * (non-Javadoc)
	 *
	 * @see org.sylvani.bot.IConversation#getConnectorId()
	 */
	@Override
	public String getConnectorId() {
		return TelegramBotConnector.class.getName();
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\section{Introduction}

Stresses induced by dislocations play an important role in many fundamental physical phenomena in crystals and thin crystalline films. This role of topological defects is manifested for example in plastic, electronic or optical characteristics. In order to have a good understanding of phenomena involving dislocations one needs to shed light on their dynamics. This is a classic problem in the theory of elasticity that was initiated at its early days and subsequently explored by many works (see e.g. \cite{eshelby_uniformly_1949,kiusalaas_elastic_1964,weertman_stress_1967,brock_dynamic_1982,markenscoff_nonuniformly_1981,markenscoff_accelerating_1982,markenscoff_dislocation_1983,brock_non-uniform_1983,pellegrini_dynamic_2010,lazar_elastic_2011,lazar_elastodynamic_2012,lazar_retardation_2013,lazar_distributional_2016,hirth_theory_1992,kazinski_self-interaction_2022}). In order to fully solve this problem one must account for both external stresses, and self-stresses due to the movement of a dislocation and a direct progress using equations of elasticity has been obstructed by many difficulties in handling the Navier's equations for displacements.

In this work the aim is to address this problem using the so-called fracton-elasticity dualities, which depart from displacement formulation of elasticity (for recent reviews see \cite{grosvenor_space-dependent_2022,Gromov:2022cxa}). The dualities originate from the works on two-dimensional crystals for which the low-energy elastic degrees of freedom can be written down as gauge variables with two-indices \cite{kleinert_duality_1982,kleinert_double_1983,beekman_dual_2017-1,beekman_dual_2017}. More recently this original framework of elastic dualities was refined, and topological defects, in the absence of crystal vacancies, interpreted as fractons, i.e. excitations with mobility constraints \cite{pretko_fracton-elasticity_2018,pretko_crystal--fracton_2019,radzihovsky_fractons_2020,radzihovsky_quantum_2020,gromov_duality_2020,surowka_dual_2021,hirono_effective_2022,caddeo_emergent_2022,zaanen_crystal_2022}. Such excitations act as sources for the tensor gauge fields. The most important part of this construction are convenient low-energy degrees of freedom together with symmetry principles that precisely capture the dynamics of defects and, allow one to get insight based purely on symmetry considerations \cite{pretko_the_2018,gromov_towards_2019}. A successful application of this line of reasoning has been in the quest of constructing hydrodynamic theories of kinematically constrained constituents \cite{gromov_fracton_2020,grosvenor_hydrodynamics_2021,Glorioso_breakdown_22,burchards_coupled_2022,Glodkowski:2022xje,Glorioso:2023chm}.

The dualities reformulate elasticity in the language of gauge theories. In the simplest incarnation a moving topological charge is therefore a generalization of the moving electromagnetic charge in U(1) gauge theories. This problem was solved by Li\'{e}nard and Wiechert who computed electromagnetic potentials of an arbitrarily moving relativistic electric charge (see e.g. \cite{zangwill_modern_2013}). Later Jefimenko generalized these results to give electric and magnetic fields due to a distribution of electric charges and electric currents in space \cite{jefimenko_electricity_1989}. Therefore, a dual gauge theory formulation of elasticity offers a unique opportunity to understand the dynamics and stresses generated by a distribution of elastic defects. As we will see separate solutions can be obtained in materials with vacancies and without vacancies. In the former case the dislocation is not constrained, however, their movement perpendicular to the Burgers vector is tightly connected to the distribution of vacancies in the material. In the later case the dislocations are kinematically restricted to move along their Burgers vector.

Modern studies of defect dynamics go much beyond original crystalline systems. Examples include topological defects in rheology \cite{furst_microrheology_2017} or active matter \cite{bowick_symmetry_2022,shankar_topological_2022}. In rheology viscoelastic properties for incompressible systems can be derived by the correspondence principle upon changing the real elastic parameters to complex transport coefficients \cite{pipkin_lectures_1986}. Therefore, a good understanding of elasticity is a convenient starting point to understand more complex viscoelastic materials.  Finally defects in active matter naturally emerge in fluids that form from collections of bacterial suspensions \cite{sokolov_emergence_2019} or other macroscopics ensembles of living organisms \cite{duclos_topological_2017,tan_odd_2022}. More recently topological defects appeared in the context of active solids and metamaterials \cite{braverman_topological_2021}.

In this work we show that the dynamics of topological defects in isotropic elasticity on a plane can be simplified considerably if elasticity is formulated as a gauge theory. Exploiting this simplification, we derive the stresses that follow from the dynamics of arbitrarily moving dislocation. We also include time dependence into the classic result of Peach-Koehler force that captures the interactions and external stresses acting on a dislocation \cite{peach_forces_1950}. The strength of our results lies in the fact that we do not attempt an analytic or numerical tour-de-force but use the simplification provided by the fraction-elasticity duality. In consequence our formalism can be generalized to study more complex theories of elasticity or viscoelasticity.

Our manuscript is organized as follows. In Sec. \ref{Sec2} we review the fracton-elasticty duality. In Sec. \ref{Sec3} we derive equations of motion in for the dual gauge potentials. Sec. \ref{Sec4} introduces the notion of defects. In Sec. \ref{Sec5} we present the solutions and discuss physical implications of the defect motion. Sec. \ref{Sec6} is devoted to interactions between dislocations. We derive the expression for the dynamical Peach-Koehler force between two dislocations. Finally in Sec. \ref{Sec7} we close with conclusions and discussion.

