Geometry - Science topic

Thanks for your help,

I learned that the error is not an error.

Energy error is just a difference between optimization steps.

Addressing the Mixing-Cell and Single-Cell Approach in Predicting MMPs

The mixing-cell approach is often preferred over the single-cell approach for predicting Minimum Miscibility Pressures (MMPs) in condensing/vaporizing gas drives because it better accounts for the multi-stage, dynamic interactions between the injected gas and the reservoir oil. Below are the key reasons for its superiority:

Field-Scale Relevance of MMP and Multi-Contact Miscibility

Laboratory and Field Modeling Challenges

Summary

The mixing-cell approach provides a better forecast for MMPs because it models the dynamic, multi-contact interactions between gas and oil more realistically, capturing the essence of miscibility development in condensing/vaporizing drives. While it simplifies field-scale phenomena, it is a more reliable predictor compared to the single-cell approach. For field applications, integrating MMP predictions with advanced reservoir simulations that account for heterogeneity and coupled physical processes is essential for optimal CO₂ EOR design.

Hi Sina,

I would guess that the set name should not contain a slash.

Regards,

Simon

Greetings. The reciprocal of the time step size is one divided by the time step size. The bigger the steps, the smaller the value. In most default transient solvers, COMSOL has the flexibility to increase or decrease the time step size as it sees fit. In your case, it seems your time step size remains constant after a certain period. A constant step size (time, space, or frequency) indicates predictability and often reduces computational overhead because the solver does not need to continuously adjust.

Thanks for the answer. The steps are pretty clear, but I will let you know if I need to add anything else.

In techplot, you need to go to the Data>Create Zone>Mirror.

Then create your zone of symmetry and display as you want to display your contours.

Geometry optimization isn't mandatory for PubChem compounds unless your research requires high precision calculations or specific conformational analysis.

1. Use PubChem structures directly for preliminary work

2. Optimize only when high accuracy is required

3. For large screenings, initial PubChem geometry is usually sufficient

Thanks very much Lucas! This solved my problem. I used NRoots = IRoot + 2.

Gives a good result

To find the tangential line, we need to determine the tangent vector at the point on the helix. Since the helix has a constant radius, we can use the following parametric equations:

x = r_cos(t)

y = r_sin(t)

z = t*(height/turns)

where r = 2.5 mm, height = 2 mm, turns = 2, and t is the parameter.

First, let's find the derivative of the position vector for t:

dx/dt = -r_sin(t)

dy/dt = r_cos(t)

dz/dt = height/turns

Now, we need to find the point on the helix where the line will be drawn. Let's assume the point has a parameter value t = t0. Then, the coordinates of the point are:

x0 = r_cos(t0)

y0 = r_sin(t0)

z0 = t0*(height/turns)

Next, we evaluate the tangent vector at the point (x0, y0, z0):

T = (-r_sin(t0), r_cos(t0), height/turns)

Now, we can use the tangent vector T to define the direction of the line. The line will pass through the point (x0, y0, z0) and have the direction vector T.

To draw the line, you can use the following steps in AutoCAD:

1. Create a helix using the "Helix" tool with the given parameters (radius = 2.5 mm, height = 2 mm, turns = 2).

2. Select the point on the helix where you want to draw the tangential line (x0, y0, z0).

3. Use the "Tangent" snap (F9) to snap to the tangent direction at the selected point.

4. Draw a line from the selected point in the tangent direction using the "Line" tool.

Alternatively, you can use geometry software like GeoGebra or Mathematica to visualize and compute the tangent line.

Obaidullah Bhuiyan Welcome. There is no way to select this. You have to optimize them by putting different values. Try to start with lower values and find where the total energy is minimum. To get an idea about the cutoff energy and k-point values to start with you can take help on any published paper about the material or the materials in the same group. Thanks.

Increasing the k-point grid density makes the calculation more computationally demanding, especially for spin-polarized systems. Make sure that your PC or laptop can handle the software. For this software to run, high configured PC or laptop is needed.

1. Try to increase the self-consistent field (SCF) convergence threshold

2. For cubic perovskite, the k-point is between 3x3x3 or 4x4x4 or 5x5x5 or 6x6x6. Not more than that.

3. Try to optimize with low cut-off energy.

4. Try setting a less strict force convergence tolerance initially and gradually increase it after reaching an intermediate optimized structure.

