Most modern engines are equipped with variable valve timing. This technology improves performance and efficiency at the same time, but how does it really work? Well, before we get into that, let's explain the terminology. You see, the technology is widely used by most manufacturers, but a lot of them have some variations on it, including a special name for it. Toyota for instance uses VVT-i, Honda has VTEC and Mitsubishi has named their system MIVEC. In all actuality, they do almost exactly the same thing.
By using complex mechanical as well as hydraulic processes inside the engine, the technology allows the engine to gain more performance when the driver demands from it, and at the same time increase efficiency when you don't really need the performance. Like we said, all systems have a few different characteristics, but they all operate on the same (rough) principles.
When driving at the lower end of the RPMs, the variable valve timing system uses a camshaft with a different. It's designed to offer a smoother idle with better fuel economy, as well as more low-end power and torque. It's a win-win, giving the driver more drivability without sacrificing efficiency.
The computer onboard monitors the RPMs in real time, the throttle position as well as the current conditions. When it feels like you're demanding more from the engine, it will switch to a different camshaft profile giving you more power.
As soon as you bury your foot on the accelerator, an electronic switch is immediately activated by the car's computer, triggering the switch over to the more aggressive camshaft profile with the help of hydraulics. This gives the driver lots more performance at higher RPMs. In most cases, drivers can actually hear and feel when the system is active, it really is that noticeable.
Not all variable valve timing engines are performance oriented however. Some manufacturers use the technology to increase fuel economy in their engines, with no emphasis being put on power whatsoever.
The other benefit of the system is that you get more internal gas recirculation. Because you have more direction for the gases, the system can actually cut down on emissions. This is crucial for manufacturers who are trying to get their vehicles under a certain limit for exhaust gasses.
The increase of power in the upper parts of the rev range is great, but the low-down torque is what makes VVT so usable. It's better for everyday driving, and not just because of it either. Thanks to more precise handling of engine valves, VVT makes engines significantly more fuel economical than their non-VVT counterparts. Naturally, there are pros and cons of the system, but the simple fact is that the pros for VVT far outweigh its cons like complexity and increased production cost.


The first bird flies and lands on a branch approx. 15 ft. directly above the mic. It then flies laterally to another tree and lands on a branch approx. 15 ft. away from the original branch. The second bird flies in and lands on a branch in a different tree, approx. 15 ft. from the first bird, and 25 ft. from the ground. Shortly after the second bird lands, at approx. :37, the first bird begins to vocalize. the second bird moves and becomes obscured. (NOTE: in this recording, the bird is possibly responding to PLAYBACK. The track being played was from Claude Chappuis and Pierre Huguet's Birds Of Madagascar And Indian Ocean Islands: Disc III, track 31 (Mauritius Bulbul).


text:
Jason Frakes
Louisville Courier Journal
LEXINGTON, Ky. – Facing Breeders' Cup Mile champion Tepin will have to wait. For now, trainer Graham Motion will be pleased enough with his Miss Temple City beating the boys.
Miss Temple City sat off the pace early and then charged down the stretch for a 1 1/4-length victory Friday, becoming the first filly to win the $300,000, Grade I Maker's 46 Mile in its 28th running at Keeneland.
Motion chose the Maker's 46 Mile for Miss Temple City's 4-year-old debut after also considering Saturday's Coolmore Jenny Wiley Stakes, where Tepin is the favorite.
"This was a very wide-open race, and I didn't want to run against Tepin in her first race back this year," Motion said. "She's probably the best miler in the country."
Miss Temple City covered the mile on turf in 1:34.09 and paid $14.60 as the fifth betting choice in the field of nine, capturing her first graded-stakes victory in front of 17,645 fans at Keeneland.
Jockey Drayden Van Dyke got a five-pound weight allowance facing the boys. Van Dyke had ridden Miss Temple City to a runner-up finish to Her Emmynency in her last start, the Grade I Queen Elizabeth II Challenge Cup at Keeneland last October.
"It's a nice break on the weights with the fillies," Motion said of racing his filly against the boys. "If Drayden couldn't have done the weight, I wouldn't have done it. The fact that he had ridden her and ridden her very well, that kind of sealed the deal for me."
Heart to Heart set fractions of 23.30 seconds for the quarter-mile and 46.03 seconds for the half-mile, with the Ken Ramsey-owned Shining Copper and Miss Temple City just behind.
Miss Temple City gained the lead with a furlong to go, with Heart to Heart finishing second.
"Couldn't have asked for a better trip," Van Dyke said. "She took off like a rocket. She's such a nice filly."
A daughter of Temple City out of the Artax mare Glittering Tax, Miss Temple City earned $180,000 for Sagamore Farm. Allen Rosenblum and The Club Racing and improved to 4-3-2 in 10 career starts.
Motion hopes to return Miss Temple City to Royal Ascot, where she finished fourth in last year's Coronation Stakes, but said the Grade 3 Gallorette at Pimlico on May 21 could serve as a tune-up before heading to England.
"We all want to go back, but we want to go back and know we belong," Motion said. "I think today we feel pretty good about belonging. … She's a big, strong filly, and she's actually grown up a lot over the winter. She's bigger and stronger than she was last year. I've been really impressed with her this winter."
Jason Frakes can be reached at (502) 582-4046 and jfrakes@courier-journal.com.

redpajama_set_name: RedPajamaCommonCrawl


text:
Ravinder Ravi Singh
Chief Information & Innovation Officer Vistra ( joint venture of Tata and Singapore Airlines )
Ravinder Pal Singh (Ravi) is an Award Winning Technologist, Rescue Pilot and Investor with over 50+ global recognition and 17 Patents. His body of work, mostly 1st in the world are making a difference within acute constraints of culture and cash via commodity technology. He has been acknowledged as world's top 25 CIO and top 10 Robotics Designer in 2018. Ravi is a Harvard alumni, global speaker and has delivered over 100+ lectures and papers in Asia, Europe, USA and Africa in 2018-19. Ravi is advisor to board of 9 enterprises where incubation and differentiation is a core necessity and challenge. He sits on the advisory council of 3 global research firms where he contributes in predicting practical future automation use cases and respective technologies.
Embracing Technology Innovation to Fly Business at a Peak Speed


As Germany's capital city, Berlin has a wealth of history that is unrivalled by anywhere else in the country. From the Thirty Years War and the Enlightenment to the Holocaust, the Cold War and the eventual fall of its eponymous Wall, Berlin is a city that has been at the forefront of major political and social change in Europe over the last centuries.
Now the city is a thriving social centre, famous for its music scene and nightlife. If you are looking to study a graduate program in Germany, there may be no better place than Berlin.
Berlin and its surrounding area is one of the most prolific areas for Higher Education in the whole European Union, with a large number of research institutions that may or may not be connected to the city's universities. Coupled with the fact that German is such a widely learnt modern foreign language, it is easy to see why almost 140,000 students have made the choice to study here.
There are also 27 colleges, which may be private or offer a technological education.
Graduate programs in Berlin generally last two years for taught courses, with research programs and PhDs taking up to three years to complete.
Berlin is a well established centre for popular culture in Europe, largely due to its music scene and the fact that it has become a haven for artists over the last few years. It is well known for its underground and often edgy nightlife – something that attracts thousands of travellers and students every year.
On a more mainstream note, Berlin has a large number of museums – including the famous Museum Island, which is a World Heritage Site. In 2005 Berlin as a whole was named City of Design by UNESCO.
It goes without saying that life in the city is framed by its history. It is only just over 20 years since the fall of the Berlin Wall, and the fact that much of Berlin and Germany's history is so recent means that it can often still be felt very heavily.
Germany is of course also famous for its markets, especially at Christmas – and Berlin is at the heart of this, with over 120 to choose from.
Non-EU international students wanting to stay on to work in Berlin after their postgraduate course will need to apply for a work visa.
Berlin is home to businesses including Deutsche Bank, Siemens and Daimler. Its fastest growing industries include life sciences, transport, IT, media, advertising, biosciences, the environment and music. Its tourism sector is also booming. There are many diverse opportunities for you to pursue in the city after completion of your graduate program.
When coming to Berlin to study on a postgraduate course you will obviously have to find somewhere to live. You may decide to live in halls owned by the university, where you will such things as bills included in your rent. You should check with your university to see if you will be eligible for a room.
Berlin has a temperate oceanic climate, which means it can experience humid summers and fairly cold winters. Temperatures may sometimes be higher in the city than in the surrounding area. Winter is roughly from October to February and summer from May to September.
Are you interested in studying a graduate program in Berlin? If so, you should sign up for our Free Application Service. We'll provide you with tailored information, courses to suit you and the option to apply online for the graduate program you want.