\section{Fracton-Elasticity Duality}\label{Sec2}

We start the theoretical study with the two-dimensional low-energy elasticity theory action:
\vspace{1mm}
\begin{equation}
S=\frac{1}{2}\int\left[(\partial_t u_i)^2-C_{ijkl}u_{ij}u_{kl}\right]d^2xdt,
\end{equation}
where $u_{ij}=\frac{1}{2}(\partial_i u_j+\partial_j u_i)$ is the linear part of the symmetric strain tensor, with $u_j$ the displacement field and $C_{ijkl}$ is the 1st-gradient elasticity matrix, with its components determined by the type of medium at hand. Since we will only be working with the defects of the theory, we are interested in the singular part $u_{ij}^{s}$ of the strain tensor field $u_{ij}=u_{ij}^{s}+\frac{1}{2}(\partial_i \overline{u}_j+\partial_i \overline{u}_j)$, with the smooth part later integrated out to provide a constrain of the theory. In order now to introduce the dual fields of the theory, we perform a Hubbard-Stratonovich transformation, by completing the square in the functional:
\begin{equation*}
Z=\int \mathcal{D}u_je^{-S},
\end{equation*}
to receive:
\begin{equation}
S=\int \left[\frac{1}{2}C^{-1}_{ijkl}\sigma^{ij}\sigma^{kl}-\frac{1}{2}\pi^i\pi_i-\sigma^{ij}u_{ij}+\pi^i\partial_tu_i\right]d^2xdt.
\end{equation}
where $\sigma_{ij}$ is elasticity stress-tensor with the symmetry $\sigma_{ij}=\sigma_{ji}$, and $\pi_i$, the elastic momentum vector. We employ Einstein's summation convention. The details of inversion of the elastic tensor are presented in App. \eqref{AppA}. If the smooth and singular part of the symmetric strain tensor are now plugged in the equation above, the smooth part is then integrated out, giving the well known Hooke's law:
\begin{equation}
\partial_t\pi^i-\partial_j\sigma^{ij}=0.
\end{equation}
We now introduce the two rotated fields:
\begin{equation}
B^i=\epsilon^{ij}\pi_j \qquad E^{ij}_{\sigma}=\epsilon^{ik}\epsilon^{jl}\sigma_{kl} .
\label{rotated}
\end{equation}
which along with the two-dimensional Levi-Civita identity
$\epsilon^{ij}\epsilon_{jk}=\delta^i_k$ transform the above equation into Faraday's Law:
\begin{equation}
\partial_t B_i+\epsilon_{jk}\partial^jE^{ki}_{\sigma}=0.
\end{equation}
It must be stated that the lower case index $\sigma$ on the rank-2 tensor electric field, signifies the relation with the rotated stress field. This field is actually the elastic counterpart of the usual electric field used in EM theory and works the same way as the electric displacement field. The relation connecting one another is given through the formula:
\begin{equation}
E^{ij}=\tilde {C}_{ijkl}^{-1}E^{kl}_{\sigma},
\end{equation}
where $\tilde {C}_{ijkl}^{-1}=\epsilon_{im}\epsilon_{jn}\epsilon_{ko}\epsilon_{lp}C_{ijkl}^{-1}$
is the rotated inverted elasticity tensor.\\
Faraday's equation can be solved by introducing the generalization of the EM theory into a rank-2 gauge theory through:
\begin{equation}
B^i=\epsilon_{jk}\partial^jA^{ki} ,\qquad  E^{ij}_{\sigma}=-\partial_t A^{ij}-\partial_i\partial_j\phi,
\label{gaugefields}
\end{equation}
where  $\phi$ is the usual scalar fractonic field, and $A_{ij}$ a symmetric tensor gauge field. Of course Faraday's equation stays invariant under the gauge transformation:
\begin{equation}
A_{ij}\rightarrow A_{ij}+\partial_i\partial_jf(x_k,t), \qquad \phi \rightarrow\phi+\partial_t f(x_k,t),
\end{equation}
where $f(x_k,t)$ is an arbitrary space-time function. Using the gauge fields now, we can rewrite the action of our theory, to also include currents and sources
\begin{equation}
S=\int\left[\frac{1}{2}\tilde{C}_{ijkl}^{-1}E^{ij}_{\sigma}E^{kl}_{\sigma}-\frac{1}{2}B^iB_i+\rho\phi-J^{ij}A_{ij}\right]d^2xdt.
\label{FE-ACTION-1}
\end{equation}
The above equation describes isolated charges of the theory in the form disclinations. Since our main concern are dislocation defects, we introduce the vector fractonic potential $\phi_i=\partial_i \phi$ and the dislocation charge density $\rho=-\partial_i\rho^i$. By performing integration by parts on \eqref{FE-ACTION-1} we get the required action describing gauge fields sourced by dislocations
\begin{equation}
S=\int\left[\frac{1}{2}\tilde{C}_{ijkl}^{-1}E^{ij}_{\sigma}E^{kl}_{\sigma}-\frac{1}{2}B^iB_i+\rho^i\phi_i-J^{ij}A_{ij}\right]d^2xdt.
\label{FE-ACTION-2}
\end{equation}
We have successfully managed to map the low energy action of the elasticity theory containing two gapless phonon modes (longitudinal and transverse motion) into another U(1) vector charge gauge theory containing two gapless gauge modes.
With the usage of the 1st (Gauss) and the 4th (Amp\`ere) Maxwell law for the duality, we can extract the continuity equation for the vector charge theory
\begin{equation}
\partial_t \rho_j+\partial_iJ_{ij}=0.
\end{equation}
\section{Equations of motions for isotropic materials in two dimensions}\label{Sec3}
We start by writing the Lagrangian for elasticity in the language of gauge fields:
\begin{equation}
\mathcal{L}=\frac{1}{2}(\tilde{C}_{ijkl}^{-1}E^{ij}_{\sigma}E^{kl}_{\sigma}-B^iB_i)-\rho^i\phi_i-J^{ij}A_{ij},
\label{Lagrangian}
\end{equation}
where for the case of an isotropic material we have the formula for the inverse elasticity tensor as a function of the elastic bulk modulus $\kappa$ and the shear modulus $\mu$,
\begin{equation}
\tilde{C}_{ijkl}^{-1}=\left(\frac{1}{4\kappa}-\frac{1}{4\mu}\right)\delta_{ij}\delta_{kl}+\frac{1}{4\mu}(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}).
\label{elasticitytensor}
\end{equation}
The above tensor obeys the Maxwell-Betti reciprocity relations
$\tilde{C}_{ijkl}^{-1}=\tilde{C}_{jikl}^{-1}=\tilde{C}_{ijlk}^{-1}=\tilde{C}_{jilk}^{-1}$. By plugging Eq. \eqref{gaugefields} in Eq. \eqref{Lagrangian} and using the Euler-Lagrange equations, we extract the two equations of motion
\begin{equation}
2C_2\partial_t\partial_i A_{ij}+C_2\partial_i^2\phi_j+C_1\partial_t\partial_j A_{kk}+C_3\partial_j\partial_k\phi_k-\rho_j=0,
\label{phifield}
\end{equation}
\begin{equation*}
2C_2\partial_t^2A_{ij}+2C_2\partial_t\partial_i\phi_j+C_1\big[\partial_t^2A_{kk}+\partial_t\partial_k\phi_k\big]\delta_{ij}-\partial_k^2 A_{ij}+
\end{equation*}
\begin{equation}
\hspace{4.5cm}+\partial_i\partial_k A_{kj}+J_{ij}=0,
\label{alphafield}
\end{equation}
where the coefficients depend on the elastic moduli in the following way
\begin{equation*}
C_1=\frac{(\mu-\kappa)}{4\mu\kappa}, \qquad C_2=\frac{1}{4\mu}, \qquad C_3=\frac{1}{4\kappa}.
\end{equation*}
Both Eq.\eqref{phifield} and \eqref{alphafield} are coupled, in analogy to classical electrodynamics. In addition the trace of the tensor gauge field $A_{ij}$ is present, signifying its relation to the motion of dislocations as we show later on.

In order to simplify the equations we need to fix a gauge. We note that in the analogous problem in electrodynamics it is convenient to choose the Lorenz gauge in order to decouple the equations. Therefore we intend to generalize the usual Lorenz gauge to the case of tensor gauge theories. This can be done as follows
\begin{equation}
\partial_i A_{ij}+\frac{1}{2\mu}\partial_t\phi_j=0.
\label{Lorenz}
\end{equation}
With this choice the second term in \eqref{alphafield} cancels with the contribution of the fifth term.
Notice that in all the equations, the density $\rho_d=1$. Generically in the gauge condition the second term in \eqref{Lorenz} shall be multiplied by $\rho_d$.

