Latest Discussions - COMSOL Forums https://www.comsol.com/forum/ Most recent forum discussions Tue, 27 Sep 2022 12:07:43 +0000 COMSOL Forum: Latest Discussions https://www.comsol.com/shared/images/logos/comsol_logo.gif https://www.comsol.com/forum/ higher order derivatives using general form PDE https://www.comsol.com/forum/thread/313771/higher-order-derivatives-using-general-form-PDE?last=2022-09-27T12:09:53Z <p>Greetings all,</p> <p>is it possible to use higher order derivatives in the PDE(g) modul, for example: <img class="latexImg" src="data:image/png;base64,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" /> = u1xx</p> <p>Thanks</p> Tue, 27 Sep 2022 12:07:43 +0000 4.2022-09-27 12:07:43.313771 wave optics: scatterer-on-substrate https://www.comsol.com/forum/thread/313761/wave-optics-scatterer-on-substrate?last=2022-09-27T11:46:28Z <p>I am very confused that when solving the scattering cross section of the scatterer-on-substrate, periodic boundary conditions are used in this model. Is this the scattering cross section of a single particle or the scattering of a periodic particle array?I express my appreciation for your views on this issue. The model link is as follows: http://cn.comsol.com/model/scatterer-on-substrate-14699.</p> Tue, 27 Sep 2022 11:46:28 +0000 4.2022-09-27 11:46:28.313761 How can I simulate noise floor of a piezoelectric sensor? https://www.comsol.com/forum/thread/313741/How-can-I-simulate-noise-floor-of-a-piezoelectric-sensor?last=2022-09-27T07:07:36Z <p>Hello all I am simulating a accelerometer. I want to simulate the noise floor of the accelerometer at low frequency? can anyone please help me for the same?</p> Tue, 27 Sep 2022 07:07:24 +0000 4.2022-09-27 07:07:24.313741 How add a weak constraint to limit the displacement https://www.comsol.com/forum/thread/313711/How-add-a-weak-constraint-to-limit-the-displacement?last=2022-09-28T01:43:32Z <p>Hi I have a model that simulates an upward(+z) large pressure on the diaphragm. And want to set a limit on the amount of displacement "w" , such as 5[um], to imitate the diaphragm being confined by a housing. I'm thinking this should be possible using weak constraint.</p> <p>Firstly, I try it only on the center point of the diaphragm. I use a "Point Probe" to acquire displacement "w" of the the center point with vaiable name "BP_center_w" . Then, add a point "Weak Inequality Constraint" and enter "comp1.BP_center_w - 5[um]" in the Constraint expression, 1e6 for spring contant of Penalty Method. This setting can work!</p> <p>Next, I try to set the whole upper boundary of the diaphragm. So, with settings like: Use a "Boundary Probe" to acquire the max. displacement "w" of the whole upper boundary with vaiable name "BP_w" . Then, add a boundary "Weak Inequality Constraint" and enter "comp1.BP_w - 5[um]" in the Constraint expression, 1e6 for spring contant of Penalty Method. However, this setting doesn't work.</p> <p>I don't understand why this happens. Do anyone can tell me how can I set it up to achieve my desired conditions?</p> <p>Thanks.</p> Tue, 27 Sep 2022 03:55:41 +0000 4.2022-09-27 03:55:41.313711 Calculating S-parameter of a meta-atom in a supercell of electromagnetic metasurfaces https://www.comsol.com/forum/thread/313702/Calculating-S-parameter-of-a-meta-atom-in-a-supercell-of-electromagnetic-metasurfaces?last=2022-09-27T03:51:01Z <p>I am interested in investigating <strong>mutual coupling effect among meta-atoms in an aperiodic metasurface</strong>. Please see the figure attached below (tmp3.png) for illustration. Here I am considering some geometric perturbations of a split ring resonator (tmp1.png shows an example).</p> <p>What I would like to compute is <strong>the transmission and phase delay (or S-paramter) of the center meta-atom</strong>. If there were no geometric perturbations, the computation would have been straightforward: using a single unit cell with peridoic boundary conditions, I can easily retrieve the S-parameter, using the built-in global evaluation in Comsol (e.g., emw.S21). But under my simulation setup with the perturbation, I try to calculate the S-paramater of a single meta-atom (or transmission and phase delay, equivalently), which would involve some deviation that obtained under the periodic boundary condition.