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# Publishing remote network access with Network Connector

Published: January 11, 2010

Updated: February 15, 2013

Applies To: Unified Access Gateway

Some of the Forefront Unified Access Gateway 2010 SP3 features discussed in this article may be deprecated and may be removed in subsequent releases. For a complete list of deprecated features, see Features Deprecated in Forefront UAG SP3.

Using Forefront Unified Access Gateway (UAG), you provide remote client VPN access to the internal corporate network by publishing the SSL Network Tunneling application. Before publishing the SSL Network Tunneling Application, you must set up the VPN client network using either Secure Sockets Tunneling Protocol (SSTP), or the legacy proprietary Forefront UAG Network Connector.

This topic describes the steps required to configure remote client access with Network Connector, as follows:

1. Configuring network adapter settings─Configure the adapter that the Network Connector server should use.

2. Modifying the default listener─By default, Network Connector listens for remote VPN client requests on TCP port 6003. You can modify the default listener (protocol and port combination), if required.

3. Assigning IP addresses to VPN clients─Assign IP addresses to remote VPN clients from a static address pool. DHCP address allocation is not supported.

4. Adding a Forefront TMG access rule─Configure a Forefront TMG access rule in order to assign IP addresses.

5. Configuring Internet access─Define how VPN clients connected to the corporate network access the Internet. You can route Internet requests through the client's original Internet connection, or through the corporate network gateway. Alternatively, you can specify that VPN clients cannot access the Internet.

6. Adding additional networks─You can define up to 200 additional network destinations that are available to VPN clients connecting with Network Connector. This is useful if your corporate network has multiple subnets, and if you want to allow VPN client access to additional subnets.

7. Logging extended Network Connector traffic─By default, IP addresses allocated to VPN clients connecting to Forefront UAG Network Connector are logged. Logged information includes the user name and domain (in the format DOMAIN\username), and the IP address allocated from the pool. If required, you can enable extended logging for Network Connector traffic. Extended logging should only be enabled when troubleshooting because it creates large, accumulative dump files. These files are not deleted automatically and may reduce the server performance. Note that dump files can be written, read, and deleted, while there are active sessions to the Network Connector application.

## Configuring network adapter settings

#### To configure network adapter settings for the Network Connector server

1. In the Forefront UAG Management console, on the Admin menu, click Remote Network Access, and then click SSL Network Tunneling.

2. On the SSL Network Tunneling Server dialog box, on the Network Segment tab, in the Complementary Data area, you can specify alternative network settings. Select Only if Network Configuration is Missing to specify that the remote VPN client should use the settings specified in the Network Connection area. Alternative settings should be used only if no data is configured for the same item in Network Connection.

3. In the Complementary Data area, select Always, Overriding Existing Network Configuration of This Server to specify that the data in Complementary Data is always used, regardless of the configuration of the selected connection. This setting is useful for connecting clients, if you want to use a different Domain Name System (DNS), Windows Internet Name Service, or default gateway. Fields that are left empty are ignored.

4. At the bottom left corner of the SSL Network Tunneling Server dialog box, select the Activate SSL Network Tunneling check box. Clearing this check box disables an active Network Connector.

5. After you have completed the configuration of the server, click OK on the SSL Network Tunneling Server dialog box to activate the Network Connector.

6. In the Forefront UAG Management console, click the Activate configuration icon to save and activate the configuration, and then on the Activate Configuration dialog box, click Activate. The configuration settings you have defined are applied to the Network Connector server. The Microsoft Forefront UAG SSL Network Tunneling Client, and the Microsoft Forefront UAG SSL Network Tunneling Server services are started, and set to automatic startup mode.

Note:
A dedicated network icon in the Windows notification area indicates to endpoints that the Network Connector Server service has started.

Leaving empty one or more of the fields in the Network Connection and Complementary Data areas, might result in a limited client session. For example, if no DNS is defined, no DNS services will be available for remote VPN users connecting with Network Connector.

It is recommended that you do not modify the name of the network adapter associated with the Network Connector. If you do change the name, and the adapter is disabled and then enabled, the Network Connector server may not start as expected.

## Modifying the default listener

#### To modify the default listener

1. In the Forefront UAG Management console, on the Admin menu, click Remote Network Access, and then click SSL Network Tunneling.

2. On the SSL Network Tunneling Server dialog box, click the Advanced tab.

3. In the Listener area, in the Type list, select the protocol, and then in the Port box, specify the port.

## Assigning IP addresses to VPN clients

#### To assign IP addresses to VPN clients

1. In the Forefront UAG Management console, on the Admin menu, click Remote Network Access, and then click SSL Network Tunneling.

2. On the SSL Network Tunneling Server dialog box, click the IP Provisioning tab.

3. In the Pool Type area, do one of the following:

• Click Corporate IP Addresses, to specify that IP addresses that belong to the IP address range configured on the Network Segment tab should be assigned to remote VPN clients. Ensure that you exclude the specified range from your internal Dynamic Host Configuration Protocol (DHCP) server. Forefront UAG cannot use a DHCP server to assign IP addresses to remote VPN clients.

• Click Private IP Addresses, to specify that IP addresses that do not belong to the IP address ranges specified on the Network Segment tab should be assigned to remote VPN clients. For example, if the corporate segment is configured to 192.168.0.0/255.255.248.0, an example of a "corporate pool" would be 192.168.6.2-192.168.6.200, and an example of a "private pool" would be 10.16.16.2-10.16.16.200.

4. In the Address Pool area, define IP address ranges that can be assigned to remote clients. You can enter up to 10 ranges of IP addresses. All the defined addresses must use the same subnet mask. Do not define IP addresses that are configured on the internal network adapter, or a private IP address range. The subnet for the IP ranges you defined is displayed in Pool Subnet.

5. At the bottom left corner of the SSL Network Tunneling Server dialog box, select the Activate SSL Network Tunneling check box. Clearing this check box disables an active Network Connector.

6. After you have completed the configuration of the server, on the SSL Network Tunneling Server dialog box, click OK to activate Network Connector.

7. In the Forefront UAG Management console, click the Activate configuration icon to save and activate the configuration, and then on the Activate Configuration dialog box, click Activate. The configuration settings you have defined are applied to the Network Connector server. The Network Connector Windows service (Network Connector Server) is started and is set to automatic startup mode.

## Adding a Forefront TMG access rule

#### To add a Forefront TMG access rule

1. In the Forefront TMG Management console, click to expand Forefront TMG (server_name).

2. In the tree, click the Firewall Policy node.

3. On the Tasks tab, click Create Access Rule.

4. On the Welcome page of the New Access Rule Wizard, type a name for the rule, and then click Next.

5. On the Rule Action page, select Allow.

6. On the Protocols page, in the This rule applies to list, select All Outbound Traffic.

7. On the Malware Inspection page, select Do not enable malware inspection for this rule.

8. On the Access Rule Sources page, click Add.

9. On the Add Network Entities dialog box, click the New menu, and then click Address Range.

10. On the New Address Range Rule Element dialog box, specify the Start Address and End Address of the IP address pool. Then click OK.

11. On the Add Network Entities dialog box, click Close. In the Access Rule Sources page, click Next.

12. On the Access Rule Destinations page, click Add.

13. On the Add Network Entities dialog box, click the New Menu, and then click to expand Network. Select Internal, and then click Add. Click Close to close the Add Network Entities dialog box.

14. On the Access Rule Destinations page, click Next.

15. On the User Sets page, leave the default settings to allow access to all users. Alternatively, click Add to limit access to the VPN client user group only. Then click Next.

16. On the final page of the wizard, click Finish

Note:
Forefront UAG assigns the first IP address from the defined pool to the SSL Network Tunneling server.

Ensure that the defined IP address pool is sufficient for your needs, and contains enough IP addresses for remote VPN clients. Note that IP addresses that end with zero, or 255, are not used for IP assignment. The last address in each mathematical subnet is allocated for system use. For example if a pool consists of addresses 192.168.0.0-192.168.0.15, the addresses 192.168.0.0, 192.168.0.1 and 192.168.0.15 will be unavailable for use. If a pool consists of IP addresses 192.168.0.1-192.168.0.10, addresses 192.168.0.1, 192.168.0.7 and 192.168.0.9 will be unavailable leaving 7 IP addresses available for client use.