The next step into deriving the wave equations uses the fact that the vector potential $\phi_i$ is given by the gradient of the scalar field $\phi$, meaning that permutation of the indices in the derivatives is allowed
$\partial_j(\partial_i\phi_i)= \partial_i^2\phi_j.$
The final form of the wave equations for the vector field $\phi_i$ and the tensor gauge field $A_{ij}$ that contain the trace reads
\begin{equation}
\Box \phi_j+\left(\frac{\mu-\kappa}{\mu+\kappa}\right)\partial_t\partial_j A_{kk}- \left(\frac{4\mu\kappa}{\mu+\kappa}\right)\rho_j=0,
\label{wave-phi}
\end{equation}
\begin{equation}
\Box A_{ij}-\left(\frac{\mu-\kappa}{4\kappa\mu}\right)\left[\partial_t^2A_{kk}-2\mu\partial_m\partial_n A_{mn}\right]\delta_{ij}-J_{ij}=0,
\label{wave-alpha}
\end{equation}
where $\Box=\nabla^2-(1/\upsilon^2)\partial_t^2$, with the velocity for the $\phi_j$ field being equal to $\upsilon_{\phi}=\sqrt{\frac{\mu(\kappa+\mu)}{\kappa}}$ and for the $A_{ij}$ field equal to $\upsilon_A=\sqrt{2\mu}$. The result is not surprising but a few clarifications need to be made. These velocities are the dual of the ones that appear in the regular elasticity theory of a two-dimensional isotropic solid. The phonon fields there propagate with velocities equal to $\upsilon_L=\sqrt{\frac{\kappa+\mu}{\rho}}$ and $\upsilon_T=\sqrt{\frac{\mu}{\rho}}$ for a longitudinal and transverse wave propagation respectively. The fracton vector charge density is now multiplied with a factor containing the elastic constants although that is not true for the currents of our theory. In the next section we briefly introduce how defects can be included in the theory.
\section{Defects}\label{Sec4}
Topological defects such as disclinations or dislocations, act as sources for the singular part of strain tensor $u_{ij}$. The disclination density is given by
\begin{equation}
s=\epsilon_{ij}\partial_i\partial_j\theta=\epsilon_{ij}\epsilon_{kl}\partial_i\partial_j\partial_k u_l=\rho,
\end{equation}
where $\theta=\epsilon_{kl}\partial_ku_l$ is the bond angle. Disclinations represent the isolated fracton charges of our theory that cannot move. However, two opposite disclinations of the same magnitude would formulate the dipole that can move albeit with mobility restrictions dubbed dislocations. Their density is represented as a function of a particular lattice vector, called the Burgers vector
\begin{equation}
b_j=\oint_{\gamma}\partial_i u_j dr_i.
\end{equation}
This lattice vector is always perpendicular to the vector joining the two disclination defects. The line element $dr_i$ encircles a specific area on the solid that encloses the defect, forming the Burgers circuit $\gamma$.

In general the system containing monopoles, dipoles and even higher combinations of particles can be represented by a charge density of the form:
\begin{equation}
\rho=q\delta(\mathbf{r}-\mathbf{r'})-\mathbf{p}\cdot\mathbf{\nabla}\delta(\mathbf{r}-\mathbf{r'})+...
\end{equation}
Since we are interested in the motion of a defect in the medium, we focus on a single dislocation, dropping both higher order terms and the immobile monopole. By comparing the above density with the vector density in our Lagrangian we can write
\begin{equation}
\rho_i(\mathbf{r'},t)=\epsilon_{ij}b_j\delta(\mathbf{r'}-\mathbf{r}_s(t')),
\label{fracton-density}
\end{equation}
where $\epsilon_{ij}b_j=p_i$ is the dipole moment. It is set to be equal to the Burgers vector but pointing perpendicular to it. This gives a current of the form
\begin{equation}
J_{ij}(\mathbf{r'},t)=\epsilon_{\left(ik\right.}\upsilon_{\left.j\right)}b_k\delta(\mathbf{r'}-\mathbf{r}_s(t')),
\label{fracton-gaugedensity}
\end{equation}
where $\upsilon_i$ is the dislocation velocity and $\mathbf{r}_s(t')$ is the dislocations trajectory as seen by the observer at retarded time $t'$. The trace of the current $J_{ii}$ is related to dislocation climb, i.e. dislocation moving perpendicular to its Burgers vector and not parallel, and is equal to 0 in the case where the are no vacancies in the crystal. We discuss the static solutions of the field equations corresponding to dislocations and disclinations in App. \eqref{AppB}. The dynamical solutions will be studied in the next section.
\section{Li\'{e}nard-Wiechert potentials and Jefimienko's equations}\label{Sec5}
\subsection{Traceless theory}
We start with the simplest exampled dubbed traceless gauge theory \cite{pretko_generalized_2017}. We note that imposing the condition can be done following different conventions \cite{beekman_dual_2017}. In this work we follow the convention used by Pretko that automatically forces the theory to obey the Ehrenfest constraint. We demand that the trace of the electric tensor field $E_{ii}$ is equal to zero and the intermediate terms of \eqref{wave-phi} and \eqref{wave-alpha} containing contributions arising from it, drop out. The equations we have then turn out to be the regular two-dimensional wave equations for the two potentials
\begin{equation}
 \Box \phi_j-2\mu\rho_j=0, \qquad \upsilon_{\phi}=\sqrt{2\mu},
\end{equation}
\begin{equation}
\Box A_{ij}-J_{ij}=0, \qquad \upsilon_{A}=\sqrt{2\mu}.
\end{equation}
It follows from the equations that the two wave velocities turn out to be the same. Before we move on to discuss the solutions, we give a physical meaning to setting the trace equal to zero. According to Pretko's theory, the vector charge case is governed by the two conservation laws of charge and dipole moment, easily seen through the first Gauss law. Dislocations of this theory are proven to be able to move only  along their Burgers vector (longitudinal motion) and not transverse. The explanation given has to do with the vacancies/interstitials present on the solid. Going to the analysis of the quadrupole moment, the trace is given by:
\begin{equation*}
D_{ii}=-\int_Vd^2x(\rho_i x_i+2E_{ii})=\text{const.}
\vspace{2mm}
\end{equation*}
where from the duality formulas we have: $E^{ii}=(1/2\kappa)E_{\sigma}^{ii}=\partial_iu_i=n_d=0$, with the smooth part taken to be very small. Here $n_d$ represents the difference between vacancies and interstitial defects. The above requirement with the physical meaning of having a component of quadrupole moment related to the trace preserved, implies that the defects of the theory only move parallel to their Burgers vector (fracton dipoles moving only transverse to the dipole moment).

The problem at hand parallels the one of finding Li\'{e}nard-Wiechert potentials in three space dimensions, however, since we are on the plane the exact form of the solution differs (see \cite{boito_maxwells_2020,watanabe_integral_2015} for an analogous problem in electrodynamics). The Green's function related to the above differential equations is given as the Heaviside step-function with a relativistic factor included, giving rise to a phenomenon called "afterglow" \cite{lazar_elastic_2011,lazar_elastodynamic_2012,dai_origin_2013}.

The afterglow phenomenon is a direct sequence of Huygens principle not being valid in 2+1 dimensions and generically in space-times in odd number of dimensions. This can be seen from the Green's function describing the equations of motion. In 3+1 dimensions the function is proportional to a Dirac's delta function, instantly having a pulsating effect and vanishing. Here the Heaviside $\Theta$ function is present, meaning that even though at times $t<t'+|\mathbf{r}-\mathbf{r_s'}|/\upsilon_s$ the contribution is zero, the pulse emitted exactly at $t=t'$ has an everlasting effect, with the denominator playing the role of an attenuation factor, eventually disappearing at large values of $t$. The full wave describing this effect can be constructed as a superposition of wave modes with velocity values ranging from 0 to $\upsilon_s$ (velocity of the outermost wave - the so-called Huygens surface). This is known as "tail" of the Green's function leading to a non-sharp wave propagation, in contrast to the (3+1) dimensions case \cite{dai_origin_2013}.