text:
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	require( "grunt" ).npmTasks( "grunt-update-submodules" ).cli();

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	console.log( e.stack + "\n" );
	console.log( "An error occurred while loading grunt, please ensure that it has been" );
	console.log( "installed correctly before continuing. You can learn more about grunt" );
	console.log( "at the grunt project page, https://github.com/cowboy/grunt/" );

	process.exit( 31 );

}

redpajama_set_name: RedPajamaGithub


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Hello everyone welcome to our Thankful Facebook Fanpage hop featuring KaDoodle Bug Designs, Too Cute By Jessica, Scrapadoodles Scrapbooking & Supply and My Life in Arts and Crafts! We are so Thankful for all of you that are joining us again as well as all of you newbies that are here for some fun!
All you have to do to be eligible to win one of these prizes is be sure to become a fan on all the pages and like and comment on each post!
Remember you still have time to enter my Thanksgiving Linky Party!!!!
Come join us on Facebook and Hop along with us.
These are adorable! You can use them every year! Love em!
So cute Tara ! These are perfect !
love your place cards! very cute!


Celebrate your newest family member with a tailor-made photo adoption announcement from Mixbook and let friends and family share in this momentous occasion with you. Young children and babies are hard to resist, and your cards will be too when you take a few moments to make your own, personalizing it in ways that only you can. It is easy to make your own adoption announcement, and you can personalize it to reflect all of the details you want to share in your own way, modifying it as you go along until you have the perfect design. Each Mixbook project is fully customizable, allowing you to experiment with color choices, photo layouts, and text designs until you create the perfect appearance for your card. Nothing is quite as special as the entrance of a young child into the world, and this is the moment you've been waiting for during the long process of adopting a child. As the first year ends, you will begin to wonder where all of the time with your newest family member went. Having a custom adoption announcement to look at whenever you want to do so offers a loving way to keep this moment special in your life forever.
When you make your own custom adoption announcements, you can include as many personal details as you like. A good place to start is with the child's name, length, weight, and adoption date. You may even want to include the birth date and time for a higher level of personalization. If it's a boy, you will want a baby boy announcement color to match. With a single photo, you can create a stunning appearance for your card. In addition to single-photo designs, you can choose a three-photo design, allowing you to pick several of your favorite photos. Mixbook offers an easy customization process that allows you to begin with a blank slate. If you prefer, you can choose one of the many themed designs and customize it by modifying different aspects of it. You can reflect your style and personality in so many different ways from the type of corner shape you select to the colors on your card to the number of photos you choose to display. You even have choices in photo orientation, making it easy to put your photo in the best presentation. These custom cards come in two sizes - 5 x 5 inches and 5 x 7 inches, making them suitable for first-class mailing. A crisp envelope accompanies each card.
Make your adoption announcements special by adding the touches that only you can include. You will be creating a tailor-made memento that you can love and cherish over many long years of happiness. The high quality of Mixbook's photo cards make them suitable for framing and placing in the baby's room. Today's parents are all about preserving special moments for longevity, and they often include adoption announcements in custom photo books for themselves, for the grandparents, and for the child. It is a great way to hold onto the moments that make life so special. Current trends in adoption announcements include using photos and selecting a contemporary theme for the card.
Whether it's a baby girl announcement or you are adopting a boy, celebrate your new family member or members with Mixbook adoption announcements. At the end of the long process of adoption often much longer than 9 months you'll be more than ready to spread your incredible news with custom baby adoption announcements. Start a new photo book at the same time, then upload a new photo or series of photos each month. By the end of your baby's first year, you'll have a beautiful memento that you'll cherish forever.


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text:
Obama vs. The Magicians
President Obama's response to crazy conspiracy narratives about him is predictable and cool. He doesn't want to wade into the nonsense, and in that much he's absolutely right: you can't argue people out of their irrational beliefs. And in general, Obama has put his faith in the public's preference for real-world results over conspiracy theories.
"I trust ... the American people's capacity to get beyond all this nonsense and focus on, 'Is this somebody who cares about me and cares about my family and has a vision for the future?' " Mr. Obama said. "And so, I will always put my money on the American people."
Obama is right. Americans prefer results over crazy mumbo-jumbo. And that's why Obama's in trouble.
If Obama's going to overcome the nutty mumbo-jumbo with practical results, he needs an actual plan that will lead to practical results. Reason trumps fantasy by bringing home the groceries at the end of the day. If all reason has to offer every day is yet another sensible, pragmatic explanation for why the cupboard is still bare, fantasy starts to look like the only game in town.
The various strands of right-wing lunacy over the last two years, the birther conspiracies and "secret Muslim" fantasies, the scapegoating and hatemongering and Glenn Beck's chalkboard and the recent Palingenetic "Rebirth of a Nation" rhetoric (h/t Digby) are all just various kinds of magical thinking: attempts to deal with overwhelming or insoluble realities through acts of belief. Can't deal with the fact the President of the United States is black? Believe that there is a piece of paper somewhere, a secret document, that will undo the election. (The giveaway with the birthers is that they don't demand that Biden be sworn in, but fantasize about overturning the last Presidential election entirely and getting rid of the Democrats.) Can't cope with the rubble of our economy? Blame a conspiracy by ACORN or The Tides Foundation or the Jewish Freemasons, a conspiracy whose effects can be reversed if you can just find and punish the conspirators.
People indulge in magical thinking for the same reason people once believed (or still believe) in magic, because it helps them deal with things they can't control. Drought killing your crops? Sacrifice a ram to Zeus, or dance the Rain Dance, or make an offering to the crocodile god. Mysterious illness killing your livestock? Use a ritual to redirect the evil magic onto a goat, and if that doesn't work, find the witches who've caused the illness and kill them.
Magic doesn't do anything, but it makes you feel like you're doing something. It takes away feelings of powerlessness before they become intolerable. And it allows you to release your fear and rage in the unholy pleasure of the witch hunt.
People give up on magic when they get better options. If you can irrigate your crops and take your cattle to the vet, you don't bother making sacrifices to the gods or dunking witches in the pond. You don't need magic to make you feel like you're doing something, because now there's actually something you can do. Modern people still resort to fantasy and superstition, of course, but mostly when their circumstances make them feel powerless or when science fails them. Superstition seems much more attractive when you can't see your way out of poverty, or when you depend on someone else for your livelihood. The anti-vaccination movement is a classic example of turning to magical thinking when science disappoints; medicine hasn't got a great list of solutions for autism yet, and so frustrated parents of autistic children look for a scapegoat to attack, and that lets them feel like they're doing something.
The sorry truth is that a large percentage of the human race, even those of us surrounded by modern technology, don't quite believe in the principles of science and reason. It's more that people believe that the bus comes in the morning, and that food you put in the fridge stays good for a few extra days, and that if you point the remote at the TV it will show you the channel you want. The average person on the street doesn't necessarily believe, deep down, in anything that happens at the Large Hadron Collider, because those things can't be seen or touched. But if the Large Hadron Collider eventually leads to, say, a new generation of tiny, powerful batteries, people will totally believe in the batteries. Reason beats superstition because it's better at miracles.
Our country is full of anxious and frightened people, who are right to be anxious and frightened. Our economy is broken. Our foreign military engagements look bleak. The future is unpredictable, so few people feel safe. People need to know that there is a plan for them, and their family, and a vision of the future, and they need a little more than that. They need that vision to start paying off.
Telling voters that the stimulus saved the economy from being much, much worse isn't useful. That statement is true, but it's only a description of the past. It does not answer the practical question, "How will we make this better?" If you're the smartest and most pragmatic leader in the world but unemployment is at 10% and you don't offer any way to fix that, people are going to start looking for someone dumber and less pragmatic. And if there are genuinely no rational solutions, you might as well sacrifice a chicken or two.
Glenn Beck is a huckster, but he's not just a huckster. He's a shaman. A white-bread witch doctor. He offers to solve his followers' problems with political voodoo. He's going to bring back the buffalo and make everyone impervious to bullets. He's going to make Obama disappear. He doesn't have real solutions, but he promises the illusion of solutions, and an illusion with no real solution looks better than no illusions and no solutions either.
Obama and his Administration can no longer appeal to "confidence" or "optimism" about the economy over the long run. Nobody pays their rent in the long run. And if the only solution people are offered is magical thinking, people are going to flock to those who can at least make that magical thinking entertaining. Obama is never going to beat our country's political witch doctors at their voodoo game.
Nor can Obama wait for the nation's economy to fix itself. The whole country can't bear to wait and do nothing. So if they're forced to wait, more and more people are going to gravitate to the magicians' tents and listen to what the magicians tell them. That has already started. And sooner rather than later, the magicians are going to tell them what every shaman or witch doctor says when their spells and and chants don't work fast enough: Someone must be interfering with the magic. Someone is keeping the spell from working. Then the magicians will send their followers to cast out the sinners, the witches, the evildoers responsible for the evil magic, and to punish them. And once that hunt begins things will happen that no reason can repair.
Labels: It's Foucault's World, Obama, The Post-Conservative Mind
Deniers and Caretakers, Republicans and Democrats
Dear Right Wing: Is This War or Not?
Judicial "Overreach" Since 1783
Undermining Traditional Marriage (Amen!)