If the IP address pool is a corporate pool, make sure you exclude the IP address range you define here from your organization's DHCP server, to avoid IP address conflict with Network Connector clients. IP address conflicts between corporate computers and endpoint computers will result in idle sessions, in which remote clients launch the Network Connector application with no errors, but have no access to the Network Connector server, or to the resources that should be enabled via the server.

When a domain client logs in using an IP address allocated from the pool, an A record for the address is created on the internal network DNS server. A new address may be allocated each time the client connects, which may result in clients having multiple A records on the DNS server.

## Configuring Internet access

#### To configure Internet access

1. In the Forefront UAG Management console, on the Admin menu, click Remote Network Access, and then click SSL Network Tunneling.

2. On the SSL Network Tunneling Server dialog box, click the Access Control tab.

3. In the Internet Access area, select one of the following:

• Click Split Tunneling (Route Internet Traffic Through Original Client Connection), to specify that remote VPN clients should access the Internet through the Internet connection configured on the client endpoint.

• Click Non-Split Tunneling (Route Internet Traffic Through the Corporate Gateway), to specify that remote VPN clients should access the Internet through the corporate Internet gateway. Select the Disable Local Area Network Access check box, to specify that client endpoints connected to Network Connector cannot access the local network on the client endpoint (for example a home network). Note that when you select non-split tunneling, the settings on the Additional Networks tab do not apply, because all network traffic passes through the Network Connector tunnel. In this mode, if the client endpoint session ends unexpectedly, users are prompted to reenable their Internet connection.

• Click No Internet Access, to specify that remote VPN clients cannot access the Internet. In this mode, client endpoints can only access networks defined in the Network Segment and Additional Networks tabs. Select the Disable Local Area Network Access check box, to specify that client endpoints connected to Network Connector cannot access the local network on the client endpoint (for example, a home network).

4. In the IP Spoofing Policy area, select the Disable Spoofed Traffic check box, to specify that the Network Connector server should check and validate the source IP address of each packet arriving at the server, and tunnel traffic only from connected Network Connector clients. Clear this setting to specify that other types of traffic should be tunneled.

5. In the Protocol Blockers area, select any protocols that should be blocked. When a setting is enabled, all traffic using the protocol is blocked.

1. In the Forefront UAG Management console, on the Admin menu, click Remote Network Access, and then click SSL Network Tunneling.

2. On the SSL Network Tunneling Server dialog box, click the Additional Networks tab.

3. Select the Enable Access to the Following Additional Networks check box, and then click Add.

4. In the Add Network dialog box, specify the IP addresses and mask for the network. Ensure that the IP address and mask are valid and do not overlap with other defined networks.

5. Specify how IP address conflicts should be handled by selecting one of the following:

• If you want to specify that if there is a conflict, and that the connection attempt will fail and the VPN remote client will not be connected to Network Connector, select Fail.

• If you want to specify that the client endpoint can choose whether to fail the attempted connection or skip the conflicting network and connect to other networks using Network Connector, select Prompt.

• If you want to specify that the conflicting network connection is skipped and that the client endpoint should connect to other non-conflicting networks using Network Connector, select Skip.

6. Repeat the steps for each additional network you want to define.

Note:
Settings on the Additional Networks tab are not used if the Internet access level defined on the Access Control tab is set to Non-Split Tunneling. In this mode, all network traffic is tunneled over the network connector VPN connection.

When the Internet access levels defined on the Access Control tab are set to Split Tunneling or No Internet Access, the corporate network must be defined as an additional network. Otherwise, remote VPN clients can access only VPN clients and not the corporate network.

## Logging extended Network Connector traffic

#### To log extended Network Connector traffic

1. On the computer on which the Network Connector server is installed, access the following registry key:

HKEY_LOCAL_MACHINE\SOFTWARE\WhaleCom\e-Gap\RemoteAccess

2. Create the following new registry key: NetworkConnector.

3. Under the key you created in step 2, create a DWORD value named log\sniff. Do one of the following:

• To enable logging of low-level network traffic to and from remote clients, set the DWORD value to 1.

• To enable logging of tunneled network traffic to and from remote clients, set the value to 2.

• To enable logging of both low-level and tunneled network traffic to and from remote clients, set the value to 3.

4. When you have finished troubleshooting, to disable logging, set the log\sniff value to 0.

5. After configuring the registry, on the Advanced tab of the SSL Network Tunneling Server dialog box, do the following:

1. In the Log Level box, specify the level of log detail required for Network Connector traffic. You can specify a level between 1 and 5, where 5 is the most detailed. It is recommended that you log Network Connector traffic when troubleshooting, and then set the value to 0 to disable logging when troubleshooting is complete.

2. In Log Path, specify one of the following locations:

• To specify that the log file is created in the same folder in which the server executable resides, select Server Executable Path. Usually this is in the following location:

\Microsoft Forefront Unified Access Gateway\common\big\whlios.log

• To specify a custom location, select Alternative Path, and then type the folder path.

Note:
The dump files are written in TCPDUMP format.

The low-level and tunneled traffic dumps consist of similar information but are not necessarily the same, because not all low-level traffic is tunneled and vice versa.

The log\sniff registry value is polled by the server executable while running, so it may be updated while the Network Connector is in session.

The dump files are created in the same location in which the log files are created, with the following file names:

• Low-level network traffic: <log_file_name>.lowlevel.dmp

• Tunneled network traffic: <log_file_name>.tunneldmp

Show:


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# changing background color of a letter template

I found the tuletter class in Overleaf (which loads the article class) and I've been using it for typing letters of correspondence. Now, I want to change the background color of the letter from the default white to another color, say yellow.

To do this, I use \pagecolor{yellow} from the xcolor package. However, the header text/elements can't be seen if this is done (see image below).

I've also used the following code from an answer but the same thing happens as when \pagecolor{yellow} is used.:

\usepackage{ocg-p,tikz,eso-pic} \AddToShipoutPictureBG {\begin{ocg}[printocg=never]{backgroundcolor}{oc1}{1} \tikz[overlay,remember picture]\fill[red](current page.north east)rectangle (current page.south west); \end{ocg}}

My question is how does one change the background color of a letter (preferably tuletter class) such that the header elements can be seen?

EDIT: Here is the MWE of the main texfile tuletter_en.tex (coming from the Overleaf template) and which I edit on Overleaf:

\documentclass[en]{tuletter}
% this package is only needed for demo (\lipsum)
\usepackage{lipsum}
\usepackage{times} %Times New Roman Font

\usepackage{xcolor}

% Signature at the end of the letter are used with \closing
\signname{J. Doe}
\signimage{signature_jdoe} % pjansen is the filename of the image of the signature (i.e. 'pjansen.png')
% if needed a second signature can be given with \signnamesec and \signimagesec

% Reference top left
\date{\today}
\ourref{UP001}
\yourref{IP1001}
\contact{Contact Person}
\phone{015-278 0000}
\email{c.person@tudelft.nl}
\subject{TU Delft Formal Letter}

% Recipient left under reference
\toname{R.E. Ceiver}
\toaddress{Here and there 22\\4242 AA Hurdieburdie}

% Sender right under logo
\fromname{Faculty of \ldots}
\frompobox{504\\2600 AA Delft}

\begin{document}
\pagecolor{yellow}
% show two paragraphs of text
\lipsum[1-2]
\closing{With kind regards,}
\end{document}

Here is the output of the MWE:

I've tried looking at tuletter.cls but my limited TeX/LaTeX knowledge can't seem to grok it.

• You have to provide a complete MWE. I changed page colour to yellow for one of my documents, and headers and footers showed up just fine. – Sveinung Oct 1 '19 at 8:24
• This worked: \documentclass{scrlttr2} \usepackage{xcolor} \pagecolor{lightgray} – Erwann Oct 3 '19 at 6:12

\RequirePackage[absolute,overlay]{textpos}

format: plain


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# Factors of 625

If it's not what You are looking for type in the field below your own integer, and You will get the solution.

Factors of 625:

By prime factorization of 625 we follow 5 simple steps:
1. We write number 625 above a 2-column table
2. We divide 625 by the smallest possible prime factor
3. We write down on the left side of the table the prime factor and next number to factorize on the ride side
4. We continue to factor in this fashion (we deal with odd numbers by trying small prime factors)
5. We continue until we reach 1 on the ride side of the table

 625 prime factors number to factorize 5 125 5 25 5 5 5 1

Factors of 625 = 1×5×5×5×5= $1 × 5^4$

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# Integral related to the modified Bessel function

I would like to solve the integral $$F_n(\kappa,\theta,\phi)=\int_{-\pi}^{\pi}{\rm e}^{\kappa\cos(x-\theta)}\cos(n\, x-\phi)\,{\rm d}x$$ that appears related to the identity $$I_n(\kappa)=\frac{1}{\pi}\int_{0}^{\pi}{\rm e}^{\kappa\cos(x)}\cos(n\, x)\,{\rm d}x,$$ where $I_n(\kappa)$ is the Modified Bessel Function of the first kind. Any ideas?