</p> <p>(Q1) Can I still retrieve the information? It need not be done by built-in functionalities in Comsol; it is also fine to compute the value via some snippet in Comsol with Matlab. I am aware that the equations on S-parameters are provided in User Guide of RF Module (tmp2.png, attache below). <strong>I would like to introduce a user-defined expression to employ the equations and calculate them</strong> (maybe using some surface integration?), if this works, but am not sure of how.</p> <p>Lastly, I am only interested in the S-parameter of the center meta-atom. But in order to take into account the mutual coupling effect, perhaps I need to excite the whole top face (the blue region in tmp1.png) as the input port, while the S-parameter of my interest will only involve the contribution by the green region in the figure. (Q2) <strong>Can I only get the S-parameter between the two regions (green and red), without running port sweep?</strong></p> <p>Any help or comments would be greatly appreciated. I can share further details if necessary.</p> <p>Thank you, Doksoo</p> Tue, 27 Sep 2022 03:44:04 +0000 4.2022-09-27 03:44:04.313702 Problem with selecting Multiphysics Domain/Boundary in Electromechanic Boundary Element Module https://www.comsol.com/forum/thread/313692/Problem-with-selecting-Multiphysics-DomainBoundary-in-Electromechanic-Boundary-Element-Module?last=2022-09-26T22:55:09Z <p>Hello,</p> <p>I am trying to use Electromechanic Boundary Element for finding the vertical displacemnt of a cantilever (horizontal beam named as Electrode 2 (middle electrod)), due to electrostatic force of two fixed vertical Electrodes (Electrode 1 and 3) in a stationary step.</p> <ul> <li><p>The fixed electrodes 1 and 3 have the Voltage of V=0 volte and the cantilever (Electrode 2)'s voltage sweeping through different numbers. Also there is a constant pressure applided on the cantilever(Electrode 2).</p></li> <li><p>All the geometries are selected for Electrostatic Boundary Element Domain.</p></li> <li><p>Electrod 2(Cantiever) is also selected for Solid Solid Mechanics domain.</p></li> </ul> <p>The problem is that I cannot select any domain or boundary for the Electromechaical Interface (Multiphysics).</p> <p>I have attached the model here. Please help. Thank you</p> Mon, 26 Sep 2022 22:55:09 +0000 4.2022-09-26 22:55:09.313692 Thickness of Arrows in Arrow Plot https://www.comsol.com/forum/thread/313691/Thickness-of-Arrows-in-Arrow-Plot?last=2022-09-26T12:38:08Z <p>Hi everyone! Does anyone know of a way to make the arrows in Arrow Plot thinner (i.e. of smaller diameter) without changing their length? I need to visualize the process in which two vectors are at about 5-degree angle to each other. The default arrows are too thick and you can't see the process clearly (see screenshot).</p> Mon, 26 Sep 2022 12:38:08 +0000 4.2022-09-26 12:38:08.313691 MEMS Electrode Stress Deformation https://www.comsol.com/forum/thread/313681/MEMS-Electrode-Stress-Deformation?last=2022-09-27T19:03:05Z <p>Hello everyone,</p> <p>I am trying to simulate a MEMS beam model with gold electrodes on top. These electrodes are made from gold and are supposed to be used to read-out the deformation of the beam resonator through the piezoresistive effect. For this reason, I am interested in the strain of the gold and start with "Solid Mechanics" and a "Stationary" study. Since the beam structure has an intrinsic stress, this is something I considered in the model, but once I actually compute the "Stationary" study I get a lot of deformation, which is apparently due to the stress. In the end what I would like to do is put different external forces on the resonator and look at the change in strain or directly in resistance of the gold.</p> <p>Does anyone have experience with using two layers of material with similar thicknesses on top of one another?</p> <p>I included a picture of the deformation and the example project I described.