text:
Big Brother Bluff () is a high, angular granite bluff,  high, along the west wall of Daniels Range,  north of Mount Burnham, in the Usarp Mountains. It was so named by the northern party of the New Zealand Geological Survey Antarctic Expedition, 1963–64, because it is visible from  north and from many points across Rennick Glacier. Hence the reminiscence from George Orwell's famous saying from Nineteen Eighty-Four, "Big Brother is watching you".

See also
Fikkan Peak

References

Cliffs of Oates Land

redpajama_set_name: RedPajamaWikipedia


The Welin Camlock Coupling provides a faster, safer and more convenient way of making and breaking flanged hose connections.
To make a connection, the two flanges to be joined are brought together and automatically positioned within the cam blocks around the coupling. With the faces parallel, the cams are rotated clockwise using a locking bar or wrench (supplied with the Camlock).
Each cam takes approximately 5 seconds to lock.
The Welin Camlock Coupling replaces the conventional time consuming and hazardous method of drift pin, nut and bolt flange connection.
expected – saving time and improving safety within the demands of the industrial and marine environment.
including cryogenic, submersible and hydraulic operations.
Welin Camlock Couplings are in everyday use throughout the world in marine loading/ discharging terminals, ports, refineries, dock facilities, chemical plants and distribution centres.
The permanently positioned 'O' ring face seal provides a dependable and leak-proof seal. This also helps to prevent finger and hand injuries that can result from trying to fix traditional gaskets between flanges.
The advanced design allows an area contact between the cam and flange face. The cam's helical arrangement ensures a definite wedging action, making it impossible to loosen during normal operating conditions when there is pressure in the line.
A round steel bar or special locking wench is the only tool needed to lock, tighten or release the cams.
Breakaway Systems prevent spillage, damage to assets and injury to personnel.
Connects and disconnects transfer lines with no spillage.
Interchangeable with other connections such as those provided by Mann-Tek, TODO, Avery Hardoll.