Using two-dimensional Green's function we get
\begin{align*}
\phi_j&=\frac{\mu}{\pi}\int d^2\mathbf{r'}\int dt'\frac{\Theta(\upsilon_s(t-t')-|\mathbf{r}-\mathbf{r'}|)}{\sqrt{(t-t')^2-|\mathbf{r}-\mathbf{r'}|/ \upsilon_s^2}}\rho_j,\\
 A_{ij}&=\frac{1}{2\pi}\int d^2\mathbf{r'}\int dt'\frac{\Theta(\upsilon_s(t-t')-|\mathbf{r}-\mathbf{r'}|)}{\sqrt{(t-t')^2-|\mathbf{r}-\mathbf{r'}|/ \upsilon_s^2}}J_{ij}  ,
\end{align*}
where $\upsilon_s$ is the speed of sound, and $t'$, $\mathbf{r'}$ the retarded coordinates. By using the definitions of the density and current from the previous section and performing the integration in space, we arrive at:
\begin{equation}
 \phi_j=\frac{\mu \epsilon_{ji}b_i}{\pi}\int \frac{\Theta(\upsilon_s(t-t')-|\mathbf{r}-\mathbf{r'_s}|)}{\sqrt{(t-t')^2-|\mathbf{r}-\mathbf{r'_s}|/ \upsilon_s^2}}dt'
 \vspace{2mm}
\end{equation}
\begin{equation}
A_{ij}=\frac{\epsilon_{\left(ik\right.}\upsilon_{\left.j\right)}b_k}{2\pi}\int \frac{\Theta(\upsilon_s(t-t')-|\mathbf{r}-\mathbf{r'_s}|)}{\sqrt{(t-t')^2-|\mathbf{r}-\mathbf{r'_s}|/ \upsilon_s^2}}dt'
\vspace{2mm}
\end{equation}
The above integrals have considerable complexity which only in
some simple cases yield results of elementary functions in a closed form. We will thus be using the formalism of near-field approximation adopted by Lazar \cite{lazar_elastic_2011,lazar_elastodynamic_2012,lazar_retardation_2013}, where the lower time limit solution is that of regular elastostatics with the defect immobile until $t=0$. The lower limit of the above integral is switched from $-\infty$ to $0$ and the upper one has the relativistic boundary value of $t-|\mathbf{r}-\mathbf{r'}|/\upsilon_s$. By assuming that the defect does not move too far from the observational point, we can take $|\mathbf{r}-\mathbf{r'}|\approx d$. The final result is
\begin{equation}
\phi_j=-\frac{\mu \epsilon_{ji}b_i}{\pi}\ln\left(\frac{d}{\upsilon_st+\sqrt{\upsilon_s^2t^2-d^2}}\right)\Theta(\upsilon_st-d),
\end{equation}
\begin{equation}
A_{ij}=-\frac{\epsilon_{\left(ik\right.}\upsilon_{\left.j\right)}b_k}{2\pi}\ln\left(\frac{d}{\upsilon_st+\sqrt{\upsilon_s^2t^2-d^2}}\right)\Theta(\upsilon_st-d)  .
\end{equation}
As it can be seen, just like the regular charged particle case a connection between the fields potentials is given in the form of $A \propto \upsilon^{-1}\cdot \phi$. This time the usual relation is inverted because we worked with $\Tilde{C}^{-1}_{ijkl}$ in our equations of motion.

By making use of Eq. \eqref{gaugefields}, we find the elastic analogue of Jefimenko's equations for a dislocation
\begin{widetext}
\begin{equation}
E^{\sigma}_{ij}=\frac{[2\mu \epsilon_{ik}b_k n_j-\epsilon_{\left(ik\right.}\upsilon_{\left.j\right)}b_k(n_m\upsilon_m)]}{2\pi d}\left(\frac{A(t,d)}{1-n_i\beta_i}\right)-\frac{\epsilon_{\left(ik\right.}\upsilon_{\left.j\right)}b_k}{2\pi}\frac{1}{B(t,d)}\left(\upsilon_s+\frac{\upsilon_s^2t}{B(t,d)-\upsilon_st}\right)-\frac{\epsilon_{\left(ik\right.}\dot{\upsilon}_{\left.j\right)}b_k}{2\pi}\ln\left(\frac{d}{B(t,d)}\right),
\end{equation}
\begin{equation}
B_i=\left[\frac{(b_in_k-b_kn_i)\upsilon_k-(b_jn_j)\upsilon_i}{2\pi d}\right]\left(\frac{A(t,d)}{1-n_i\beta_i}\right),
\end{equation}
\end{widetext}
where in the above $n_i$ is the unitary vector component of $\mathbf{r}-\mathbf{r_s}$ and we have also introduced the relativistic factors $\beta_i=\upsilon_i/\upsilon_s$, $A(t,d)=1+d^2/[B(t,d)(B(t,d)-\upsilon_st)]$ and $B(t,d)=\upsilon_st+\sqrt{\upsilon_s^2t^2-d^2}$.\\
We can now invert the duality in order to find the dynamical time dependent stress-tensors components to be
\begin{equation*}
\sigma_{xx}=\frac{[-2\mu b_yn_x+\upsilon_xb_y(n_i\upsilon_i)]}{2\pi d}\left[\frac{A(t,d)}{1-n_i\beta_i}\right]-\hspace{10cm}
\end{equation*}
\begin{equation*}
+\frac{\upsilon_xb_y}{2\pi}\frac{1}{B(t,d)}\left(\upsilon_s+\frac{\upsilon_s^2t}{B(t,d)+\upsilon_st}\right)+\frac{\dot{\upsilon}_xb_y}{2\pi}\ln\left(\frac{d}{B(t,d)}\right),
\end{equation*}
\begin{equation*}
\sigma_{yy}=\frac{[2\mu b_xn_y-\upsilon_yb_x(n_i\upsilon_i)]}{2\pi d}\left[\frac{A(t,d)}{1-n_i\beta_i}\right]+\hspace{10cm}
\end{equation*}
\begin{equation*}
-\frac{\upsilon_yb_x}{2\pi}\frac{1}{B(t,d)}\left(\upsilon_s+\frac{\upsilon_s^2t}{B(t,d)-\upsilon_st}\right)-\frac{\dot{\upsilon}_yb_x}{2\pi}\ln\left(\frac{d}{B(t,d)}\right),
\end{equation*}
\begin{equation*}
\sigma_{xy}=\frac{[-2\mu b_xn_x+(\upsilon_xb_x-\upsilon_yb_y)(n_i\upsilon_i)]}{2\pi d}\left[\frac{A(t,d)}{1-n_i\beta_i}\right]+   \end{equation*}
\begin{equation*}
+\frac{(\upsilon_xb_x-\upsilon_yb_y)}{2\pi}\frac{1}{B(t,d)}\left(\upsilon_s+\frac{\upsilon_s^2t}{B(t,d)-\upsilon_st}\right)+
\end{equation*}
\begin{equation*}
\hspace{4cm}+\frac{(\dot{\upsilon}_xb_x-\dot{\upsilon}_yb_y)}{2\pi}\ln\left(\frac{d}{B(t,d)}\right).
\end{equation*}
From the static limit of the theory and by requiring a symmetric stress tensor, another condition extracted is $b_xn_x=-b_yn_y$. Both of these are a result of our initial symmetry of $\partial_i\phi_j=\partial_j\phi_i$, since the the field $\phi_j$ is the gradient of the scalar fracton field $\phi$.\\ The strains now can be easily given by making use of the $u_{ij}=C_{ijkl}^{-1}\sigma_{kl}$. We present the full expression in App. \ref{appc}. One can see that the components containing velocities of the dislocation contribute the less to stresses and strains, the higher the numerical values of the elastic moduli are.
\subsection{Vacancies present in the crystal}
The next physical system we are interested in studying is a solid with vacancies present. In order to get a better intuition about the solution we note that elastodynamics is described by a system of field equations representing the transmission of elastic waves. This can be easily appreciated in the language of displacements since taking the curl of Navier's equations one obtains two wave equations for dilatational and rotational disturbances \cite{eringen_elastodynamics_1975}. This is not so easy to implement in the stress formulation of elastodynamics, that parallels our gauge theory formulation, and in consequence the stress approach is less developed (see e.g. \cite{ostoja-starzewski_ignaczak_2019}). Our strategy to obtain wave solutions from \eqref{wave-phi} and \eqref{wave-alpha} requires that, on top of fixing a gauge, we need to impose an additional constraint
\begin{equation} \label{eq:cosntraint}
\partial_tA_{ii}+C\partial_i\phi_i=0.
\end{equation}
The physical interpretation of this constraint is that the climb motion of a topological defect requires the addition or removal of a particle from the regular lattice. In other words the only way to move a dislocation is to excite an interstitial.
Eq. \ref{eq:cosntraint} constitutes a general condition how this process happens since the trace, related to non-topological defects is now a part of the solution. In order to have a better intuition we can rewrite \eqref{eq:cosntraint} using the definition of electric field \eqref{gaugefields}
\begin{equation}
(1-C)\partial_i\phi_i =2\kappa n_d.
\end{equation}
In consequence $C$ parameterizes the configuration of non-topological defects in the theory.