-
After elementary trig manipulations it seems that the problem could be solved if the integral $$\int_{-\pi}^{\pi}e^{\kappa \cos(x)}\sin(n\, x){\rm d} x$$ was known. – Arrigo Benedetti Sep 13 '12 at 0:52
And this integral is zero so I think the problem is solved... – Arrigo Benedetti Sep 13 '12 at 1:14
Why is the integral zero for any $\kappa$ and $n$? – marty cohen Sep 13 '12 at 1:25

Assume $n$ is a non-negative integer. Then the integrand is periodic with period $2\pi$. Then: $$F_n= \int_{-\pi}^\pi \exp\left( \kappa \cos(x-\theta) \right) \cos(n x - \phi) \mathrm{d}x = \int_{-\theta-\pi}^{-\theta+\pi} \exp\left( \kappa \cos(x) \right) \cos(n x + n \theta- \phi) \mathrm{d}x$$ The latter integral, using periodicity can be reduced to pieces of $(-\pi, \pi)$ interval, which can be rearranged, so that $$\int_{-\pi}^\pi \exp\left( \kappa \cos(x-\theta) \right) \cos(n x - \phi) \mathrm{d}x = \int_{-\pi}^{+\pi} \exp\left( \kappa \cos(x) \right) \cos(n x + n \theta- \phi) \mathrm{d}x$$ Denote $\varphi = n\theta - \phi$, and use $\cos(n x + \varphi) = \cos(n x) \cos(\varphi) - \sin(n x) \sin(\varphi)$ to write: $$\begin{eqnarray} F_n &=& \cos(\varphi) \int_{-\pi}^{\pi} \exp\left( \kappa \cos(x) \right) \cos(n x) \mathcal{d} x - \sin(\varphi) \int_{-\pi}^{\pi} \exp\left( \kappa \cos(x) \right) \sin(n x) \mathcal{d} x \\ &=& 2 \pi \cos(\varphi) I_n(\kappa) - \sin(\varphi) \cdot 0 \end{eqnarray}$$ The last integral is zero as integral of an odd function $\sin(n x) \exp(\kappa \cos(x))$ over a symmetric domain. Thus: $$F_n(\kappa, \theta, \theta) = 2 \pi \cos(n \theta - \phi) I_n(\kappa)$$
Alternatively, we could establish that $F_n$ satisfies ODE in $\kappa$. $$\begin{eqnarray} \kappa^2 \partial_\kappa^2 F_n + \kappa \partial_\kappa F_n &=& \int_{-\pi}^\pi \exp(\kappa \cos(x-\theta)) \left(\kappa^2 \underbrace{\cos^2(x-\theta)}_{1-\sin^2(x-\theta)}+ \kappa \cos(x-\theta) \right) \cos(n x - \phi) \mathrm{d} x \\ &=& \kappa^2 F_n - \int_{-\pi}^\pi \left(\frac{\mathrm{d}^2}{\mathrm{d}x^2} \exp(\kappa \cos(x-\theta)) \right) \cos(n x-\phi) \mathrm{d} x \\ &\stackrel{\text{by parts}}{=}& (\kappa^2 + n^2) F_n + \text{boundary terms} \end{eqnarray}$$ where the boundary term vanishes, if $n$ is an integer: $$\begin{eqnarray} \text{boundary terms} &=& - \left(\left. \left(\frac{\mathrm{d}}{\mathrm{d}x} \exp(\kappa \cos(x-\theta)) \right) \cos(n x-\phi) \right|_{x=-\pi}^{x=\pi} \right) \\ &\phantom{=}& - \left(\left. n \exp(\kappa \cos(x-\theta) ) \sin(n x-\phi) \right|_{x=-\pi}^{x=\pi} \right) \\ &=& 2 \sin(\pi n) \exp( -\kappa \cos(\theta) ) \left( n \cos(\phi) - \kappa \sin(\theta) \sin(\phi) \right) = 0 \end{eqnarray}$$ Thus $F_n$ satisfies the differential equation of $I_n(\kappa)$: $$\kappa^2 \frac{\mathrm{d}^2}{\mathrm{d} \kappa^2} F_n + \kappa \frac{\mathrm{d}}{\mathrm{d} \kappa} F_n - (\kappa^2 + n^2) F_n = 0$$ Because for $\kappa = 0$, $F_n$ is finite: $$\left.F_n \right|_{\kappa = 0} = \int_{-\pi}^\pi \cos(n x -\phi) \mathrm{d} x = 2 \cos(\phi) \frac{\sin(\pi n)}{n} = 2 \pi \cos(\phi) \delta_{n,0}$$ we conclude that $$F_n = g_n(\theta, \phi) I_n(\kappa)$$ Thus $g_{0}(\theta, \phi) = \cos(\phi)$. One can similarly establish an ordinary differential equation for $F_n$ as a function of $\theta$: $$\frac{\mathrm{d}^2}{\mathrm{d} \theta^2} F_n = \int_{-\pi}^\pi \left(\frac{\mathrm{d}^2}{\mathrm{d}x^2} \exp(\kappa \cos(x-\theta)) \right) \cos(n x-\phi) \mathrm{d} x = -n^2 F_n$$ and trivially $$\frac{\mathrm{d}^2}{\mathrm{d} \phi^2} F_n = - F_n$$ Combining these, with initial conditions, we arrive at the same result: $$F_n(\kappa, \theta, \phi) = 2\pi \cos\left(n \theta - \phi\right) I_n\left( \kappa \right)$$


text:
Home Nginx HTTPS subdomain redirect
Reply: 1

Nginx HTTPS subdomain redirect

MorganR
1#
MorganR Published in 2018-02-12 12:39:45Z
 I have a couple of websites configured with Nginx (nginx/1.10.3 (Ubuntu)) Server Blocks. Browsing to any of the configured domains listed below works as expected: Those that are configured to use HTTPS get automatic HTTP -> HTTPS redirects (morgrowe.com for example). The issue is when I browse to a subdomain that doesn't exist (for example: doesnotexist.morgrowe.com). If I go to http://doesnotexist.morgrowe.com, I get redirected to the default Nginx page (which is what I want). However, if I go to https://doesnotexist.morgrowe.com, I get redirected to https://api.morgrowe.com. This wouldn't be so bad, but if I go to https://doesnotexist.carpyslocksmiths.com, I also get redirected to https://api.morgrowe.com. Where can I find the configuration that makes this happen? Ideally, I'd like the default nginx 404 page to appear like it does for http connections. I imagine I have to configure something in /etc/nginx/sites-available/default, but I don't know where to start. Here's my /etc/nginx/sites-available/default file contents: server { listen 80 default_server; listen [::]:80 default_server; # SSL configuration # # listen 443 ssl default_server; # listen [::]:443 ssl default_server; # # Note: You should disable gzip for SSL traffic. # See: https://bugs.debian.org/773332 # # Read up on ssl_ciphers to ensure a secure configuration. # See: https://bugs.debian.org/765782 # # Self signed certs generated by the ssl-cert package # Don't use them in a production server! # # include snippets/snakeoil.conf; root /var/www/html; # Add index.php to the list if you are using PHP index index.html index.htm index.nginx-debian.html; server_name _; location / { # First attempt to serve request as file, then # as directory, then fall back to displaying a 404. try_files $uri$uri/ =404; } # pass the PHP scripts to FastCGI server listening on 127.0.0.1:9000 # #location ~ \.php\$ { # include snippets/fastcgi-php.conf; # # # With php7.0-cgi alone: # fastcgi_pass 127.0.0.1:9000; # # With php7.0-fpm: # fastcgi_pass unix:/run/php/php7.0-fpm.sock; #} # deny access to .htaccess files, if Apache's document root # concurs with nginx's one # #location ~ /\.ht { # deny all; #} }
solvease
2#
solvease Reply to 2018-02-12 14:32:05Z
 use a Default “Catch All” Server Block using _ in server_name both for http and https. _ is just an invalid value which will never trigger on a real host. Please see example From below link https://www.nginx.com/resources/wiki/start/topics/examples/server_blocks/
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Nonequilibrium fluctuations as a distinctive feature of weak localization

Abstract

Two-dimensional materials, such as graphene, topological insulators, and two-dimensional electron gases, represent a technological playground to develop coherent electronics. In these systems, quantum interference effects and in particular weak localization, are likely to occur. These coherence effects are usually characterized by well-defined features in dc electrical transport, such as a resistivity increase and negative magnetoresistance below a crossover temperature. Recently, it has been shown that in magnetic and superconducting compounds, undergoing a weak-localization transition, a specific low-frequency 1/f noise occurs. An interpretation in terms of nonequilibrium universal conductance fluctuations has been given. The universality of this unusual electric noise mechanism has been here verified by detailed voltage-spectral density investigations on ultrathin copper films. The reported experimental results validate the proposed theoretical framework and also provide an alternative methodology to detect weak-localization effects by using electric noise spectroscopy.