text:
AbstractIntroductionConclusionConflicts of InterestAcknowledgmentsReferencesCopyright
Pierre Gaspard, Raymond Kapral, "Active Matter, Microreversibility, and Thermodynamics", Research, vol. 2020, Article ID 9739231, 20 pages, 2020. https://doi.org/10.34133/2020/9739231
Active Matter, Microreversibility, and Thermodynamics
Pierre Gaspard 1 and Raymond Kapral2
1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
2Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada
Received15 Mar 2020
Accepted19 Apr 2020
Published21 May 2020
Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature, active matter systems exist in nonequilibrium states. In this paper, the active agents are small Janus colloidal particles that use chemical energy provided by chemical reactions occurring on their surfaces for propulsion through a diffusiophoretic mechanism. As a result of interactions among these colloids, either directly or through fluid velocity and concentration fields, they may act collectively to form structures such as dynamic clusters. A general nonequilibrium thermodynamics framework for the description of such systems is presented that accounts for both self-diffusiophoresis and diffusiophoresis due to external concentration gradients, and is consistent with microreversibility. It predicts the existence of a reciprocal effect of diffusiophoresis back onto the reaction rate for the entire collection of colloids in the system, as well as the existence of a clustering instability that leads to nonequilibrium inhomogeneous system states.
Active matter is composed of motile entities or agents interacting with each other either directly or through the velocity and concentration fields of the medium in which they move. Such interactions lead to collective dynamics giving rise to states of matter that may differ from those in equilibrium systems. The study of such collective behavior presents challenges and is currently a topic of considerable scientific interest. Systems with many complex agents can be investigated in different ways. One way is to describe collective dynamics at the macroscale in terms of fields representing the distribution of the agents across the system. These fields are ruled by partial differential equations that are established using general symmetries and experimental observations. Another approach is to model active matter as being composed of active particles moving in space according to specific rules that are postulated on the basis of empirical considerations.
Both of these approaches have been used to explore the origins and types of collective dynamics that can be found in active matter systems, and research on this topic ranges from studies of simple active particle models, often satisfying minimal rules, to suspensions of more complex active synthetic or biological agents [1–11]. The collective behavior in systems where the active agents are chemically propelled colloids, the subject of this paper, has also been the topic of experimental and theoretical research [12–25].
Systems containing colloidal particles are governed by physicochemical laws, so that their time evolution can be understood from first principles using statistical-mechanical methods. This approach was pioneered by Einstein [26] and Smoluchowski [27–29] at the beginning of the twentieth century and systematically developed since then for passive colloidal particles [30–33]. In active matter, the colloidal particles are propelled with energy supplied by the surrounding solution, so that the description should be extended to include the molecular concentrations of fuel and product powering their motion, in addition to the velocity field of the fluid. Through such an approach, active matter can be described from the scale of a single colloidal motor moving in the surrounding fluid, up to the macroscale where many colloidal motors generate collective motion by interaction. At the macroscale, collective dynamics is described in terms of the distribution function giving the orientation as well as the position of the colloidal motors. This statistical-mechanical approach has the advantage that the parameters characterizing active matter at the macroscale can be deduced from the microscopic level of description. The knowledge of these parameters in terms of the properties of materials composing the colloidal motors and the surrounding solution is fundamental for engineering active systems.
The present paper contributes to the statistical-mechanical and nonequilibrium thermodynamic approaches for active matter systems [34–42], and considers systems whose active agents are Janus colloids with catalytic and noncatalytic faces moving by diffusiophoresis generated by chemical reactions taking place on their catalytic faces or caps [43, 44, 40]. Because of diffusiophoresis, the velocity and concentration fields are coupled together in the fluid around the Janus particle [45]. We start from the calculation of the diffusiophoretic force and torque on a single Janus particle moving in a fluid in the presence of molecular species corresponding to the fuel and the product of the reaction taking place on its catalytic surface. The concentrations of these molecular species may develop gradients on large scales under nonequilibrium conditions, and these gradients should be included in the calculation of the force and torque. The resulting diffusiophoretic force and torque enter the coupled Langevin equations ruling the displacement, rotation, and overall reaction of a single active particle.
Next, the evolution equation is established for the distribution function of the ensemble of active particles in a dilute colloidal solution. In order to be consistent with microreversibility, the principles of nonequilibrium thermodynamics are used to relate the thermodynamic forces or affinities to the current densities with linear response coefficients satisfying Onsager's reciprocal relations [46–53]. This method allows us to obtain all the possible couplings compatible with microreversibility, including a priori unexpected reciprocal effects. Moreover, this method provides an expression for the entropy production rate density for active matter in agreement with the second law of thermodynamics and including the contribution of the reaction powering activity. Through this procedure, macroscopic evolution equations are obtained that govern the collective dynamics of colloidal motors coupled to the molecular concentrations of fuel and product. These equations can be shown to generate the reciprocal effect of diffusiophoresis back onto the reaction rate that has been obtained previously for a single particle [39, 40], but now at the macroscale. Furthermore, pattern formation due to a clustering instability manifests itself under nonequilibrium conditions induced by a bulk reaction replenishing the solution with fuel.
The paper is organized as follows. Section 2 is devoted to the dynamics of a single colloidal motor. The force and torque due to diffusiophoresis are deduced by solving the diffusion equations for the molecular concentrations coupled to the Navier-Stokes equations for the fluid velocity, including the contributions of concentration gradients at large distances from the particle. These contributions were neglected previously [39, 40] and are calculated in detail here. In Section 3, the diffusiophoretic force and torque obtained in Section 2 are incorporated into the evolution equation for the distribution function describing the ensemble of colloidal motors, and the entropy production rate density is explicitly obtained. Two implications of these results are presented in Sections 4 and 5. First, the reciprocal effect due to the diffusiophoretic coupling of an external force and torque back onto the reaction rate is recovered, now at the level of the collective dynamics. Second, a clustering instability leading to pattern formation is shown to manifest itself. The conclusions of the research are given in Section 6. The appendices provide additional details of the calculations.
2. Diffusiophoresis and Colloidal Motors
This section describes the motion of a single spherical Janus colloidal motor of radius that is propelled by self-diffusiophoresis generated by a reversible reaction, with rate constants taking place on its catalytic surface, as depicted in Figure 1. In this reaction, is the fuel and the product, which are present in the solution surrounding the particle. Moreover, the concentrations of the and molecular species are assumed to have gradients with at large distances from the particle that also contribute to motion by diffusiophoresis; thus, the motion of the particle is determined by processes in the fluid surrounding the particle.
Schematic representation of a Janus particle with its catalytic (C) and noncatalytic (N) hemispheres where the surface reaction (1) takes place between fuel and product supplied by the solution surrounding the particle. The particle is also subjected to some external force and torque . The position of its center of mass is , and is the unit vector giving its orientation and pointing in the direction of the catalytic hemisphere.
2.1. Chemohydrodynamics around a Colloidal Motor
In order to determine the force and the torque due to diffusiophoresis, as well as the overall reaction rate, the velocity of the fluid and the concentrations of fuel and product should be obtained by solving the Navier-Stokes equations for the fluid velocity coupled to the advection-diffusion equations for the molecular concentrations with : where is the constant mass density (the fluid being assumed to be incompressible), the hydrostatic pressure, the shear viscosity, and the molecular diffusivity of species .
The coupling between the velocity and concentration fields is established with the boundary conditions [40, 54] where is the unit vector normal to the solid surface, , is the slip length, , denotes the transpose, is the diffusiophoretic coefficient of species coupling the velocity field to the corresponding concentration field because of different interactions between the solid surface with the molecules of different species. The velocity field inside the solid particle is given by in terms of the translational and angular velocities of the particle, respectively, denoted by and , and position of the center of mass of the particle. Equations (5) and (6) are the boundary conditions on the components of the velocity field that are, respectively, normal and tangential to the interface , which is located on the sphere . The last equation, i.e., equation (7) is the boundary condition for the two reacting species , where is the stoichiometric coefficient of species in the reaction ( and ), and are the forward and reverse surface rate constants per unit area.