</p> <p>Thank you very much in advance for any help you can provide. Johannes</p> Mon, 26 Sep 2022 12:01:15 +0000 4.2022-09-26 12:01:15.313681 Parametrized surface https://www.comsol.com/forum/thread/313671/Parametrized-surface-?last=2022-09-27T13:36:50Z <p>Hello everyone,</p> <p>I would like to visualize the result of a simulation on a parameterized surface, but I have a problem. In particular, COMSOL does not "see" part of the surface due to the deformation.</p> <p>Do you know how I can fix this?</p> Mon, 26 Sep 2022 11:48:15 +0000 4.2022-09-26 11:48:15.313671 Failed To Evaluate Variable. https://www.comsol.com/forum/thread/313661/Failed-To-Evaluate-Variable?last=2022-09-26T05:59:30Z <p>Hi, can any one help me solve these errors from my graduation project model? Emergency~~ Many thanks!</p> <p>The errors are:</p> <ul> <li>Feature: Time-Dependent Solver 1 (sol1/t1) Division by zero. <ul> <li>Function: / Failed to evaluate variable.</li> <li>Variable: comp1.gop.k2</li> <li>Defined as: 1/comp1.gop.r2 Failed to evaluate variable.</li> <li>Variable: comp1.gop.matd1.k_uui</li> <li>Defined as: (comp1.gop.k1&#42;(cos(comp1.gop.matd1.thetapi/unit_rad_cf)^2))+(comp1.gop.k2&#42;(sin(comp1.gop.matd1.thetapi/unit_rad_cf)^2)) Failed to evaluate variable.</li> <li>Variable: comp1.gop.matd1.k_uur</li> <li>Defined as: comp1.gop.matd1.k_uui-((2&#42;comp1.gop.matd1.k_uus)&#42;cos(comp1.gop.matd1.thetai/unit_rad_cf)) Failed to evaluate variable.</li> <li>Variable: comp1.gop.matd1.r1r</li> <li>Defined as: 1/(((comp1.gop.matd1.k_uur&#42;(cos(comp1.gop.matd1.thetapr/unit_rad_cf)^2))+((cos(comp1.gop.matd1.thetapr/unit_rad_cf)&#42;(2&#42;comp1.gop.matd1.k_uvr))&#42;sin(comp1.gop.matd1.thetapr/unit_rad_cf)))+(comp1.gop.matd1.k_vvr*(sin(comp1.gop.matd1.thetapr/unit_rad_cf)^2))) Failed to evaluate expression.</li> <li>Expression: comp1.gop.matd1.r1r</li> </ul></li> </ul> Mon, 26 Sep 2022 01:49:59 +0000 4.2022-09-26 01:49:59.313661 How to Simulate the Energy Storage Density and Efficiency of Materials https://www.comsol.com/forum/thread/313631/How-to-Simulate-the-Energy-Storage-Density-and-Efficiency-of-Materials?last=2022-09-25T00:51:21Z <p>How to simulate the energy storage density and energy storage efficiency of energy storage ceramic whose material is 0.76NaNbO3-0.24 ( Bi0.5Na0.5 ) TiO3</p> Sun, 25 Sep 2022 00:51:21 +0000 4.2022-09-25 00:51:21.313631 Vanadium Redox Flow Battery, Undefined values https://www.comsol.com/forum/thread/313601/Vanadium-Redox-Flow-Battery-Undefined-values?last=2022-09-23T13:30:48Z <p>The below post is related to an <a href="//www.comsol.com//forum/thread/37522/undefined-value-found">archived discussion</a></p> <hr /> <p>[start here]</p> <p>Hi,</p> <p>I have the same issue as reported in an earlier post 9 years ago. Is there a fix for this problem?</p> Fri, 23 Sep 2022 13:30:48 +0000 4.2022-09-23 13:30:48.313601 Compressible Euler equations https://www.comsol.com/forum/thread/313591/Compressible-Euler-equations?last=2022-09-23T10:16:40Z <p>I want to model the 1D inviscid compressible Euler equations without using the predefined physics node.</p> <p>I have three PDEs: - for density rho: <img class="latexImg" src="data:image/png;base64,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" /> - for velocity u: <img class="latexImg" src="data:image/png;base64,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" /> - for temperature T: <img class="latexImg" src="data:image/png;base64,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" /></p> <p>Using the EOS, the pressure term in the velocity equation can be rewritten into <img class="latexImg" src="data:image/png;base64,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" /></p> <p>Instead of using the Compressible Euler Equations node, I have added three General Form PDE nodes. Unfortunately, COMSOL throws the "Repeated error test failures. May have reached a singularity." error. What can be the cause of this?</p> Fri, 23 Sep 2022 10:12:56 +0000 4.2022-09-23 10:12:56.313591 OTFT simulation in comsol´╝č https://www.comsol.com/forum/thread/313573/OTFT-simulation-in-comsol?last=2022-09-23T17:59:16Z <p>I want to simulate the OTFT device, use pentacene as the channel, and simulate its electric field distribution and heat distribution under ESD stress. Is there any relevant case support?