Introduction

Perturbative corrections to the Drude model, due to the quantum mechanical nature of the electron, are collectively known as quantum transport phenomena. One of the most studied examples of these phenomena, arising from electron interference, is weak localization (WL)1. Recently, WL has been observed in innovative two-dimensional systems like graphene2, topological insulators3, and two-dimensional electron gases4, which are considered very important for the development of future quantum computing applications. This discovery has attracted the attention of the scientific community, increasing the interest on the topic of charge carriers localization effects.

A striking feature of WL is represented by a resistivity increase below a characteristic crossover temperature, usually occurring at low temperatures5. This behaviour has been found in ultrathin metallic films (Cu, Mg, Ag, Au, Pt, with thickness t < 20 nm)6; in alloys and composites such as Au-Pd, Cu-CuO, Al-Al2O3, Au1−x Gex, Nb1−x Six6; in doped semiconductors as Si:P7, or Ge:Sb8. Metallic oxides, being strongly correlated electronic systems, can show a crossover temperature at values higher than 30 K9,10. In two relevant cases of oxide conductors, peculiar electric noise properties have been related to WL and interpreted in terms of nonequilibrium universal conductance fluctuations11,12. In particular, it has been reported that the bias current plays a fundamental role when quantum interference effects become significantly evident, giving origin to an unusual linear dependence of the voltage-spectral density12. Noise spectroscopy has already demonstrated its potentialities by providing information on the dynamic behaviours and the kinetic processes of the charge carriers in several condensed matter systems13,14,15,16,17. However, a conclusive response on the strict connection between this type of fluctuations and WL can only be obtained by investigating simple metals, like copper, that have unambiguously shown the presence of quantum conduction mechanisms at low temperatures18,19,20.

In view of all these considerations, detailed dc electric- and magneto-transport measurements, as well as voltage-noise analysis, of ultrathin Cu samples are here reported and interpreted in the framework of nonequilibrium universal conductance fluctuations. Seven different films, with thickness from 7 to 200 nm, have been deposited by dc magnetron sputtering on Si(100) substrates. This choice of analyzing a wide thickness range is necessary in order to focus the attention only on samples characterized by the presence of WL at sufficiently high temperatures, useful to overcome the limitations related with used experimental setup. The results are shown in the following, together with a theoretical discussion and confirm the hypothesis made. As a consequence, noise spectroscopy could represent a very sensitive tool to detect WL effects in different systems.

Results

dc transport and magnetic properties

Below a thickness of 30 nm, the investigated thin copper films exhibit a change in their resistivity, as evident in the inset of Fig. 1 at room temperature. To better understand this feature, the temperature dependence of the resistivity of films with thickness tCu = 30 nm and tCu = 12 nm has been measured and shown in Fig. 1. The 30 nm sample is characterized by a metallic behaviour down to the lowest investigated temperature, while the sample of 12 nm shows a resistance minimum at temperature Tmin = (28.0 ± 0.1) K and then the resistance rises as T → 0. This behaviour has been extensively studied and several mechanisms have been considered for its interpretation5. In particular, WL, electron-electron interactions and the presence of Kondo impurities can be equally responsible for a resistivity upturn in the low-temperature limit. In this respect, the comparison of experimental results obtained with different techniques (such as standard dc characterizations, magnetic measurements and noise spectroscopy) is necessary to identify the specific transport process of the charge carriers.

In nonmagnetic metals, the temperature dependence of the electrical resistivity arises mainly from the electron-phonon interaction, as described by the Bloch-Gruneisen formula21

with

where A is a constant depending on the electrons velocity at the Fermi surface and their density in the metal; ΘD is the Debye temperature; ρ0 is the residual resistivity, due to defects, impurities, size effects and grain boundary scattering. In particular, it is assumed that all these scattering mechanisms contribute only to the elastic scattering rate, thus ρ0 1/τ0. Conversely, the temperature-dependent contribution ρi (T) is related to electron-phonon and electron-electron interactions22. Moreover, the exponent n in equation (2) is usually fixed at 2, 3, or 5 depending on the nature of interaction: in the case of copper n = 523,24.

For thin disordered metallic films the Bloch-Gruneisen model is not able to reproduce the low-temperature resistivity behaviour, which is usually characterized by an upturn associated with the two-dimensional (2D) WL. This phenomenon is a well-known transport process for Cu ultrathin films, as widely reported in the scientific literature1 and produces a logarithmic quantum correction to the Drude conductivity (e.g., see the curve of the 12 nm thick sample in Fig. 1). WL contributions are expected to become significant at temperatures for which the elastic scattering rate 1/τ0 becomes larger than the inelastic dephasing rate 1/τΦ, and the low-temperature correction to the normalized conductivity for a 2D film of thickness t can be expressed as

where α is a constant of the order of unity; e and ħ are the electron charge and reduced Planck constant, respectively; τΦ is the characteristic time of electron phase memory relaxation due to inelastic processes. Electron-phonon and electron-electron interactions produce a τΦ Tp, where p varies between 0.5 and 35. By including this WL correction, the total resistivity ρ(T) can then be written as

in which T0 identifies an upper limit of the WL onset. To evaluate the temperature dependence of ρi, a best fit of ρ(T) as given by equations (1) and (2), with n = 5, to the experimental data has been performed and shown in Fig. 1 for both films (red solid lines). For the thicker film the Debye temperature ΘD and the coefficient A are considered as free fitting parameters, obtaining the best values with ΘD = (283 ± 1) K and A = (11.87 ± 0.02) μΩ cm. For the sample showing the resistance minimum, the same fit is performed in the temperature range 50−300 K by considering also the residual resistivity ρ0 as a fitting parameter. The values ρ0 = (280.0 ± 0.5) μΩ cm and A = (88.2 ± 0.1) μΩ cm are now obtained, while ΘD is found to be the same as for the 30 nm film, within the experimental error. By substituting into equations (3) and (4) all these parameters evaluated with the procedure previously described, it is possible to reproduce the ρ versus T behaviour of the thinner film by considering αp and T0 as free fitting coefficients. The best fitting curve, shown in Fig. 2 as red solid line, testifies a good agreement with the experimental data also in the low-temperature limit (see the inset to Fig. 2 for details) and is obtained with αp = (0.63 ± 0.05) and T0 = (68 ± 3) K. The value of αp is consistent with that reported in the literature for Cu ultrathin films18,25.

The results of the dc electrical characterization, alone, can not discriminate the specific transport process responsible for the low-temperature conduction in the disordered Cu ultrathin films, here investigated. To this purpose, resistance versus magnetic field measurements R(H) can give an effective proof of the existence of WL effects. Figure 3 shows the R(H) data for the 12 nm sample in the temperature range between 1.6 and 25 K for two field orientations, perpendicular H (a) and parallel H// (b) to the film surface, with the bias current always perpendicular to the field. The measured magnetoresistance MR = [R(H) − R(0)]/R(0) is negative and shows large anisotropy according to the direction of the applied magnetic fields. The negative and anisotropic magnetoresistance has been extensively reported on thin copper films and well described within the WL theory. Conversely, for thicker films the standard metallic magneto-transport behaviour has been reported18,26. A positive magnetoresistance can be observed at low fields and below 10 K and is usually ascribed to the presence of the spin-orbit coupling27.