In the next step we calculate the distribution of fields. The equations of motion read
\begin{equation}
\Box \phi_j-2\kappa\rho_j=0, \qquad \upsilon_{\phi}=\sqrt{\frac{2\mu^2}{\kappa}},
\end{equation}
\begin{equation}
\Box A_{ij}+\frac{(\kappa-\mu)}{2\kappa\mu}\partial_t^2A_{kk}\delta_{ij}-J_{ij}=0, \qquad \upsilon_A=\sqrt{2\mu}.
\label{Trace}
\end{equation}
We identify two wave equations characterized by different velocities. One important consequence of the above equations is that the vector charge density is coupled to the bulk modulus as opposed to the case without vacancies or interstitials. The dipoles in the theory are now allowed to move parallel and perpendicular to the Burgers vector.

Solutions for the $\phi_i$ and the off-diagonal component of $A_{ij}$ of course have the same form as before. The differential equation that is left to compute is taken by tracing Eq.\eqref{Trace} to get
\begin{equation}
\Box A_{ii}-J_{ii}=0, \qquad \upsilon_{\text{trace}}=\sqrt{\frac{2\kappa\mu}{\mu(1-C)+C\kappa}}.
\end{equation}
The final solution for this case will be mixing contributions for two waves propagating with two different velocities. We have:
\begin{equation}
\phi_j=-\frac{\kappa b_j}{\pi}\ln\left(\frac{d}{\upsilon_{\phi}t+\sqrt{\upsilon_{\phi}^2t^2-d^2}}\right)\Theta(\upsilon_{\phi}t-d),
\end{equation}
\begin{equation}
\underset{i\neq j}{A_{ij}}=\frac{(\upsilon_xb_x-\upsilon_yb_y)}{2\pi}\ln\left(\frac{d}{\upsilon_At+\sqrt{\upsilon_A^2t^2-d^2}}\right)\Theta(\upsilon_At-d),
\end{equation}
\begin{equation*}
\underset{i=j}{A_{ij}}=-\frac{\epsilon_{ik}\upsilon_{\left(j\right.}b_{\left.k\right)}}{2\pi}\ln\left[\frac{d^2}{(\upsilon_{tr}t+\sqrt{\upsilon_{tr}^2t^2-d^2})B(t,d)}\right]-
\end{equation*}
\begin{equation}
\hspace{2cm}-\frac{\epsilon_{ik}\upsilon_{\left[j\right.}b_{\left.k\right]}}{2\pi}\ln\left(\frac{\upsilon_{tr}t+\sqrt{\upsilon_{tr}^2t^2-d^2}}{B(t,d)}\right) . \end{equation}

\section{Dynamical Peach-Koehler force}\label{Sec6}

In this section we focus on the interaction between dislocations (for a recent review of the developments in this subject in the conventional formulation of elasticty see \cite{lubarda_dislocation_2019}). We derive the formula describing the force between two dislocations for the traceless theory. An analogous computation for vacancies present is straightforward. The Lorentz force exerted by one dipole on another reads:
\begin{equation*}
F_j=-p_i(E_{ij}+\epsilon_{jk}\upsilon_k B_i)=\epsilon_{jk}b_i(\sigma_{ik}+\upsilon_k\pi_i).
\end{equation*}
The first term represents the usual Peach-Koehler force, which will have contributions from both gauge fields, which account for relativistic corrections depending on time and the defect's velocity, along with the usual term that encapsulates the material's elastic properties. The second term is the Biot-Savart analogue for the elastic force-interaction and it purely depends on the velocity. The full force written as a function of the Burgers vectors and the velocity reads:
\begin{widetext}\label{eq:PKforce}
\begin{align}
F_{j1\rightarrow 2}^{\text{PK}}&=\frac{2\mu(b_ld_l)n_j+\left[(1/2)(\upsilon_kb_k)d_j+2(\upsilon_kd_k)b_j-\upsilon_j(b_kd_k)\right]n_b\upsilon_b-n_j(b_k\upsilon_k)(d_m\upsilon_m)}{2\pi d}\left(\frac{A(t,d)}{1-n_i\beta_i}\right)\nonumber \\
&-\frac{(1/2)(\upsilon_kb_k)d_j+(\upsilon_kd_k)b_j-\upsilon_j(b_kd_k)}{2\pi}\frac{1}{B(t,d)}\left(\upsilon_s+\frac{\upsilon_s^2t}{B(t,d)-\upsilon_st}\right)\\
&-\frac{(1/2)(\dot{\upsilon}_kb_k)d_j+(\dot{\upsilon}_kd_k)b_j-\dot{\upsilon}_j(b_kd_k)}{2\pi}\ln\left(\frac{d}{B(t,d)}\right). \nonumber
\end{align}
\end{widetext}
The force contains also a contribution from the acceleration (if present) of the defect just like in electrodynamics. The first term on the right hand side of Eq. \eqref{eq:PKforce} is the regular "electrostatic" component in the low velocity limit. This can be seen if the relativistic correction is equal to unity. It happens when one interchanges $b_i\longleftrightarrow d_i$ and then fixes $n_i\rightarrow -n_i$. The result will be the force on the first dislocation produced by the second one, $F^{PK}_{2\rightarrow 1}$. The contributions from the first terms will cancel each other out, but this is not the case for the rest of terms containing corrections from velocities (i.e. magnetic part). This parallels results in electrodynamics. We know that two moving charged particles exert forces that are not reciprocal. The explanation being that the difference in rate of change of the system's momentum is carried out as electromagnetic radiation. In our case the stress field carries the disturbance and as a consequence of the elastic radiation from a moving dislocation.
\section{Discussion}\label{Sec7}

In this work we show that a dual gauge theory formulation of elasticity simplifies the analysis of defect dynamics. Using this simplification, we extend existent results focused on edge dislocations. We construct solutions to the equations of tensor gauge theory, dual to Cauchy's isotropic elasticity in a gauge, that is analogous to the Lorenz gauge in electrodynamics, for an arbitrarily moving dislocation. We use this to determine elastic stresses and strains due to the moving defect. We discus separately two physical scenarios, when non-topological defects are absent and when they are present. The former case corresponds to dislocations obeying the glide constraint, which in the static limit has been studied. We generalize this result to account for vacancies and interstitials. This leads to a new constraint that both topological and non-topological defects must satisfy, that we formulate as a relationship between gauge potentials. We interpret this result as a physical mechanism that forces that dislocations to excite non-topological defects if they move perpendicularly to their Burgers vector. Finally, we use the duality to extend the formula of Peach and Koehler for the interactions between dislocations. We give an analytic formula that describes the dynamical Peach-Koehler force for two dislocations with different Burgers vectors or charges.