The velocity field is assumed to vanish at large distances from the particle, so that the fluid is at rest except in the vicinity of the colloid. With the aim of obtaining mean-field equations for a dilute suspension of active particles, we also assume that the concentration fields can have nonvanishing gradients on large spatial scales. Accordingly, the concentration gradients are taken to exist at large distances from the colloidal particle.
We suppose that the diffusiophoretic coefficients take the values and on the catalytic and noncatalytic hemispheres, respectively, while the surface rate constants per unit area take positive values on the catalytic hemisphere and vanish on the noncatalytic hemisphere, . Using spherical coordinates with polar angle defined with respect to the axis of the cylindrical symmetry of the Janus particle, we have where denotes the Heaviside function such that on hemisphere and is zero otherwise. The catalytic hemisphere is taken as , and the noncatalytic hemisphere as .
Solving equations (2)–(4) with the boundary conditions (5)–(7), the velocity and concentration fields can be obtained in the vicinity of the colloidal motor [45, 40, 41]. Accordingly, the force and the torque exerted by the fluid on the motor, as well as the overall reaction rate at its catalytic surface, are given by the following surface integrals at the fluid-colloid interface , where is the pressure tensor of the fluid. The fluctuating contributions from thermal noise can also be included [40, 41].
2.2. Coupled Langevin Equations for the Motor
The orientation of the Janus particle is described by the unit vector attached to the axis of the cylindrical symmetry of the Janus particle and pointing towards the catalytic hemisphere. Accordingly, the displacement and rotation of the particle are ruled by in terms of the translational and rotational velocities. These velocities, as well as the number of reactive events taking place on the particle, are governed by the following coupled Langevin equations [39, 40, 41]: where and denote the mass and inertia tensor of the motor, is the translational friction coefficient, the rotational friction coefficient, and the diffusiophoretic force and torque, and the external force and torque exerted on the particle, while and are the contributions to the force and torque due to thermal fluctuations. The overall net reaction rate is , is the reciprocal contribution of diffusiophoresis back onto the reaction rate, and is the fluctuating reaction rate. If the Janus particle has a magnetic dipole and is subjected to an external magnetic field , then the external torque would be given by . In the overdamped regime, the coupled Langevin equations are obtained by neglecting the inertial terms in equations (11) and (12).
Solving the Navier-Stokes equations (2) and (3) coupled to equation (4) for molecular concentrations with the boundary conditions (5)–(7), the force and the torque exerted on a spherical particle of radius in a fluid with shear viscosity and the overall net reaction rate are given by [40] expressed in terms of the surface average
The expressions (14) and (15) find their origin in the generalization of Faxén's theorem to a sphere moving in a time-dependent velocity field [55, 56]. When writing these equations, we have taken into account the possibility that the diffusiophoretic coefficients and the surface rate constants may be nonuniform on the particle surface.
2.3. Motion in Molecular Concentration Gradients
If molecular diffusion is fast enough so that the concentration fields adopt stationary profiles around the catalytic particle in the concentration gradients , the diffusiophoretic translational and rotational velocities can be written as follows (see Appendix A): where the parameters , , and are given in equations (A.35)–(A.40) in terms of the diffusiophoretic coefficients , the rate constants per unit area , the slip length , the molecular diffusivities , and the geometry of the Janus particle. The identity matrix is , while
The self-diffusiophoretic velocity, expressed in terms of the molecular concentrations extrapolated to the center of the particle, is since the parameters may be written in the forms and (see Appendix A, equations (A.33)-(A.34).
In the absence of a reaction, we recover the diffusiophoretic velocities given in Refs. [57, 58]:
Moreover, if the diffusiophoretic coefficients are the same on both hemispheres , the angular velocity is equal to zero, .
In the presence of a reaction, but without gradients (), we have and the linear velocity reduces to the contribution of self-diffusiophoresis, , characterizing the activity of the Janus particle.
The overall reaction rate can be written as follows: in terms of rate constants and a parameter given in equation (A.45). In the absence of the concentration gradients, we recover the expression obtained in Ref. [40]. In the presence of the concentration gradients , there is an extra contribution depending on the direction of the Janus particle. However, this last term is normally negligible because we typically have for micrometric particles and macroscopic gradients of molecular concentrations.
We note that both the self-diffusiophoretic velocity (21) and the leading term of the reaction rate (23) are proportional to each other. Their ratio defines the self-diffusiophoretic parameter which was introduced in Refs. [39, 40], where the last equality was obtained using .
3. Active Suspension of Colloidal Motors
3.1. Onsager's Reciprocal Relations
We now show that Onsager's principle of nonequilibrium thermodynamics [46–53] can be used to establish coupled diffusion-reaction equations of motion for active matter that are consistent with microreversibility. According to Onsager's principle, currents are related to thermodynamic forces (or affinities) by where the linear response coefficients satisfy the Onsager reciprocal relations, if the affinities are even under time reversal. The thermodynamic entropy production rate density is given by where is Boltzmann's constant.
3.2. Mean-Field Equations for the Active Suspension
The system we consider is a dilute solution containing the reactive molecular and species together with colloidal motors in an inert solvent . The motors are spherical Janus particles and, as described in Section 2, have hemispherical catalytic surfaces where the reaction takes place. Moreover, we suppose that the solution is globally at rest, so that the velocity field is equal to zero on scales larger than the size of colloids. The solution is described at the macroscale in terms of the molecular densities and , as well as the distribution function of the colloidal motors, , where is the position and is the unit vector giving the orientation of the Janus particles (expressed in spherical coordinates in the laboratory frame). The distribution function is defined as where are the positions and orientational unit vectors of the colloidal motors. For a dilute suspension, the evolution equation of this distribution function can be deduced from the Fokker-Planck equation for the probability that a single colloidal motor is located at the position with the orientation [39, 40, 41]. Once, this distribution function is known, we can obtain the successive moments of : where , is the density or concentration of colloidal motors, is the polar order parameter or polarization of the colloidal motors, and is the traceless order parameter analogous to that for apolar nematic liquid crystals expressed in terms of the tensor (20) and, thus, satisfies .
At the macroscale, the reaction is with the rate constants . For the colloidal suspension treated here, the reaction should be described by a reaction rate density that is proportional to the distribution function of colloidal motors and determined by the surface reaction taken into account with the boundary conditions (7) in Section 2.
The mean concentrations of molecular species are defined by , where is the volume fraction of the suspension. Their corresponding gradients are related to those considered in Section 2 by for a dilute enough suspension. The coupled diffusion-reaction equations for the different species take the following forms: where are the molecular current densities, is the total drift velocity obtained by adding the drift velocity due to the external force to the diffusiophoretic velocity (18) giving with the self-diffusiophoretic velocity (equation (21)) now expressed in terms of the mean concentrations , and the inverse temperature . In equation (34), is an effective translational diffusion coefficient related to the effective translational friction coefficient by Einstein's formula and is an effective rotational diffusion coefficient related to the effective rotational friction coefficient by . Since the shear viscosity increases as with the volume fraction of the suspension [26, 31], both friction coefficients and also increase, and the diffusion coefficients decrease. In particular, it is known that [31]. A similar dependence on the volume fraction is expected for the parameters , , , and given in Appendix A, since these parameters are proportional to the diffusiophoretic coefficients that are known to be inversely proportional to shear viscosity, [54, 57, 58]. The effects of this dependence would manifest themselves if the colloidal suspension became dense enough. Here, such effects are assumed to play a negligible role.
The Janus particles have a spherical shape so that their random rotational and translational motions are decoupled. In this case, the rotational diffusion operator is given by expressed in terms of the rotational energy associated with the torque exerted by an external magnetic field on some magnetic dipole of the particle [52] and that due to the diffusiophoretic effect, we have the following:
3.3. Translational and Rotational Current Densities
Before proceeding with nonequilibrium thermodynamics, we need to identify in equation (34) the current densities associated with the translational and rotational movements of the colloidal motors. The distribution function for colloidal Janus particles is defined in the five-dimensional space , where are the Cartesian coordinates for the position and the spherical coordinates for the orientation . Vector calculus is used in these coordinates to obtain the corresponding gradients and divergences [59].
For the rotational degrees of freedom we have
The scalar product between a pair of rotational vectors is given by , and the scalar product of such a vector with itself is denoted . In spherical coordinates, the rotational gradient and divergence are given, respectively, by [59]
In the five-dimensional space, the gradient is given by and the divergence of a five-dimensional vector, , is
Using these notations, equation (34) can be written in the form of a local conservation law involving the five-dimensional current density, , as with translational current density where is the translational potential energy due to the external force , rotational current density and their translational and rotational divergences, and , where is the operator (37).