Noise properties

In consideration of the strict connection between unusual 1/f electric noise and WL, reported for superconducting cuprates11 and manganite compounds12, a detailed voltage-spectral density analysis has also been performed on Cu ultrathin films. The low-frequency power spectral densities SV, measured at several temperatures and bias currents, are shown in Fig. 4 (left panel) for the 12 nm sample. When a current is supplied, the typical 1/f frequency dependence is clearly visible over a flat background spectrum, corresponding to the thermal Johnson noise and the electronic chain noise 1.4 × 10−17 V2/Hz (for reference see the black traces in Fig. 4). Spurious contributions, due to external contact noise, are removed by using the experimental procedure described in ref. 28. The shape of SV is the same above and below Tmin, as shown by the experimental data at 300 K and 20 K in Fig. 4. Conversely, the amplitude of the noise is different when the crossover between WL and metallic region occurs. This can be clearly observed in Fig. 4 (right panel), where the temperature dependence of SV, at a reference frequency of 90 Hz and fixed bias current of 0.6 mA, is shown as black dots. In these conditions, the standard theory of resistance fluctuations in metals predicts the direct proportionality SV R229. A good agreement between the experimental quantities is obtained by a fitting procedure only above Tmin (see the red dashed curve in Fig. 4). This is not found below Tmin, where quantum interference effects produce an upturn of the resistivity. In particular, the WL region is characterized by unconventional features of the noise level not trivially related to resistance fluctuation processes, as at higher temperatures.

A theoretical explanation of this behaviour has been given in ref. 12 by addressing the universal conductance fluctuation (UCF) mechanism as the source of 1/f noise in WL regime. In this context, a linear dependence of the 1/f noise on I at temperatures below Tmin is expected. Conversely, above the crossover at T > Tmin a standard quadratic current dependence of SV is predicted12. The same analysis has been performed for the 12 nm Cu ultrathin film and the results are shown in Fig. 5(a). In this figure, it is evident a linear current dependence of the voltage-noise at low temperatures, in the WL regime, while at higher temperatures, in the normal conductance regime, although with comparable resistance values a quadratic bias dependence is found. This behaviour seems to be a universal feature of WL systems.

The bias dependence of the experimental data of Fig. 5(a) can be reproduced in terms of the power law

where SA is the temperature-dependent amplitude of the spectral density at the reference frequency of 90 Hz; η is the power exponent. The best fitting curves by using equation (5) are also shown in Fig. 5(a). A good agreement between the functional form considered and the measured voltage-noise is obtained with values of η switching from 1.00 ± 0.01 in the WL region to 2.00 ± 0.01 in the metallic region. This can also be seen in the temperature dependence of η, shown in Fig. 5(b). Here, it is visible the presence of a region close to Tmin, where a sign of a transition appears. This behaviour suggests that a simple probe of WL can be done by means of noise spectroscopy, by looking at the transition from a linear to a quadratic current dependence of the 1/f spectral density. The reproducibility of the experimental evidence of Fig. 5(b) in different samples and materials (such as Cu, Nd1.83Ce0.17CuO4+δ, and La0.7Ba0.3MnO3 films reported here, in ref. 11 and in ref. 12, respectively) gives the clear indication for a common universal origin of the fluctuation processes of the charge carriers in WL regime.

Discussion

The specific feature of the voltage-spectral density can be understood from the model described in ref. 12. Here, the main steps of the model derivation are briefly recalled. In WL the length LΦ, over which the diffusive motion of the electrons preserves the phase memory, is much longer than the electronic mean free path . Consequently, quantum corrections to the classical motion become relevant and produce localization as the result of the destructive interference of time reversed loop trajectories triggered by a specific impurity configuration. The relic of the quantum nature of the electrons (i.e., the interference effects) manifests itself macroscopically with an increase of the sample resistance. However, the effect on the fluctuation properties of the system is much more pronounced, compared to the small change of the resistance. Indeed, the partial phase coherence of the sample below Tmin makes effective the coupling between impurity motion and universal conductance fluctuations. The nonequilibrium dephasing mechanism affecting a coherent region of linear dimension LΦ dresses the fluctuation mechanisms responsible for the conventional 1/f noise at high temperature (T > Tmin) and produces, below Tmin, a peculiar linear dependence on the bias current. Close to the crossover temperature Tmin, the voltage-spectral density SV (f) depends on the variance of the conductance of a single coherent subsystem averaged over the relevant transport energy window ΔE (i.e., ). From elementary statistics considerations it follows (ΔE > Ec)

being the Thouless energy. Equation (6) implies that the fluctuations of the energy averaged conductance of a generic coherent region exhibit a reduced variance compared to the universal value (e2/h)2 as the effect of the incoherent contribution of several uncorrelated energy intervals of size Ec contained in ΔE. Following ref. 12, it is found that ΔE = kBT in the metallic region (T > Tmin), while ΔE = eVΦ = χeV in the WL regime (T < Tmin). The former is the energy available to promote thermal excitation of electrons above the Fermi level, the latter is an energy scale induced by the average voltage drop VΦ experienced by the generic coherent region. The dimensionless factor χ relates the macroscopic voltage drop across the sample V to VΦ and contains statistical information on the topology of the random network explored by the current. For the simple topology given by the one dimensional random resistors network of length L biased by the voltage V, the average voltage drop experienced by a coherent region of length LΦ is given by vΦ = (LΦ/L)V, being L/LΦ the number of coherent subsystems. An estimate of VΦ in two dimensions can be obtained averaging the one dimensional result over a representative set of path lengths, i.e., with γ = LM/L > 1. Increasing the temperature T, the energy scale eVΦ Tp/2, with the same index p as in equation (4) depending on scattering process and dimensionality5, is progressively reduced making the thermal dephasing as the main inelastic mechanism (i.e., ΔE = kBT). In order to capture the above mentioned mechanisms using a minimal model suitable for a 2D random network, a temperature-independent parameter χ is introduced and ΔE ~ max[eVΦ, kBT] is assumed. By identifying χ with , its temperature independence is recognized for T < Tmin as induced by the low-temperature saturation of LΦ to some constant value related to the geometric confinement and to the boundary effects. This provides an upper limit to the sample coherence.

This model of ΔE is just a crude approximation having the advantage of minimizing the number of free parameters of the theory, while it can not describe in detail the crossover region (T ≈ Tmin) where thermal and bias dephasing can produce combined effects. As a consequence, in WL regime the current flowing through the system provides a dephasing mechanism of the UCF with a characteristic dephasing time ~ħ/(eVΦ), while a thermal dephasing time ~ħ/(kBT) describes the high-temperature regime (T > Tmin). Equation (6) reproduces the asymptotic behaviour of the fluctuation mechanisms close to Tmin and induces the following model for the voltage-spectral density12

where the energy scale has been introduced, while the proportionality factor depends on the number of fluctuators coupled to the current within a typical coherent region. This number is proportional to and saturates in the low-temperature limit to the constant value according with a freezing effect. In Fig. 6, equation (7) (solid lines) is compared with the experimental data (full symbols) and the relevant energetic scales involved in the nonequilibrium dephasing mechanisms affecting the coherence of the UCFs are extracted. Despite the limited number of free fitting parameters, an agreement is clearly evident above and below Tmin, while in the crossover region an interpolation line (dashed) is added just as a guide for the eyes.

The analysis of the energetic scales reconstructed by the fitting procedure of equation (7) (see in Supplementary Fig. 1) validates the dephasing model of UCFs. As expected, in the temperature range here considered, the applied bias represents a relevant dephasing source (eVΦ > Ec), under the specific condition that the energy window induced by the external currents is higher than the thermal energy kBT (see in Supplementary Fig. 1). These results have been already shown in oxide conductors12, but not yet reported in metals exhibiting quantum transport phenomenology. Such nonlinear effects of the voltage fluctautions have not been described in previous works30,31, because very small values of the bias currents were used. Moreover, differently from these old experimental findings on disordered simple metals, the noise data here presented cover nonequilibrium fluctuations across the whole metal-insulator transition. It is worth noting, that the temperature behaviour of the 1/f amplitude changes when the quadratic and linear bias dependencies are explored. In particular, from Fig. 6 it is clearly visible a low-temperature enhancement of the 1/f voltage-spectral density for small bias currents (e.g., see the red curve at I = 0.1 mA), as also reported in previous experiments32,33. Conversely, at large bias currents (e.g., see the curves at I ≥ 0.4 mA in Fig. 6) an opposite effect on the 1/f component is observed. These evidences give a strong indication of the crucial role played by the bias current in quantum transport phenomena.