</p> Thu, 22 Sep 2022 10:43:27 +0000 4.2022-09-22 10:43:27.313573 Measuring Electric Field Depth in a multi-slice model https://www.comsol.com/forum/thread/313562/Measuring-Electric-Field-Depth-in-a-multi-slice-model?last=2022-09-22T01:56:38Z <p>I am trying to measure the penetration depth of an electric field into a multi slice model. Currently the electric field is shown with electric field lines but I am unsure of how to get a value for that depth of penetration. !</p> Wed, 21 Sep 2022 21:11:59 +0000 4.2022-09-21 21:11:59.313562 Heat flux thru a surface https://www.comsol.com/forum/thread/313552/Heat-flux-thru-a-surface?last=2022-09-21T12:09:34Z <p>New user here. How do I set up a table showing heat flux across a surface? I'm interested in doing this for both solid (non-moving) and fluid ( with flow ) boundaries.</p> <p>the derived terms look like the right place to start, but I'm seeing very weird results when I integrate temp over an area. ( average seems to work )</p> <p>Thx.</p> Wed, 21 Sep 2022 12:09:34 +0000 4.2022-09-21 12:09:34.313552 ISFET Tutorial Changing Dimensions https://www.comsol.com/forum/thread/313551/ISFET-Tutorial-Changing-Dimensions?last=2022-09-21T14:39:47Z <p>Hello,</p> <p>I am attempting to run some simulations with the ISFET tutorial but I would like to change the dimensions of the isfet to be more similar to modern devices. Does anyone have some experience with this? I cannot seem to find all the parameters that need to be changed to run a succesful simulation.</p> Wed, 21 Sep 2022 09:32:41 +0000 4.2022-09-21 09:32:41.313551 Selection based on boundary area https://www.comsol.com/forum/thread/313542/Selection-based-on-boundary-area?last=2022-09-20T14:09:17Z <p>There is any way to perform geometry boundary selections based on their surface area?</p> <p>I ask because i have many designs and they have to run on same mesh, so every time i update The geometry i lost my selections.</p> Tue, 20 Sep 2022 14:09:17 +0000 4.2022-09-20 14:09:17.313542 How to calculate effective dielectric constant? https://www.comsol.com/forum/thread/313541/How-to-calculate-effective-dielectric-constant?last=2022-09-20T13:53:41Z <p>Greetings to all,</p> <p>I have recently started using COMSOL to simulate a system from which I want to calculate the effective dielectric constant. I contruct the system as follows:</p> <ol> <li>I generate a "bulk" material_1 (rectangular shape)</li> <li>I generate N circles to represent particles of material_2; unite these circles (dont keep input objects nor interior boundaries)</li> <li>I make the difference between material_1 and material_2 systems, keeping both input objects and interior boundaries;</li> <li>On electrostatics physics I set the lower edge of material_1 to be ground and upper edge to be the electric potential;</li> </ol> <p>At this point, from this construction I want to calculate mostly the effective dielectric constant, but if I can calculate effective resistivity and piezoelectric constant would be great as well. I do my simulations on Static solver but I also tried Frequency domain (1 kHz to 1 MHz) and the results do not change. Moreover, for such simulations I have already done their experimental counterparts so I know what to expect.</p> <p>How do I calculate the effective dielectric constant and my simulations appear to be incorrect?</p> <p>Best regards,</p> <p>VR</p> Tue, 20 Sep 2022 13:31:52 +0000 4.2022-09-20 13:31:52.313541 not sure where the problem is https://www.comsol.com/forum/thread/313531/not-sure-where-the-problem-is-?last=2022-09-19T09:59:09Z <p>I have built here a simple model with PDMS(0.4 to 20 um). I have been trying to plot the graph for visible spectrum(0.3 to 1.1) but I am not getting any results. For the same model I am getting results above 4um wavelength. I have used mesh size of extremely fine and for selective boundaries/domain I used 0.3/3, this is the least mesh I could use or it runs out of memory. Could someone please help in figuring it out where I am making mistake. really appreciated. Thank you</p> Mon, 19 Sep 2022 09:59:09 +0000 4.2022-09-19 09:59:09.313531