3.4. Nonequilibrium Thermodynamics of the Active Suspension
Local thermodynamic equilibrium is assumed on scales larger than the size of the colloidal motors where the description by the mean-field equations (33) and (34) is valid and the fluid is at rest. According to this assumption, thermodynamic quantities can be locally expressed in the active suspension in terms of the molecular densities and the distribution function . Furthermore, we suppose that the system is isothermal and isobaric and the solution is dilute in the species , , and . The appropriate thermodynamic potential is thus Gibbs' free energy given by the following volume integral of the corresponding density: where the first term is the contribution from the solvent of density , the next terms from fuel and product dilutely dispersed in the solvent [52], and the last terms from all the orientations of the colloidal motors moving in the mechanical potential energies due to the external force and the external torque exerted by the magnetic field on the magnetic dipoles of the colloids. We can thus deduce the following chemical potentials:
Here, , where is the standard chemical potential of species and is the standard concentration. Since the solution is dilute, we have taken the solvent density to be essentially uniform in space and constant in time.
Next, we use the principles of nonequilibrium thermodynamics in order to express the current densities in terms of the affinities or thermodynamic forces given in Table 1. For the reaction (32), the affinity is given by and the corresponding current density is the rate density introduced in equation (33). At chemical equilibrium, we have , , and . In the linear regime close to equilibrium where , the chemical affinity (51) can be approximated as where is the diffusivity of the reaction taking place on the colloidal motors [39, 40]. For the diffusion processes of species , the affinity associated with the current density is given by in terms of the chemical potential . For molecular species, the gradient is tridimensional in Euclidian space, so that . For the colloid with chemical potential (50), the affinity is given by the five-dimensional gradient (42) as if the magnetic field is uniform. In this five-dimensional space, the associated current density given by equations (45) and (46) can thus be written in the following form: where is the identity matrix. In this form, we see that the first term is related to the reaction affinity since the self-diffusiophoretic velocity can be written as . The next two terms can be related to the affinities of molecular species, and the last term to the affinity of the colloidal species.
Process Current Affinity Dimension
Molecular diffusion of fuel
Molecular diffusion of product
Translational diffusion of colloids
Rotational diffusion of colloids
Current densities and corresponding affinities or thermodynamic forces in the active suspension: is the reaction rate density introduced in equation (33) corresponding to the affinity (51), and are the molecular current densities of fuel and product , is the translational current density of colloids given by equation (45), is the rotational current density of colloids given by equation (46). The translational and rotational current densities of colloids form the five-dimensional current density (55) according to . Similarly, the translational and rotational affinities of colloids form the five-dimensional affinity (54). denotes the inverse temperature, the chemical potentials, the gradient in Euclidean space, and the rotational gradient (40). We note that colloidal motors with the given orientation are considered as so many independent species in the free energy (47), which is expressed by equation (56).
According to the Curie principle, there is no coupling between processes with different tensorial characters. However, the Janus particles have a director given by the unit vector and we have adopted a description in terms of the distribution function for the Janus particles. Consequently, it is possible that a vectorial process such as diffusion may be coupled to a scalar process such as reaction if it is polarized by the unit vector . If we introduce the densities for Janus particles having their orientation in cells with a size of , along with the associated current densities, we may write a general coupling (25) of the following form: up to possible nonlinear contributions that may be required in order for the reaction rate to obey the mass-action law. In equation (57), we have that is , , , , , , , , and (for ).
According to Onsager's reciprocal relations (26), the linear response coefficients should obey for and where again denotes the transpose.
We assume that the molecular species and undergo Fickian diffusion without cross-diffusion, so that and that the reaction rate does not depend on the gradients or , whereupon
This last assumption consists in neglecting the terms with the coefficient in equation (23), which is usually justified as mentioned in Section 2.
The scalar coefficient associated with the reaction can be identified as and the linear response coefficients , , and in equation (57) can be determined using the current density (55), as described in Appendix B. As a consequence of Onsager's reciprocal relations, we can conclude that the reaction rate and the current densities should be given by
In equation (62), the second term describes the reciprocal effects of diffusiophoresis back onto reaction. The second term in equation (63) is due to cross-diffusion between the molecular and colloidal species due to diffusiophoresis. We see that the linear response coefficients depend on the unit vector in a manner similar to that already shown in Refs. [39, 40].
With respect to standard expressions, the terms involving the integral in equation (63) are required in order to satisfy Onsager's reciprocal relations and for these quantities to be compatible with microreversibility. However, these extra terms can be shown to be negligible, although the reciprocal terms are not negligible in equations (45) and (46). In order to show that the extra terms are negligible, we suppose that the self-diffusiophoretic and diffusiophoretic velocities take the typical value [60]. According to Ref. [58], the molecular gradients used in experiments of diffusiophoresis are of the order of , so that diffusiophoretic parameters have the value . Moreover, we have , but since , the effect of the coefficients is again of the same order of magnitude as and . Molecular diffusivities typically have the value , while the translational diffusion coefficient of a micrometric colloidal particle is of the order of . The molecular concentrations used in experiments on self-diffusiophoresis are about , while the density of micrometric colloidal particles is approximately , or lower. If we assume that the molecular and colloidal gradients take comparable values , the ratio between the extra term and the standard molecular diffusion term in equation (63) is given by which shows that the second term in equation (63) is negligible. Accordingly, the standard Fickian expressions are very well justified for the molecular current densities. In the presence of colloidal motors, the expressions compatible with microreversibility are nevertheless given by equations (62) and (63). In contrast, the terms associated with the diffusiophoretic parameters in the colloidal current density (55) have effects that are not negligible.
The conclusion from these considerations is that active matter can be described as generalized diffusion-reaction processes in complete compatibility with microreversibility and Onsager's reciprocal relations. In this way, the program of nonequilibrium thermodynamics is complete and application of equation (27) gives the following expression for the thermodynamic entropy production rate density:
The second law is satisfied if , , , and , which is expected.
The results derived in this section provide the basis for the analysis of collective effects in suspensions of active Janus particles. In Sections 4 and 5, we describe two collective phenomena that emerge from this theoretical framework: the effect of an external force and torque on the reaction rate, and a clustering instability.
4. Effect of External Force and Torque
Using a thermodynamic formulation that is consistent with microreversibility, we showed earlier [39–41, 61] how the application of an external force and torque on a single colloidal motor can change the reaction rate on its surface and even lead to a net production of fuel rather than product. Now we show how these considerations can be extended to a suspension of such motors.
4.1. Local Evolution Equations
We suppose that the colloidal motors are subjected to an external force and an external torque induced by an external magnetic field exerted on the magnetic moment of the colloidal particles, both oriented in the -direction. If is large enough, the distribution function is given by so that with . Moreover, the terms with the coefficients , , and are assumed to be negligible in equation (34). If the concentrations are uniform in the - and -directions, the process is ruled by obtained by integrating equation (34) over the orientation . This equation for is coupled to equation (33) with the Fickian molecular current densities and the local reaction rate given by equation (62), as predicted by Onsager's reciprocal relations.
4.2. Global Evolution Equations
Defining the mean value of the -coordinate for the colloidal motors as and using equation (67), we obtain the evolution equation, with mean reaction rate,
Furthermore, integrating equation (33) with over the position with the local rate (68), we get the total reaction rate where is the total number of colloidal motors in the suspension. Equations (70) and (72) have precisely the same structure as for a single colloidal motor. However, one should note that the mean reaction rate in equation (71) contains spatial correlations between the solute and colloid concentration fields. Given the structure of the equations, the results obtained in Refs. [39, 40] also apply here. In particular, there exists a regime where the entire ensemble of colloidal motors is propelled and carries out work against the external force by consuming fuel. In addition, there is also a regime where fuel is synthesized if the external force that opposes motion is sufficiently large to reverse the reaction . The efficiencies of these processes are given by the same expressions as in Refs. [39, 40].
5. Clustering Instability and Pattern Formation