In order to further characterize the occurrence of WL, the typical lengths involved in the WL regime have been analyzed. The coherence length LΦ and the spin-orbit length Lso, that estimates the intensity of spin-orbit coupling, can be experimentally extracted from magnetoresistance measurements. In particular, the magnetic field dependence of the correction to the conductance in two dimensions is expressed as34

where the function f2(x) is given by f2(x) = ln (x) + Ψ(1/2 + 1/x) with Ψ as the digamma function and δ0 is a proportionality factor. The characteristics fields HT and HS are the triplet and singlet fields, defined, in absence of magnetic impurities, as

The experimental data can be modelled with equation (8), allowing the extraction of the characteristic lengths from equations (9). More in detail, the best fitting curve of the magnetoresistance at the lowest investigated temperature of 1.6 K (see inset of Fig. 7) gives Lso = (91 ± 2) nm. On the other hand, in the temperature range from 4.2 to 25 K, Lso takes a temperature-independent value of (84 ± 2) nm, in accordance with the Fermi-liquid theory35. By fixing the spin-orbit length to this constant value, it is possible to evaluate LΦ for the same temperatures of Fig. 3. The agreement between the theoretical prediction and the data points is clearly visible in Fig. 7. From this fitting procedure, the low-temperature behaviour of LΦ can be obtained and is shown in Fig. 8 as green squares. Here, it is deduced that below Tmin the effect of the spin-orbit coupling is negligible and equation (8) reduces to the 2D WL formula (LΦ < Lso). Conversely, in the low-temperature regime (T < 4.2 K) LΦ becomes comparable with Lso, inducing antilocalization corrections in the low-field magnetoresistance curve (see inset of Fig. 7).

The WL regime requires . In order to verify this condition, the mean free path can be computed from the sample resistivity according to ref. 36. A value of nm has been extracted for the 12 nm Cu film, in a temperature range close to Tmin. This estimation (see Fig. 8 for details) implies that the WL transition occurs when . A distance of is sufficient to enable closed electronic (phase coherent) trajectories, which link several grain boundaries (4 in average). It is worth mentioning here, that ultrathin Cu films manifest the tendency to present a system growth based on coalescence of mesoscopic grains, whose linear dimensions increase with the thickness. Therefore, the resistivity of ultrathin films characterized by a microscopic granular structure is generally much higher than the resistivity of a thicker sample, this critical thickness being of the order of 40 nm. This is confirmed by the inset to Fig. 1, where the sample with tCu = 12 nm shows a resistivity value of two orders of magnitude higher than the thickest film (tCu = 200 nm), having a bulk-like behaviour. Assuming a grain boundary limited mean free path, an average grain diameter of 6 nm can be deduced for the 12 nm Cu film. This value is in agreement with the resistivity of the investigated samples, while for more conducting films a grain size of the order of the thickness is expected. Such evaluation is also compatible with the assumption of a grain size about 15−20 nm, as reported in ref. 37, by considering an additional intragrain scattering mechanism which limits the mean free path.

In conclusion, several Cu ultrathin films of different thickness have been fabricated and electrically characterized. The sample of thickness tCu = 12 nm shows an upturn of the resistivity below the crossover temperature Tmin ≈ 28 K. The analysis of the resistivity and the characteristic negative magnetoresistance indicates that a localized regime is established at low temperature. The signature of the spin-orbit interaction has been also detected in the low-field magnetic response of the sample. Once a weak-localization regime (T < Tmin) has been confirmed, detailed voltage-spectral density analysis has been performed. While the high-temperature (T > Tmin) behaviour of SV versus I takes the usual quadratic form, in the WL regime an anomalous linear dependence on the applied bias is detected. These findings present the same distinctive features described in ref. 12. In particular, in the WL regime, the voltage fluctuations are strongly affected by the temporal variation of the UCFs, being the latter a coherence effect. The variance of these fluctuations is reduced due to the dephasing effect of the bias current I. As a consequence, it has been confirmed, also in the case of a simple metallic thin film, that the anomalous linear dependence of SV versus I is due to the dephasing effect on the local conductance fluctuations of the current bias exploring the percolative network of the sample. Thus, the anomalous fluctuation behaviour detected in the WL regime seems to be a material-independent feature only associated with partial restoration (and its local destruction by the measuring action of the current) of the sample coherence. Once the anomalous SV behaviour has been unambiguously associated with the WL regime, it will also provide a simple diagnose of localization effects in innovative two-dimensional systems like graphene, topological insulators and two-dimensional electron gases. These materials represent the technological platform to develop topological computation (for instance, based on Majorana modes), which requires a fixed magnetic bias for the stabilization of the device working point. In this case, magnetoresistance measurements are difficult to be performed and a purely electric probe of WL mechanisms, such as noise spectroscopy, could be very useful.

Methods

Ultrathin Cu films were deposited on Si(100) substrates covered by 200 nm thick SiO2 in ultra-high-vacuum by dc magnetron sputtering. The system is equipped with a movable sample holder which allows to fabricate different samples in the same run under the same deposition conditions.

The samples were structured in a standard Hall geometry of length L = 1 mm and width W = 100 μm allowing four contact electrical measurements. The pattern was realized on the SiO2/Si substrates using standard optical lithography and lift-off procedure. Subsequently, the films were deposited in a base pressure in the high 10−8 mbar range and a sputtering argon pressure of 5.5 × 10−3 mbar at typical rates of 0.29 nm/s, controlled by a quartz crystal monitor, calibrated with low-angle X-Ray reflectivity measurements.

Seven different films were prepared with thickness tCu = 7, 8, 10, 12, 30, 48, 200 nm. To prevent the surface degradation or oxidation of the active area between electrical pads, a 10 nm thick insulating cap layer of SiO2 was selectively rf sputtered on the structures just after lift-off using a metallic shadow mask. The electrical contacts were made through rf sputtered 50 nm thick Au pads defined by optical lithography and lift-off. The thickness dependence of the room temperature resistivities ρ300K, shown in the inset of Fig. 1, reminds the ones reported in the literature for high quality Cu films38,39. Concerning the resistivity values, it is useful to compare them with the values of the sheet resistance of island-like thin Cu films deposited by the same technique and in similar depositions conditions37. For the thinnest films here investigated, the sheet resistance, Rs = ρ300K/tCu, spans from Rs = 250 Ω/□ for tCu = 12 nm to Rs = 330 Ω/□ for tCu = 8 nm, whereas in ref. 37 for a 5-nm film it is Rs ≈ 800 Ω/□. This result indicates that the samples under study have a more continuous morphology and that the crucial role in the scattering process seems to be played by the scattering at grain boundaries.

The dc electric transport and magnetoresistance measurements were carried out in a Cryogen Free Magnet system by Cryogenic Ltd., equipped with an integrated cryogen-free variable temperature insert (operating range between 1.6 and 300 K) and a superconducting magnet able to generate a magnetic field up to 9 T. In this system, the samples were biased with a fixed current of 10 μA by using a Keithley 2430 Sourcemeter and the output voltage was recorded with a Keithley 2182 Nanovoltmeter. Electric noise measurements, instead, were performed by using a closed-cycle refrigerator, operating in the 8- to 325-K range. The temperature stabilization, realized through a computer-controlled feedback loop, was better than 0.1 K. The sample temperature was measured with a Cernox resistor thermometer, in contact with the sample holder. A low-noise Keithley dc current source was used for the biasing of the samples. The dc voltage drop was measured with a digital multimeter, while the ac voltage signal was amplified with a low-noise PAR5113 Preamplifier and analyzed by a dynamic signal analyzer HP35670A.

How to cite this article: Barone, C. et al. Nonequilibrium fluctuations as a distinctive feature of weak localization. Sci. Rep. 5, 10705; doi: 10.1038/srep10705 (2015).

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Acknowledgements

The authors would like to thank S. Abate of CNR-SPIN Salerno for his technical support.

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Contributions

C.B., F.R. and S.P. wrote the main manuscript text. C.C., G.C. and C.A. wrote the Methods. C.B. and S.P. performed the voltage-noise measurements, while dc transport and magnetic characterization was performed by A.N., A.L., G.G. and A.Gu.. F.R. and A.Ga. contributed to the theoretical interpretation of the experimental findings. The investigated films were prepared and structurally characterized by C.C. and C.A. and P.S. was principally involved in the sample patterning. All authors discussed the results and implications and commented on the manuscript by reviewing it accurately.