5. Ensure all file paths are accessible and that there are no restrictions on the directories where the output files are saved. Also, verify that no temporary files are left from previous runs that could interfere with the current job.

6. The "Abort" error could indicate that the node or process is running out of memory or computational resources, especially if you're using a high cutoff energy (500 eV) and a large k-point grid (e.g., 10x10x10).

Thanks.

Steftcho P. Dokov Your approach is correct, my solution is the same.

The essential is the fact that the two cevians from A , AO and the perpendicular from A to PN, make equal angles with the sides AB and AC of triangle ABC( we say that the two cevians are isogonal cevians) due to the fact that quadrilateral APON is inscriptible. Analogous, BO and the perpendicular from B to PM, CO and the perpendicular from C to MN are pairs of isogonal cevians.

Now all we have to make is to apply Ceva's theorem, Steiner's ratio theorem and the reciprocal Ceva's theorem.

Independent of current problem, the following theorem can be obtained using Ceva's theorem, Steiner's ratio theorem and the reciprocal Ceva's theorem:

THEOREM 1: In a triangle the isogonals of three cevians having a common point are three cevians which have a common point.

Steiner's theorem is a generalization of bisector theorem in a triangle:

THEOREM (Steiner) Let AM, AN be two isogonal cevians in triangle ABC, with M,N on BC. Then (AB^2)/(AC^2)=(BM*BN)/(CM*CN).

Clearly, when M and N move towards each other( conserving the property of Isogonality), lines AM and AN will be identical, representing the bisector of angle BAC.

Steiner's ratio theorem can be proved constructing two pairs of similar triangles, or simpler, using areas of triangles( the most famous proofs).

Now I think is clear how THEOREM 1 can be proved.

Regarding the problem from above question, it's possible to obtain a solution intersecting two perpendiculars, from A and B, let us say, in a point S, then proving CS is orthogonal to MN. I think is not easy!

Wow!

Above text is brillant !!!

Since it seems open ended and expanding,

Hyperbolic works better than elliptic?

Right at the beginning, when the geometry icon opens.

Alvin Molberg Will try it but your answers seems to me like it is generated with ChatGPT ;)

Dear Sarawud Saleesongsom ,

just a crazy idea...

You may acquire a second glass reactor and cut the upper part.

After that you may arrange the sensor of the power meter upside down inside the reactor close to the inner wall, as indicated in the attachment.

You will get a rough estimate about the UV intensity there.

When the reactor is filled with the liquid you will have a bit higher intensity close to the inner wall because of the lack of a sharp jump of the refractive index at the glass to liquid interface.

Good luck and

best regards

G.M.

I'm not sure how you would use a circular specimen geometry to measure fracture toughness using a J-integral method. You will likely need to provide more details of your testing methodology in order for others to weigh in.

After trigonotric solution (pretty tedious way, not worth publication) I have found a geometric way same as Dinu Teodorescu, but in a somehow different order:

If one adds to the pic by Liudmyla Hetmanenko the center O of AB , then the following becomes clear:

property 1. AO=CO, which implied ∠CAO = ∠ACO =2 α

property 2. CD=CO, which implies that D and O lie on a circle with center at C

property 3. ∠DBO = α = 0.5 ∠DCO, which implies that D,O and B lie on a circle with center at C, which in turn imples that CB=CD, which means that

3 α = π/4 radians = 15^o

Alex Ravsky Sorry for not read carefully the last part of your comment! Yes, in fact a lot of triangles with lenghts 1, 1, m do not admit the second solution! To have 2 solutions, condition 2-2cosA<=1/2 i.e. cosA>=3/4 is necessary! Very restrictive and cosA>=3/4 an weird limitation for angle A.

Liudmyla Hetmanenko A nice and interesting problem!

Dear Ivan A. Trussov ,

the fact, when shifting the primary slit towards the sample and then the background onset shifts a bit, may show that you struggle with Compton scatter from parts of the sample support which are left and/or right to the net expected beam footprint at the sample surface. You should mask (cover) these areas with a bit of lead foil (strips) or similar strong absorbing foil. For a first trial, the gap between these shield(s) may be (a bit) smaller than the sample width.