The motion of defects in crystal lattices is essential to our understanding of material strength and plasticity.  Nevertheless, despite much effort dedicated to the subject, solving the defect dynamics in conventional formulation of elasticity has led only to partial results. On top of that isotropic Cauchy's elasticity describes only the most basic crystalline solid. This renders those results unfeasible to be generalized to more complicated systems involving anisotropy, rotational degrees of freedom or incommensurate lattices. On the other hand, the simplicity of our approach allows one to extend results presented here to ask more detailed questions in crystals, such as radiation or problems related to fast-moving dislocations as well as understand defect dynamics in more general theories of elasticity that can be formulated in the language of gauge theories.

Finally we note that the problem of defects has recently reappeared in the context of active solids. Generalizing our results to the case of non-Hermitian elasticity could shed light on the dynamics of defects in active media. This will be useful in understanding recent experiments on active solids with odd elasticty.

\begin{acknowledgments}
  PS acknowledges support form the Polish National Science Centre (NCN) Sonata Bis grant 2019/34/E/ST3/00405. LT was supported in part by the Deutsche Forschungsgemeinschaft through the cluster of excellence ct.qmat (Exzellenzcluster 2147, Project 390858490).
\end{acknowledgments}

\onecolumngrid
\begin{appendices}
\section{Inversion of the elasticity tensor} \label{AppA}
We present here the supplementary theory regarding the inversion of the elasticity tensor. The most general case represented in the form of the three projector operators, is given by
\begin{equation}
C_{ijkl}=p^1P_{ijkl}^0+p^2P_{ijkl}^1+p^3P_{ijkl}^2.
\end{equation}
We define
\begin{equation}
P_{ijkl}^0=\frac{1}{2}\delta_{ij}\delta_{kl},
\end{equation}
\begin{equation}
P_{ijkl}^1=\frac{1}{2}(\delta_{ik}\delta_{jl}-\delta_{il}\delta_{jk}),
\end{equation}
\begin{equation}
P_{ijkl}^2=\frac{1}{2}(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk})-\frac{1}{2}\delta_{ij}\delta_{kl},
\end{equation}
where $p^1$, $p^2$, $p^3$ are functions of the elastic parameters $\kappa$ and $\mu$. The projectors satisfy the closure identity $P_{ijkl}^0+P_{ijkl}^1+P_{ijkl}^2=\delta_{ij}\delta_{kl}$ and $P_{ijkl}^aP_{klmn}^b=P_{ijmn}^a$ if $a=b$ and otherwise. The inversion then is easily performed giving
\begin{equation}
C_{ijkl}^{-1}=\frac{1}{p^1}P_{ijkl}^0+\frac{1}{p^2}P_{ijkl}^1+\frac{1}{p^3}P_{ijkl}^2,
\end{equation}
For the case of an isotropic solid, we require the system to be invariant under the improper rotations group O(2) satisfying the relation $P_{ijkl}^1\sigma_{ij}=2\omega_{kl}=0$, where $\omega_{ij}$ is the angular velocity.
Using the above formulas the elasticity tensor and its inverted counterpart for this case are given by
\vspace{1mm}
\begin{equation}
C_{ijkl}=(\kappa-\mu)\delta_{ij}\delta_{kl}+\mu(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk})   ,
\end{equation}
\begin{equation}
C_{ijkl}^{-1}=\left(\frac{1}{4\kappa}-\frac{1}{4\mu}\right)\delta_{ij}\delta_{kl}+\frac{1}{4\mu}(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}) .
\end{equation}
For the rotated inverted tensor now, we have
\begin{equation*}
\Tilde{C}_{ijkl}^{-1}=\epsilon_{ia}\epsilon_{jb}\epsilon_{kc}\epsilon_{ld}C_{abcd}^{-1}
=(\delta_{ij}\delta_{ab}-\delta_{ib}\delta_{ja})(\delta_{kl}\delta_{cd}-\delta_{kd}\delta_{cl})C_{abcd}^{-1}=C_{ijkl}^{-1}.
\end{equation*}
proving Eq.\eqref{elasticitytensor} used in deriving the equations of motion.

\section{Fracton Elastostatics} \label{AppB}
\subsection{Disclination}
In the case of no time dependence in the equations of motion, the differential equation for the fractonic vector field is
\vspace{1mm}
\begin{equation}
\nabla^2 \phi_j=\left(\frac{4\mu\kappa}{\mu+\kappa}\right)\rho_j\Longrightarrow \nabla^4\phi=-\left(\frac{4\mu\kappa}{\mu+\kappa}\right)\rho.
\end{equation}
The scalar field $\phi$ acts as an Airy's stress function and the differential equation at hand is a non-homogeneous biharmonic equation in two dimensions, appearing often in linear elasticity and linearized fluid mechanics.
The solution is given as special case of the Mitchell solution with no radial dependence, for $\rho=q\delta^2(r-r_s)$. $q$ represents the disclination charge. A simple and easy way of solving the above is by noticing that $\nabla^2\ln(r-r_s)=2\pi\delta^2(\bold{r}-\bold{r}_s')$. This gives the Poisson differential equation:
\begin{equation}
\nabla^2\phi=-\frac{2q\mu\kappa}{\pi(\mu+\kappa)}\ln(\bold{r}-\bold{r}'_s)
\vspace{1mm}
\end{equation}
The solution is given by having the potential drop to zero at the boundary $R$ of the material
\begin{equation}
  \phi=-\frac{q}{2\pi}\frac{\mu\kappa}{(\mu+\kappa)}(\bold{r}-\bold{r}'_s)^2\ln\left(\frac{|\bold{r}-\bold{r}'_s|}{R}\right)
\end{equation}
where again the logarithmic behaviour is expected. The vector field $\phi_i$ has components
\begin{equation}
\phi_i=-\frac{q}{2\pi}\frac{\mu\kappa}{(\mu+\kappa)}|r_i-r'_{is}|\left[2\ln\left(\frac{|\bold{r}-\bold{r}'_{s}|}{R}\right)+1\right]  .
\end{equation}
Upon inversion of Eq.\eqref{rotated} one can extract the stress and electric tensors:
\begin{align*}
\sigma_{xx}&=\frac{q}{2\pi}\frac{\mu\kappa}{(\mu+\kappa)}\left[2\ln\left(\frac{\sqrt{x^2+y^2}}{R}\right)+\frac{2y^2}{x^2+y^2}+1\right],\\
\sigma_{yy}&=\frac{q}{2\pi}\frac{\mu\kappa}{(\mu+\kappa)}\left[2\ln\left(\frac{\sqrt{x^2+y^2}}{R}\right)+\frac{2x^2}{x^2+y^2}+1\right],\\
\sigma_{xy}&=\sigma_{yx}=-E_{xy}=-E_{yx}=-\frac{q}{2\pi}\frac{\mu\kappa}{(\mu+\kappa)}\frac{2xy}{x^2+y^2},
\end{align*}
where, $\sigma_{xx}=E_{yy}$, $\sigma_{yy}=E_{xx}$. The above equations are in full agreement with those in \cite{braverman_topological_2021}.
The strain tensor is given by making use of $u_{ij}=C_{ijkl}^{-1}\sigma_{kl}$, to get
\begin{align*}
u_{xx}&=\frac{q}{4\pi(\mu+\kappa)}\left[2\mu \cdot \ln\left(\frac{\sqrt{x^2+y^2}}{R}\right)+3\mu+\kappa\left(\frac{y^2-x^2}{y^2+x^2}\right)\right],\\
u_{yy}&=\frac{q}{4\pi(\mu+\kappa)}\left[2\mu \cdot \ln\left(\frac{\sqrt{x^2+y^2}}{R}\right)+3\mu+\kappa\left(\frac{x^2-y^2}{x^2+y^2}\right)\right],\\
u_{xy}&=u_{yx}=-\frac{q}{2\pi}\frac{\kappa}{(\mu+\kappa)}\frac{xy}{x^2+y^2}
\end{align*}
\subsection{Dislocation}
For the case of a dislocation now, we assume a density of the form $\rho_j=b_j\delta^2(\bold{r}-\bold{r_s})$ and get a solution
\begin{equation}
\phi_j=-\frac{2b_j\mu\kappa}{\pi(\mu+\kappa)}\ln\left[\frac{|\bold{r}-\bold{r_s}|}{L}\right].
\end{equation}
For the electric field and the stress tensor we calculate
\begin{align*}
\sigma_{xx}&=\frac{2b_y\mu\kappa}{\pi(\mu+\kappa)}\frac{(y-y_s)}{(x-x_s)^2+(y-y_s)^2},\\
\sigma_{yy}&=\frac{2b_x\mu\kappa}{\pi(\mu+\kappa)}\frac{(x-x_s)}{(x-x_s)^2+(y-y_s)^2},\\
\sigma_{yx}&=-\frac{2b_x\mu\kappa}{\pi(\mu+\kappa)}\frac{(y-y_s)}{(x-x_s)^2+(y-y_s)^2},
\end{align*}
where $\sigma_{xx}=E_{yy}$, $\sigma_{yy}=E_{xx}$, $\sigma_{yx}=\sigma_{xy}=-E_{xy}=-E_{yx}$. Finally we obtain the expressions for the strains
\begin{align*}
u_{xx}=&\frac{1}{2\pi(\mu+\kappa)}\frac{(b_y\mu+b_x\kappa)(y-y_s)+(b_y\mu-b_x\kappa)(x-x_s)}{(x-x_s)^2+(y-y_s)^2},\\
u_{yy}=&\frac{1}{2\pi(\mu+\kappa)}\frac{(b_y\mu+b_x\kappa)(x-x_s)+(b_y\mu-b_x\kappa)(y-y_s)}{(x-x_s)^2+(y-y_s)^2},\\
u_{xy}=&u_{yx}=-\frac{b_x\kappa}{\pi(\mu+\kappa)}\frac{(y-y_s)}{(x-x_s)^2+(y-y_s)^2}.
\end{align*}