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Barone, C., Romeo, F., Pagano, S. et al. Nonequilibrium fluctuations as a distinctive feature of weak localization. Sci Rep 5, 10705 (2015). https://doi.org/10.1038/srep10705

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• DOI: https://doi.org/10.1038/srep10705

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text:
# Relative Motion Analysis: Acceleration

Tags:
1. Mar 3, 2016

### Smoker

Mentor note: moved to homework forum later, therefore no template.

When doing a rigid body relative motion (accel) problem using vector analysis, how do I know when it's appropriate to substitute sin/cos values vs when to use just the numbers given as the velocity?

Last edited by a moderator: Mar 4, 2016
2. Mar 4, 2016

### Simon Bridge

It sounds like you are trying to use formulas without understanding them.
vis: sine and cosine are usually used to compute components of vectors resolved against a coordinate system, or against other vectors ... so that is when you use them. You should use whichever trig functions you need to in order to work the problem, not just sine and cosine.

The trouble with this sort of question is that the people who can answer you find this stuff intuitively obvious - this means there is a bit more information needed to get us (me) to understand where the trouble lies.

Please provide an example of where you get in trouble deciding what to use.

3. Mar 4, 2016

### Smoker

• Post moved from the technical forums, so no HH Template is shown
I am to determine the velocity of slider block C. Given angular velocity of AB (4.1) and angular rotation of AB (5.5).

4. Mar 4, 2016

### Staff: Mentor

Okay, and which velocity value where do you want to calculate how, where you ran into the problem of post 1?

5. Mar 4, 2016

### Smoker

Basically I want to know the x and y components of the velocity of B, A is zero because it's fixed and C is (Vc)i because it's restricted to the x axis, but what is Vb? and why?

6. Mar 4, 2016

### Staff: Mentor

Okay. Can you find the speed of B, and the direction of motion?
That allows to find the velocity components.

I think this thread fits better to the homework section.

7. Mar 5, 2016

### Simon Bridge

Just a note re initial question about when to use sine and cosine:
If the speed of C is $v_c$ then the x-component is $v_{cx}=v_c\cos\theta$ but, here, $\theta = 180^\circ$ (it is the angle $\vec v_c$ makes to the +x-axis). So you get $\vec v_c = -v_c\hat\imath$ ... which is to say, the sine and cosine values are still used, it's just that they are easy.


text:
# Pressure at center of earth (or any planet)

1. ### Bill Wells

2
I have seen several references which give the pressure at the center of the earth at about 3 x 10^11 Pa. (I've seen 3.0 - 3.6). An earlier post on this forum gives the equation for the pressure at the center of a planet as
2*(pi*G/3)*(R^2)*(rho)^2. When I crunch the numbers, I get 1.73 x 10^11, which is about half what most references give. I'm using rho = 5515 kg/m^3.
Where am I going wrong.
The above assumes constant density (rho). If you like the above problem, is there an equation which would give central pressure if the density increases with depth?

Thanks Much
Bill


text:
# In Batch Normalisation, are $\hat{\mu}$, $\hat{\sigma}$ the mean and stdev of the original mini-batch or of the input into the current layer?

In Batch Normalisation, are the sample mean and standard deviation we normalise by the mean/sd of the original data put into the network, or of the inputs in the layer we are currently BN'ing over?

For instance, suppose I have a mini-batch size of 2 which contains $$\textbf{x}_1, \textbf{x}_2$$. Suppose now we are at the $$k$$th layer and the outputs from the previous layer are $$\tilde{\textbf{x}}_1,\tilde{\textbf{x}}_2$$. When we perform batch norm at this layer would be subtract the sample mean of $$\textbf{x}_1, \textbf{x}_2$$ or of $$\tilde{\textbf{x}}_1,\tilde{\textbf{x}}_2$$?

My intuition tells me that it must be the mean,sd of $$\tilde{\textbf{x}}_1,\tilde{\textbf{x}}_2$$ otherwise I don't think it would be normalised to have 0 mean and sd of 1.

So, if this layer receives an input $$\mathrm{x}=\left(x^{(1)} \ldots x^{(d)}\right)$$, the formula for normalizing the $$k^{th}$$ dimension of $$\mathrm{x}$$ would look as follows: $$\widehat{x}^{(k)}=\frac{x^{(k)}-\mathrm{E}\left[x^{(k)}\right]}{\sqrt{\operatorname{Var}\left[x^{(k)}\right]}}$$
Note that in practice a constant $$\epsilon$$ is also added under the square root in the denominator to ensure stability.
• Right. There are a few locations in the text where they define it in an explicit manner (like in the abstract or when they define $x$ ). In some places, they may also refer to the process as “normalizing the activations”. – user5093249 Jun 8 '20 at 17:26


text:
# Experimental observation of the Anderson metal-insulator transition with atomic matter waves.

@article{Chab2008ExperimentalOO,
title={Experimental observation of the Anderson metal-insulator transition with atomic matter waves.},
author={Julien Chab{\'e} and Gabriel Lemari{\'e} and B. Gr{\'e}maud and Dominique Delande and Pascal Szriftgiser and Jean Claude Garreau},
journal={Physical review letters},
year={2008},
volume={101 25},
pages={
255702
}
}
• Published 27 September 2007
• Physics
• Physical review letters
We realize experimentally an atom-optics quantum-chaotic system, the quasiperiodic kicked rotor, which is equivalent to a 3D disordered system that allows us to demonstrate the Anderson metal-insulator transition. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to extract both the critical parameters and the critical exponent of the transition, the latter being in good agreement with the value obtained in numerical simulations of…
277 Citations

## Figures from this paper

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• 2009
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### Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor.

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• 2015
This work experimentally study Anderson localization in dimension 2 and shows that the localization length depends exponentially on the disorder strength and anisotropy and is in quantitative agreement with the predictions of the self-consistent theory for the 2D Anderson localization.

### Universality of the Anderson transition with the quasiperiodic kicked rotor

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We report a numerical analysis of the Anderson transition in a quantum-chaotic system, the quasiperiodic kicked rotor with three incommensurate frequencies. It is shown that this dynamical system

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We show that quantum wavepackets exhibit a sharp macroscopic peak as they spread in the vicinity of the critical point of the Anderson transition. The peak gives a direct access to the mutifractal

### Field theory of Anderson transition of the kicked rotor

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We present a microscopic theory of Anderson transition in the quantum kicked rotor. The behavior of the system is shown to depend sensitively on the value of the effective Planck constant, . For the