The equations of motion developed in Section 3 that describe a dilute suspension of colloidal motors moving in a dilute solution of fuel and product molecular species will be shown in this section to lead to a clustering instability. This instability can be described by the mean-field equations obtained above for the concentrations of the molecular species and the distribution function of the colloidal motors in the absence of an external force and torque ( and ). A number of other mean-field descriptions that predict instabilities and the formation of various clustering states of collections of diffusiophoretic colloidal particles have appeared in literature [62, 18, 6, 19, 20], and use techniques involving coupled moment equations similar to those adopted in this section.
5.1. Molecular Diffusion and Reaction
The equation for the colloidal motors is coupled to the reaction-diffusion equations for the molecular species and , accounting for the fact that the reaction occurs both at the surface of the catalytic hemisphere of the colloids and in the bulk: where the total reaction rate density is given by
The system is driven out of equilibrium if [61].
5.2. Colloidal Density and Polarization
If the second moment (31) as well as higher moments are assumed to be negligible, the evolution equations for the density of colloidal motors (29) and the polarization (30) are given by in terms of the fourth-order tensor with the following components: .
If is large enough so that dominates the other terms involving in equation (76), we can neglect these other terms and this equation can be inverted to obtain under which circumstances the field is driven by the gradients of the colloid and species densities. Substituting this result into equation (75) for the density of colloidal particles, we find with the effective diffusion coefficient expressing the enhancement of diffusivity due to the self-diffusiophoretic activity [17].
5.3. Coupled Colloidal and Molecular Diffusion-Reaction Equations
In the following, we suppose that the diffusion coefficient is the same for both molecular species: . Consequently, remains uniform during the time evolution if initially so. Therefore, is known and only needs to be determined. Introducing the notations we have the following coupled equations describing the system: with
Moreover, consistency with the existence of equilibrium requires that is equal to the diffusiophoretic parameter (24) that is the ratio between the self-diffusiophoretic velocity (21) and the leading term of the overall reaction rate (23).
For this system, there exists a uniform nonequilibrium steady state, where keeps its initial uniform value and the molecular density is also uniform at the value in order to satisfy the stationary condition . For this molecular concentration , we notice that the rate of the catalytic reaction on the colloids is not vanishing under the nonequilibrium condition .
5.4. Pattern Formation
To analyze the stability of this homogeneous steady state, for simplicity we consider a one-dimensional system where the fields and only depend on the variable . Accordingly, the gradients can be replaced by partial derivatives in equations (81) and (83). The set of equations (81)–(84) is then numerically integrated by spatial discretization over the grid with with and . The integration is performed with a Runge-Kutta algorithm of varying order 4-5 over a long enough time interval to reach a steady state. Figure 2 shows numerical results for the parameter values: and increasing values of . We observe the formation of clusters of colloidal motors in regions where the fuel is depleted, as expected.
Nonequilibrium steady state of the one-dimensional system for the parameter values (87): (a) with ; (b) with .
5.5. Linear Analysis of the Clustering Instability
The threshold of this clustering instability can be found from a linear stability analysis. Linearizing the equations around the uniform steady state, we find that the perturbations obey with
Supposing that the perturbations behave as , we obtain the dispersion relations
These dispersion relations are depicted in Figures 3(a)–3(c), respectively, below, at, and beyond the threshold. The leading dispersion relation is associated with the conserved unstable mode of the colloidal motors because . The subleading dispersion relation is associated with the reactive mode of the molecular species because . We notice that, since , there is no possibility for a Hopf bifurcation to uniform oscillatory behavior, which would be the case if the eigenvalues were complex. We also note that there is no wavelength selection at the level of linear stability analysis in this clustering instability.
Dispersion relations of linear stability analysis for , , and , respectively, below, at, and beyond the threshold of clustering instability. The dispersion relations are obtained in (a)–(c) with the approximation (90), and in (d)–(f) by truncating equation (C.5) into a matrix. The other parameter values are given in equation (87) and .
Therefore, instability manifests itself if and the threshold is given by the condition which leads to the value for the parameter values (87).
The dispersion relations can also be obtained from the evolution equation (34) for the distribution function. Supposing that and , we have where with . Equation (93) is coupled to the diffusion-reaction equation (81) for the concentration field with .
The linear stability analysis can be carried out for equation (93) coupled to equation (81) with the rate (82) in a similar manner to that for equations (81)–(84). This analysis is presented in Appendix C. The dispersion relations can be computed by truncating the infinite matrix (C.5) in order to obtain the eigenvalues as a function of the wave number . The result converges to the dispersion relations shown in Figures 3(d)–3(f) below, at, and beyond the threshold, for the parameter values (87) and . The convergence occurs faster for the leading dispersion relation than for the subleading ones. For the chosen parameter values, we can see that the approximation where we suppose that the vector field is driven by the gradients (which corresponds to truncating to a matrix) constitutes a good approximation to describe the instability. Indeed, the leading dispersion relation of Figure 3(b) is already very close to that in Figure 3(e).
The conclusion is that equations (81)–(84) provide a robust description of the clustering instability and of the emerging patterns.
Autonomous motion is not possible at equilibrium and active matter relies on the presence of nonequilibrium constraints to drive the system out of equilibrium. As a result the theoretical formulations provided by nonequilibrium thermodynamics and statistical mechanics are a natural starting point for the description of such systems.
Many of the active matter systems currently under study involve active agents such as molecular machines or self-propelled colloidal particles with linear dimensions ranging from tens of nanometers to micrometers. The transition from microscopic to macroscopic description for fluids containing active agents of such sizes takes place in the upper range of this scale. Suspensions of active colloidal particles are interesting in this connection since, as described earlier in this paper, the colloidal particles are large compared to the molecules of the medium in which they reside. The dynamics of the suspension can then be described by considering the equations for the positions, velocities, and orientations of the colloidal particles in the medium, or through field equations that describe the densities of these particles.
Nonequilibrium thermodynamics provides a set of principles that these systems must obey. Most important among these is microreversibility that stems from the basic time reversal character of the microscopic dynamics. On the macroscale, this principle manifests itself in Onsager's reciprocal relations that govern what dynamical processes are coupled and how they are described. For example, for single Janus particles propelled by a self-diffusiophoretic mechanism, microreversibility implies the existence of reciprocal effect where the reaction rate depends on an applied external force [39–41, 61].
This paper extended the nonequilibrium thermodynamics formulation to the collective dynamics of ensembles of diffusiophoretic Janus colloids. In particular, we considered Janus colloids driven by both self-diffusiophoresis arising from reactions on the motor catalytic surface as well as motion arising from an external concentration gradient. This latter contribution is essential for the extension of the theory to collective motor dynamics. The resulting formulation is consistent with microreversibility and an expression for the entropy production is provided. From this general formulation of collective dynamics, one can show that if an external force and torque are applied to the system, the overall reaction rate depends on the applied force. In addition, a stability analysis of the equations governing the collective behavior predicts the existence of a clustering instability seen in many experiments of Janus colloids. Such considerations can be extended to ensembles of thermophoretic Janus colloids [63].
A. Force and Torque on a Colloidal Motor
A.1. Stationary Molecular Concentration Fields. We suppose that molecular diffusivity is large enough so that the concentration fields adopt a quasistationary profile in the vicinity of every Janus particle. Accordingly, the concentration fields should obey the following equations: for the two reacting species , where is the concentration gradient of species at large distances from the center of the catalytic particle. In Ref. [40], we considered the special case where , so that the concentration fields are uniform at large distances. The upper hemisphere is catalytic, while the lower one is noncatalytic. The axis of the Janus particle is oriented from the noncatalytic towards the catalytic hemisphere and taken along the -axis in the frame of the particle.
We introduce the fields in terms of the characteristic length of the reaction
The fields and have the units of , and the concentration fields are recovered from them by
Similar expressions hold for the concentration gradients at large distances: , , , and .
The fields (A.2) and (A.3) obey the equations where is the Heaviside function of the catalytic hemisphere.
The solution of the equations for is given by which obeys reflective boundary conditions on the sphere and represents a gradient at large distances. Defining to be the dimensionless Damköhler number of the reaction on the spherical catalytic particle, the field can be decomposed as in terms of a field similar to equation (A.8) and another field obeying
In the equations above, the concentrations may be considered as their extrapolations to the center of the Janus particle or the mean concentrations at that position in a dilute suspension of Janus particles. Similarly, may also be considered as the mean gradients of concentrations at the location of the Janus particle in a dilute suspension.
A.2. Calculation of the Diffusiophoretic Velocities. The diffusiophoretic force (14) and torque (15) are thus given by the following expressions: <