\section{Strain} \label{appc}
The strain field extracted by using the relation $u_{ij}=C_{ijkl}^{-1}\sigma_{kl}$ reads
\begin{equation*}
u_{ij}=\left[\left(\frac{\mu-\kappa}{4\pi\kappa}\right)\left(b_kn_k+\frac{\epsilon_{km}\upsilon_kb_m(n_l\upsilon_l)}{2\mu}\right)\delta_{ij}+\frac{1}{2\pi}\left(b_in_j+\frac{1}{2\mu}\epsilon_{\left(ik\right.}\upsilon_{\left.j\right)}b_k(n_l\upsilon_l)\right)\right]\left[\frac{A(t,d)}{1-n_i\beta_i}\right]+\hspace{3.5cm}
\end{equation*}
\begin{equation*}
+\frac{1}{4\pi\mu}\left[\left(\frac{(\mu-\kappa)\mu}{2\kappa}\right)\epsilon_{km}\upsilon_kb_m\delta_{ij}+\epsilon_{\left(ik\right.}\upsilon_{\left.j\right)}b_k\right]\frac{1}{B(t,d)}\left(\upsilon_s+\frac{\upsilon_s^2t}{B(t,d)-\upsilon_st}\right)+
\end{equation*}
\begin{equation}
\hspace{7.8cm}+\frac{1}{4\pi\mu}\left[\left(\frac{(\mu-\kappa)\mu}{2\kappa}\right)\epsilon_{km}\dot{\upsilon}_kb_m\delta_{ij}+\epsilon_{\left(ik\right.}\dot{\upsilon}_{\left.j\right)}b_k\right]\ln\left(\frac{d}{B(t,d)}\right)    .
\end{equation}
\end{appendices}
\twocolumngrid
\bibliographystyle{utphys2}

redpajama_set_name: RedPajamaArXiv


Lostly did a tremendous job compiling and mixing Disc 3 of the just-released Pure Trance 7 compilation, creating a mean yet melodic journey packed with his own Originals, Remixes and Collaborations. Here are two of those Original productions in a full-length club-friendly format. Although cut from the same cloth sonically i.e. in Andre's inimitable style, they are very different tracks. Distant Shore is all about the on-beat melody, sustained drone-like pads, fluttering acidic sequences and an orgasmic high-string payoff. On the flip of this double A-side (let's pretend it's a vinyl record for a moment) Reflection is a darker, meaner piece of driving, filtered trance music, perfect for those long all-nighters when it doesn't matter how late it gets – you are never going home!
Tagged Lostly, Pure Trance, Pure Trance 7.


I have some corrections for names in Serbia.
- Serbian Cup is now just Kup Srbije, it's not Lav Kup Srbije anymore.
- Jelen SuperLiga is Jelen Super Liga.
- Prva Liga Srbija is Prva Liga Srbije.
- Contains all transfers that didn't make it into the game due to extended Serbian transfer window.
- Serbian Head Researcher, Dusan Stamenkovic, helped me with this update by sending me most of the data.
- The update is compatible with 13.3.0 and every patch after that.
- Contains over 2.100 changes in the database.
- List of all transfers is included in the .rar file.
- Installing this file will enable Serbian Zone Leagues for Football Manager 2013 on your computer. In addition, you will have Serbian Media Sources so you will held your press conferences in front of a real Serbian media.
- League is tested on holiday.
- League is playable on every Football Manager 2013 version since the release date.
- Clubs may move to the wrong divisions in Zone leagues. It happens in real life also but rarely.
If you don't have "editor data" folder, create it yourself.
In game, when selecting database check the "Change" box and then check my file. After that, continue playing as usual.
When choosing leagues, tick the "Add Key Staff" and "Add Players To Playable Teams" options so that newly created teams have staff and players in them.
If you want to post this on your forum/site, you can do so, but please credit the author.
- Installing this file will enable Serbian Lower Leagues for Football Manager 2013 on your computer. In addition, you will have Serbian Media Sources so you will held your press conferences in front of a real Serbian media.
- Please report any bugs in this thread. THANKS!
This file was downloaded over 3000 times for FM12.
Serbian Lower Leagues are finally here.
- League is tested for 4 seasons on holiday.
- Play off between Super and First league doesn't work propertly due to league coding and change of league structures after 2 season by default in the game. If I create new competitions to fix that, new bugs appear, so I left it like this.


The Rode Video Mic Short Shotgun Condenser Microphone is a high quality mic that can be mounted to video camera's, DSLR's and to a boom pole via a 3/8" thread. The VideoMic features a super-cardioid capsule which makes the microphone highly directional and prevents surrounding unwanted noise from being captured.
The Rode Video Mic frequency response is 40hz-20khz which let's you capture a large variety of sounds from the rumble of thunder claps to the airiness of cymbals and additionally features a 80hz high pass filter to eliminate rumbles such as air conditioning or traffic noise when they are unwanted.