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text: How to Quickly Add the Integers From 1 to 100 - Part 1 We are currently experiencing playback issues on Safari. Great for schools, public places and homes. 9. The term “Arithmetic addition” is used to describe adding two or more numbers together to form the addition table and the math symbols used to denote an addition operation is a plus sign. If you’re anything like me, you probably enjoy a good number trick every now and then. Last updated at July 9, 2019 by Teachoo. And, continuing in this manner, we have 50 pairs of numbers that each add to 101. Divide the series into two equal groups. In A2 enter =RAND() and drag down to A5. Pseudocode to Add Two Numbers; Pseudocode to Find the biggest of three (3) Numbers PseudoCode to Print Numbers from 1 to 100; Pseudocode to Calculate Area and Perimeter of Rectangle; Pseudocode to Check a Number is Positive or Negative; Pseudocode to Solve Quadratic Equation 165k Followers. Below Adding Consecutive Squares Chart shows the sum of consecutive squares from 1 to 100. Next, it’s going to add those numbers to find the sum of prime numbers between 1 and 100. :) – idjaw Mar 24 '16 at 12:18. add a comment | 1. For this lesson, we'll be working with easy numbers just to get you used to how this stuff works. Numbers 0 to 100. Use the start/stop to achieve true randomness and add the luck factor. In mathematics, a addition table is a mathematical table used to define a addition operation for an algebraic system. Thanks! 0 Comments. Square Numbers from 1 to 100. Thank you for investigating this. Show Hide all comments. Therefore, 50 * 101 = 5050. About Game ------------ Find the number from 1 to 100 is a addictive game for number and alphabet finder. Is this bringing a nuclear missile to a gun fight? Google Classroom Facebook Twitter. It displays the sum of any given numbers. English Resource. I want to run a Unix command 100 times using a for loop from 1 to 100. Select odd only, even only, half odd and half even or custom number of odd/even. The numbers from 10 to 100 are: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, But notice when we add the first number, 1, and the last number, 100, we get 101. If the hundreds digit is a 9, then change the 9 to a 0 and increase the thousands digit by 1 instead. How big are they? We learned various methods to count numbers between 1 to 100 when using KSH, bash, sh and other shell running on Linux or Unix-like systems. Now add up the numbers that appear on the screen (or roll up 2 dice in such a manner that only 1-5 are displayed) and move the kitty that many steps on the path to reach to the goldfish bowl. It also displays columnar addition of these numbers, the carrying (regrouping), partial sums etc. We will count up in hundreds by adding 100 each time. Because each of these pairs of numbers adds up to 101. The first line defines the variable. R's range does something else entirely. The even numbers from 1 to 100 are: 2 4 6 8 10 Email. Pick unique numbers or allow duplicates. But how about Calculus? 118k 50 50 gold badges 372 372 silver badges 318 318 bronze badges. At every position on the x-axis, we put in a number and get the same one out. But using the Calculus equation we get: Uh oh: there's a difference. Before we figure out how to add up all the integers from 1 to n, let’s recap how to add up all the integers from 1 to 100.The key to this is our friend the associative property of addition which says that you are free to add together a group of numbers in any order you like. Demonstrate and explain the effect of adding zero to, or subtracting zero from, any number. Enjoy the article? Check my answers: Email my answers to my teacher Cancel: Text box style: Font: Size: px. Worksheets and interactive online activities to help children learn how to add 1 to numbers within 10. The second line loops it to 100, the third adds 1 to a and the 4th divides a by 3 and if there is no remainder (0) it will print that number otherwise it will print a blank line. Learning Calculus: Overcoming Our Artificial Need for Precision, A Friendly Chat About Whether 0.999... = 1, Quick Insight: Easier Arithmetic With Calculus. Lets you pick a number between 1 and 100. Something that would be easy for me to understand. An interactive math lesson about whole numbers to 100. Imagine that on a table in front of you you have arranged stacks of pennies, in a long neat row left to right, to equal each of these numbers. It seems that regular arithmetic, algebra, geometry, or even statistics could help work out the equation. 99.9%. I will write int number = 1 + (int) (Math.random() * 100); share | improve this answer | follow | answered Sep 23 at 18:17. user14329366 user14329366. Learn counting numbers from 1 to 100. The indefinite integral is $\frac{1}{3} x^3$, the running total for how much we have. With Calculus, we'd say: The pattern isn't continuous, but it looks like $f(x) = x^2$. ... Random Numbers Combination Generator Number Generator 1-10 Number Generator 1-100 Number Generator 4-digit Number Generator 6-digit Number List Randomizer Popular Random Number Generators. In a set of consecutive integers, the mean and the median are equal. Listen to the pronunciation of the numbers from 1 to 100: English Teacher Resource. From the rules of Calculus (or using Wolfram Alpha) we get this: Intuitively: Add up things following the $f(x) = x$ pattern and you end up with $\frac{1}{2} x^2$. For example 4 + 4. 73. Let's suppose that you want to add all the numbers from 1 to 100 in your head. Write a Python Program to print Prime numbers from 1 to 100, or 1 to n, or minimum to maximum with example. Counting & Number: Addition: Subtraction: Multiplication: Division: Mixed Bag: Curriculum: Other Stuff: Adding 1 (within 10) and Extensions. There is a large one page version and … Np! How to Quickly Add the Integers From 1 to 100 - Part 1. This program finds the prime numbers between 1 and 100. Well, let's see: the actual sum from 1 to 100 is 5050. Missing numbers between 0 and 120. Better Explained helps 450k monthly readers PS. But notice when we add the first number, 1, and the last number, 100, we get 101. Build addition skills with sums up to 100. within 100 mixed regrouping support MMM: Sets A & B Sets C & D Add. If we have 100 numbers (1…100), then we clearly have 100 items. Should but I'll add it just in case. 467k Followers. Go beyond details and grasp the concept (, “If you can't explain it simply, you don't understand it well enough.” —Einstein Practice addition or Subtraction. 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Line or no-space English ; numbers Spelling Game ; we also have a function is  repeatedly adding bunch. Random numbers Combination Generator number Generator 6-digit number List Randomizer Popular Random number Generators each has! Column by 1 instead get matlab to List all numbers from one to a 0 and increase thousands!


text:
# Combinatorics/Multisets problem question

I wonder how a problem of the following type can be solved. I have looked for a solution but I am not to identify the kind of problem I am facing. I would like to know if there is a close formula or if it has to be solved with an algorithm.

I expose the problem through an specific example:

I have N=7 bags. Each bag contains aways a single element, but elements can be repeated. For instances:

bag 1: Element 1
bag 2: Element 1
bag 3: Element 1
bag 4: Element 2
bag 5: Element 2
bag 6: Element 3
bag 7: Element 3

On how many ways I can withdraw for example i=4 elements from which S=3 are different. For example:

1 (Bag 1)
1 (Bag 2)
2 (Bag 4)
3 (Bag 6)

Or:

1 (Bag 1)
1 (Bag 3)
2 (Bag 4)
3 (Bag 6)

I think the problem is related to multisets since the elements of the set are repeated but I am not sure

Regards

-

Let's solve the particular problem, then see whether we can say anything more general.

To draw 4 elements, three different, you can draw 1123, 1223, or 1233.

The number of ways to draw 1123 is 3-choose-2 times 2-choose-1 times 2-choose-1, which is $3\times2\times2$, which is 12.

The number of ways to draw 1223 is 3-choose-1 times 2-choose-2 times 2-choose-1, which is $3\times1\times2$, which is 6.

1233 is the same, another 6. So the answer is $12+6+6=24$.

Now let's pose the general problem. You have $n_1$ bags containing element 1, $n_2$ bags containing element 2, and so on, to $n_r$ bags containing element $r$. You want to take $i$ elements, with $s$ of them being different. So we may assume $s\le i$, $s\le r$, $i\le n_1+\cdots+n_r$.

Since there are $r$ types of element, and you want exactly $s$ types of element, there are $r\choose s$ ways of choosing which types of element you get. For each such choice, you have $$x_{j_1}+x_{j_2}+\cdots+x_{j_s}=i,\quad1\le x_{j_m}\le n_{j_m},\quad m=1,2,\dots,s\tag1$$ Now there are standard ways of finding the number of solutions of (1), then you have to add that up over the $r\choose s$ ways of choosing which types of element you get. No doubt one could make a formula out of that, but there would be little to distinguish such a formula from an algorithm.

-
Thank you very much for your explanation. Probably I am not very familiar with the notation for this kind of problems, so in eq. (1) I don't understant de meaning of $x_{j_{m}}$ or $n_{j_{m}}$. Also, if there is a standard way to solve eq. (1), could you point me to any reference? Thank you very much! – Ricard Dec 4 '12 at 10:14
$n_{j_m}$ is the number of bags containing element $j_m$. $x_{j_m}$ is how many of those bags you pick. Pretty much any introductory discrete math or combinatorics text will tell you how to solve (1), how to find the number of ways of getting $s$ numbers that add up to $i$, with inequality constraints on the numbers. Sometimes, it goes by the name "stars and bars," and it has been discussed many times on this website. – Gerry Myerson Dec 4 '12 at 11:27


text:
## Cryptology ePrint Archive: Report 2011/194

Cryptanalysis of Chen \textit{et al.}'s RFID Access Control Protocol

Masoumeh Safkhani, Nasour Bagheri and Majid Naderi

Abstract: Recently Chen \textit{et al.} have proposed a RFID access control protocol based on the strategy of indefinite-index and challenge-response. They have claimed that their protocol provides optimal location privacy and resists against man in the middle, spoofed tag and spoofed reader attacks. However, in this paper we show that Chen \textit{ et al.} protocol does not provide the claimed security. More precisely, we present the following attacks on the protocol:

\begin{enumerate} \item Tag impersonation attack. \item Reader impersonation attack. \item Location traceability attack. \end{enumerate} All attacks presented in this paper have the success probability of '1' on the cost of only one or two runs of protocol.

Category / Keywords: cryptographic protocols / RFID, Access Control, Spoofed Reader Attack, Authentication, Desynchronization Attack.

Date: received 15 Apr 2011, last revised 15 Apr 2011

Contact author: nbagheri at srttu edu, na bagheri@gmail com

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Short URL: ia.cr/2011/194

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