The above examination for Pharmacist apprentices who have completed two years of apprenticeship under Section 56 (1)(a) of the Medical Ordinance will be held on October 14, 2017. Only apprentices who have completed two years apprenticeship on August 21, 2017 are eligible to apply for this examination. Those who do not achieve a satisfactory standard acceptable to the Ceylon Medical College Council at the written examination will not be called for the practical and viva voice examinations.
The fee of Rs. 5,000/ = should be paid at any Branch of People's Bank to the credit of Town Hall People's Bank Branch A/C No. 167-1001-1317-0313, and the receipt should reach me on or before August 11, 2017 with this application. (Name of the applicant should be written on the top left-hand corner of the receipt). No refund of fees will be made under any circumstances. Applications by post should be posted on or before Tuesday August 8, 2017.
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(Update) COD Mobile to finally get Night Mode in Season 12
February 2, 2021 November 8, 2020 by Vivek Singh
(September 16) – It has been around a fortnight since the latest season update of Call of Duty Mobile released, bringing in the brand new content update. This time, season 10, dropped new maps – Terminal and Pine, new multiplayer game-modes – Headquarters and Hardcore, and four new operators. Pretty interesting!
Well, as mentioned in our previous post, Call of Duty Mobile Season 11 will be arriving around mid-October. Frankly, waiting for this long will not be easy, but it is what it is. If you are interested in following the latest leads on the Call of Duty Mobile Season 11 update, you can visit the link mentioned below.
MUST-READ: Call of Duty Mobile Season 12 Battle Pass Character
Season 11 is going to be the biggest ever update in Call of Duty Mobile. Activision has, kind of, confirmed officially that the upcoming seasonal update would be full of surprises. After all, the franchise will be celebrating the first anniversary of CODM, which was released back on October 1, 2019.
Well, it's evident that the new update is not arriving on October 1. In our recent post, we mentioned the release date of CODM season 11 with some more details; check out the post here.
Talking about the upcoming content in the new season. It looks the Night Mode feature is in the works and will be releasing in next season. Recently, the social media account of Garena Call of Duty Mobile posted a video in which the background can be seen switched to dark mode or night mode. This gave a little indication about the upcoming night mode.
Well, this was not enough, and as we mentioned in our Call of Duty Mobile Season 11 post, the official account of Call of Duty Mobile confirmed while replying to a user that Night Mode is in the pipeline. But, no official announcement has been made yet.
This isn't hard at all for the developers to bring a Night Mode to the BR mode. We have seen Tencent introducing the feature for PUBG Mobile. That's why it is possible that the developers may introduce Night Mode to CODM's BR. How are the developers going to implement this feature? Well, we will see.
Fans have been asking if there is a Night Mode feature planned for the multiplayer maps too. Well, to be honest, there are no official details on the same. And Activision's official reply to the comment does not confirm the arrival of Night Mode in MP mode.
Modern Warfare Night Map; Source: Activision
Some theories suggest that the Night Mode feature in MP will be inspired by Modern Warfare's Night Maps. Infinity Ward gathered a lot of appreciation from critics, especially for the Night Mode. The mode sports features like Night Vision goggles, tactical laser, for real-life graphics experience.
MUST-READ: Call of Duty: Warzone Mobile Release Date, Official Details
Well, Modern Warfare set a benchmark in FPS games, and Night Mode was another cherry on the cake. But, unfortunately, it pleased just a small portion of the MW players. The reasons were simple; the MW's Night Mode was tough to play, as one needs to put more focus and attention in the mm. This is the reason why SBMM (Skill based matchmaking) is not popular among players, as it decreases the chance of having casual matchmaking with not-so-good-in-games friends.
Source: Activision
To conclude this, we will only say that there are still chances that Activision may introduce night maps in CODM, but do not expect the Night Mode anything like that of Modern Warfare. Also, BR in CODM will surely get the features if the developers do not change their plans.
(Update – November 8)
Call of Duty Mobile Season 12 is around the corner and now it looks like the rumors of the arrival of Night Mode and Night Maps wasn't a hoax. It's almost official now, Activision will be bringing Night mode/ Night Maps to Call of Duty Mobile with the new season update.
Below, you can check out the official teaser poster of the upcoming Season 12 seasonal update. The new season is named "Going Dark" is a very clear indication of the arrival of Night Mode. Rumors were true.
On top of this, the teaser video also confirmed the arrival of the new skin-variant of Captain Price and Ghost. CODM Garena posted different images of the upcoming character skins – VELIKAN MEGALITH and Urban Tracker – By the Night, in the new season 12.
Follow us on Twitter & join our Telegram channel for more post-updates.
Vivek has been a fan of the COD franchise since forever. Perfection is his forte and the same can be seen in his work. He loves to invest his time in creating awesome content on YouTube and discovering the latest games.
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J. Morton "Mort" Dunn
J. Morton (Mort) Dunn, beloved widower of Sylvia G. Dunn, of West Hartford, died on November 10, 2020 at age 94, from complications from a stroke. He was born in Hartford the son of John T. Dunn, Jr. and Norma (Mairson) Dunn, and resided in West Hartford his entire life. He attended Kingswood School, and was a graduate of Phillips Academy, Andover, MA, where he played varsity baseball and soccer. In his later years he became the class agent for the Andover Class of 1944. He was commissioned a Second Lieutenant in the Infantry in World War II and served in Korea in the army of occupation. He returned to Harvard, where he met the love of his life, Sylvia Guild, whom he married in 1949. They remained married until Sylvia died after 66 years of marriage. At Harvard he was a member of the Speakers Club and the Hasty Pudding Club and played varsity soccer and varsity baseball. One of the highlights of his athletic career was playing against Navy in 1949, a game which Harvard won at Annapolis 6-5 in 17innings. The game is considered the longest in Collegiate Baseball, in which both pitchers pitched the entire 17 innings, and in which the game did not end in a tie. He was a Captain in the 76th Division, Army Reserve. Upon graduation from Harvard, he became associated with his father, John T. Dunn, Jr's. Real Estate and Insurance Agency until he graduated from the University Of Connecticut School Of Law in 1955, and was admitted to the practice of law in 1955. He was a sole practitioner, a member of the Hartford County and State of Connecticut Bar Associations and practiced law for 48 years until he retired in 2003. Among many interesting legal matters with which Mort dealt, was the well publicized Hope Baxter Probate Case which ended with the State of Connecticut becoming involved. An oddity was the fact that the three attorneys representing different interests and the Probate Judge assigned to hear the case, all served together as 2nd Lieutenants in the 76th Infantry Division. Mort enjoyed poetry and took delight in writing verses for various occasions for family and friends. He won several poetry contests. He was a past President and Board member for many years of The World Series Club Of Hartford County. He was a past President of The McAuley Resident's Association. Mort was a 75 year member of the Universalist Church of West Hartford and served in many capacities over the years. In 2007 he was awarded the church's Distinguished Service Award. He coached youth baseball in West Hartford for twenty years, the last ten as coach of the West Hartford American Legion Baseball Team. He was a member for more than 50 years of the Hayes-Velhage American Legion Post 96 of West Hartford. He was a lifetime member of the Harvard-Radcliffe Club of Northern Connecticut, a past member of the University Club of Hartford and a member of the Varsity Club of Harvard. He was a member of the Old Guard of West Hartford and greatly enjoyed the fellowship and activities of this fine organization. Mort was an avid fan of the Brooklyn Dodgers and followed them in spirit when they moved to Los Angeles. Mort had a love of Cape Cod, where he spent many summers at Camp Monomoy, a boy's camp, as a camper and a counselor and in later years at their summer home in Harwich and then Brewster with Sylvia, his wife, of 66 plus years. Besides his wife, he leaves three children: Dianne C. Dunn, of Louisville, KY; Jeffrey D. Dunn, and his wife, Karen (Denuzze) Dunn of Boston, MA and their two children, Christopher and Robert; Andrew M. Dunn and his wife, Elizabeth (Drew) Dunn of Avon and their two children, John and his wife Marissa (Grassi) and Carolyn. He was a devoted husband, father and grandfather, who cared deeply for his family and friends. A memorial service will be celebrated at The McAuley Retirement Home, 275 Steele Rd., West Hartford at a future date. Burial will be private. In lieu of flowers, the family requests that memorial contributions be made in Mort's memory to the McAuley Resident's Assistance Fund, 275 Steele Rd., West Hartford, CT 06117. The Molloy Funeral Home, 906 Farmington Ave, West Hartford is in charge of the funeral arrangements.
J. Morton (Mort) Dunn, beloved widower of Sylvia G. Dunn, of West Hartford, died on November 10, 2020 at age 94, from complications from a stroke. He was born in Hartford the son of John T. Dunn, Jr. and Norma (Mairson) Dunn, and resided in... View Obituary & Service Information
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To fill this aching void?
Or movie stars in tabloid?
You know you're rich with the strangest treasure?
Come on, come on, what's holding you back?
Kiss the ones you meet for kismet?
Right now is your past, present and future . . .