Rebel Legion :: View topic - Visiting for 2 weeks!
Posted: Mon Sep 26, 2016 11:24 pm Post subject: Visiting for 2 weeks!
Hi! I'm from Central Base in N. America and I'll be in Tokyo for about two weeks the beginning of October. Are there any events/troops happening so I can stop in and meet you all? I won't be bringing a costume, but I can be a handler/photographer!
At this moment we will have events on 1st October and 29th (undecided).
Ooh we were flying in on the 1st, and leaving on the 15th, but I'm loving my time here so far!


text:
The Hardy Boys 2020 season 1
13 episodes (0 views)
Genre:, Drama, Mystery
Channel:Hulu
The story will tell about two brothers who will have to unravel many secrets and sinister stories. 16-year-old Frank and 12-year-old Joe go to their aunt in the small town of Bridgeport, where the parents of the main characters once lived. Here the boys hoped that they would take a break from the unpleasant adventures, but that was not the case. Their vacation ends after they learn that their father, Detective Fenton Hardy, has taken up a dangerous case. Soon, the teenage brothers, along with their friends, begin their own investigation. However, the young detectives could not even imagine that a small town keeps many terrible secrets ...
The Hardy Boys 2020 season 1 episodes list:
Episode #1: Welcome to Your Life (air date: 2020-12-04)
After a devastating tragedy, Frank and Joe Hardy, together with their father Fenton, move to the small town of Bridgepoint to spend the summer with their Aunt Trudy. Their simple summer plans quickly come to an end when they discover their dad has taken on a secret investigation and Joe's life is threatened. Realizing that their Dad may be onto something, the boys take it upon themselves to start an investigation of their own.
360p (mp4 444.5 MB)
Episode #2: Where the Light Can't Find You (air date: 2020-12-04)
When Fenton heads overseas to find Mrs. Khan's nephew, Rupert, he quickly realizes that whatever Rupert and Laura were working on garnered attention in Bridgeport. Meanwhile, Frank discovers an old note of his mom's in Bridgeport that mentions the sunken fishing boat and Joe and his new friend Biff befriend a man on the beach who asks them to help him by delivering a message.
Episode #3: Of Freedom and Pleasure (air date: 2020-12-04)
Joe finds a strange golden idol hidden in his room, but when he accidentally breaks it, inside is a strange piece of broken stone that he stashes in his pocket. Later that day at the Bridgeport Fair Joe gets lucky, but he also draws the attention of the Tall Man. Meanwhile, Frank discovers some information about an old mining expedition that ended in tragedy and the boys start to wonder what their Mom was investigating.
Episode #4: Secrets and Lies (air date: 2020-12-04)
When the thief's campsite is discovered, Joe is terrified that the toolbox he lent the man on the beach has been found by the police. Trying to hide his connection to the criminal, Joe enlists Biff to help him get his monogrammed soldering iron – that he kept in the toolbox – out of evidence at the police department. Frank confronts his Grandmother after learning she had an argument with his mom.
Episode #5: The Drop (air date: 2020-12-04)
Joe and Frank decode a message that leads them to try and make a drop at the warehouse, despite the fact the message was intercepted by Police Chief Ezra Collig. The drop goes awry, but later when the boys return looking for more clues, they find a piece of fabric that the person fleeing the warehouse left behind. When the Tall Man escapes from the hospital, the boys reveal their entire investigation to their friends and get their help to lure the Tall Man to Chet's farm.
Episode #6: In Plain Sight (air date: 2020-12-04)
Frank relents and takes the entrance exam to Rosegrave Preparatory School. Callie Shaw is also taking the test and the two become close as they work together to solve the exam's last escape room puzzle in Gloria's study. Unwittingly they discover a hidden door, marked by a similar symbol they've seen before. Meanwhile, when Joe finds out the Tall Man has escaped from jail, he quickly tries to find a safe place for his lucky charm.
Episode #7: A Figure in Hiding (air date: 2020-12-04)
Frank and Callie make a visit to Rosegrave Prep where Frank learns the Dean had a close connection to his mother… one the Dean feels unsafe discussing with Frank. Joe and Biff continue to investigate the scrap of fabric from the warehouse and make a discovery that leaves Biff conflicted. Mrs. Khan makes a play for the missing piece of The Eye by enlisting the Tall Man. However, things don't exactly go as planned when the Tall Man goes after Frank and Joe to get the missing piece.
Episode #8: What Happened in Bridgeport (air date: 2020-12-04)
Frank befriends Stacy, the new girl in town, after an accident. The Hardy boys start the school year in Bridgeport, since their dad is still away. Frank discovers his mom used to write for the high school paper and was investigating the most powerful families in Bridgeport… including the Estabrooks. J.B. Cox tries to put the squeeze on Joe to find out what he knows about The Eye, but Joe denies having what J.B. wants… his lucky charm.
Episode #9: The Key (air date: 2020-12-04)
When J.B. Cox offers Joe up to Gloria, he is hired to find the other two pieces of the Eye. Joe's lucky charm goes missing and Aunt Trudy uncovers the boys' investigation. Elsewhere, Fenton rescues Rupert Khan and learns what he and Laura were working on. Frank and Joe discover their mother's music box holds a secret.
Episode #10: The Secret Room (air date: 2020-12-04)
After gaining access to George Estabrook's Secret Room, Frank and Joe take their great-grandfather's journal and maps to learn more about The Eye. Despite Frank warning them of danger, Joe and Biff strike out alone to find the Chamber of the Eye. Meanwhile, Callie grows increasingly suspicious and jealous of Stacy, upsetting Chet in the process. Frank confronts Stacy and discovers the truth behind her move to Bridgeport.
Episode #11: No Getting Out (air date: 2020-12-04)
The town of Bridgeport is put under curfew with Joe and Biff missing. Frank realizes they must have gone looking for the Chamber of the Eye. When Frank asks Gloria for help finding the Chamber, Gloria doesn't know anything about an entrance to the old, sealed, mine tunnels so Frank must turn to Stacy for help. Frank lets Officer Jesse Hooper in on their investigation, and the boys find themselves in more danger than they'd expected.
Episode #12: Eye to Eye (air date: 2020-12-04)
Frank has no choice but to side with his grandmother and play her game if he wants to get close enough to destroy The Eye. Fenton returns to Bridgeport with Rupert Khan and learns that Joe and Frank have gotten themselves farther along in their investigation than he could imagine. But when Fenton tries to get Frank to leave the Estabrook Estate, his son refuses. Stacy, being spurned by Frank, takes revenge, and puts one of Frank's friends in danger.
Episode #13: While the Clock Ticked (air date: 2020-12-04)
Frank and Chet find a way to rescue their friend without giving up the Estabrook piece of The Eye to Stacy, while Joe, Biff and Phil break into the Estabrook Estate looking for the missing piece, but they're too late. The Hardy boys with Fenton's help will have to find their way to the hidden Chamber to stop the Circle from reuniting the Eye. What happens next changes everything for the Hardy boys!
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For the beginner usually aged between 4 years and 7 years. We hold several sessions a week both at Barr Beacon Community Centre and Walsall Campus of the University of Wolverhampton. At a very early age, children are expected to become familiar with water and to feel at ease in their surroundings. No more than half an hour is needed and very young children cannot be expected to co-ordinate proper swimming skills, so play is the theme at first. When they are ready (this depends on the individual, some take time, some adapt more quickly) the first stages of learning swimming skills begins. From then on, as ability increases, more teaching is applied and we can then accommodate children who wish to take more than one lesson a week.
For the junior swimmer (usually aged between 7 years – 10 years) children make the transition from widths to lengths gradually by attending one of their sessions in lengths at first. Again as ability increases a child can quite easily adapt to more junior sessions. The focus is on teaching and implementing correct skills in all sessions. Providing regular training is maintained children should be competitive swimmers by the age of 9- 10 years.
The club provides ample water time for junior coaching, a maximum of 5 sessions per week are available. All staff are ASA qualified and are always on hand to give advice that might be needed.
For the senior swimmers (aged 11 years upwards) first class facilities are provided. A season's training begins in September and is aimed at County success and Midland and National qualifying times.


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