Just have a look what happens to your background...

Good luck and

best regards

G.M.

Dinu Teodorescu Steftcho P. Dokov

Dear colleagues,

I am grateful for your interest in my geometric problem. Both of your solutions are correct and they are excellent!

I also want to express my heartfelt appreciation for your words of support for my country during these difficult times.

Draw a triangle on a sphere with a base on the equator.

The internal angles are more than 180 deg.

Thats Elliptic for Ellipse , circle is special case rotate and you get sphere.

Galilean is like ordinary Eucledian space

Does your device ensure laminar or turbulent motion of fluid?

Thats correct

Metric space in math is space with a

Distance.

Simply, go to the design modeller/ File/ Open and see the files which can be imported by the DM.

Why you don't design your blade geometry using ANSYS/ BladGen?

Use crystal field theory. You have a 3d⁷ metal with four strong field ligands. If you compare the tetrahedral and square planar geometries for this case, you should find that square planar gives a larger CSFE because of the big Δ.

try this input and run it different in full path name :

! B3LYP 6-311G NormalPrint Grid3 FinalGrid5 NOSOSCF

%pal nprocs 32 end

%scf

MaxIter 99999

end

%output

print[P_AtCharges_M] 1

print[P_AtCharges_L] 1

end #output

* xyz 0 2

O 6.52685 -0.73958 -0.60612

O 6.00262 -1.67364 1.36686

N 0.02656 1.02768 -0.14143

N -1.96580 -1.10331 0.21717

N -2.14235 2.92651 0.10135

N -4.01394 0.76086 0.44309

C 2.28855 0.42545 -0.42274

C 2.19580 1.88101 -0.46468

C 0.91718 -0.07010 -0.22669

C 3.54463 -0.36382 -0.56170

C 0.78607 2.20981 -0.28425

C 3.32043 2.84128 -0.65602

C 4.48542 -0.06213 0.59139

C 0.28815 3.45265 -0.25755

C -2.92922 -2.05161 0.38431

C -1.13332 3.80888 -0.07277

C 5.72390 -0.88460 0.47560

C -1.61130 5.10437 -0.05281

C -4.22648 -1.77583 0.55990

C -2.97758 5.01700 0.14249

C -3.26625 3.66749 0.23242

C -4.78734 -0.41009 0.59448

C -6.20792 -0.04567 0.78294

C -0.79409 6.34344 -0.21226

C -4.93426 1.82287 0.53553

C -6.28304 1.28839 0.74599

C -4.62309 3.12217 0.44428

C -7.40736 -0.93939 0.98445

C -3.96952 6.10751 0.24266

C -7.53241 2.09796 0.89398

C -3.64660 7.39609 0.15056

C 7.68363 -1.46287 -0.77870

C 0.43867 -1.47026 -0.11628

C -0.83713 -1.81563 0.07726

C 1.16544 -2.77232 -0.18274

C 0.23678 -3.78127 -0.01692

C -1.04183 -3.13945 0.14773

C -2.38149 -3.34113 0.34626

C -3.08246 -4.64855 0.48648

N 0.56372 -5.09275 -0.02589

C 1.86711 -5.45840 -0.20700

C 2.87912 -4.46116 -0.38749

C 2.50060 -3.10065 -0.37134

C 4.31844 -4.78149 -0.59510

O 4.74862 -6.06913 -0.61164

C 6.06101 -6.43909 -0.81471

C 6.43157 -6.29546 -2.28009

O 5.12041 -3.86953 -0.75075

C 2.17416 -6.91743 -0.21020

C -7.08726 -2.42226 0.99213

*

Thank you Leonard. That was really helpful.

Reference 1 is not a publication at all.

Reference 2:

1) It's an SCIRP publication. SCIRP's academic integrity is under severe doubts so I would not rate that very serious.

2) If you look into it, you see that the author modifies the Scrödinger equation, so it does not support your claim.

3) It also writes about general relativity which is not part of the Schrödinger equation.

In reference 3 you also refer to a predatory publisher (https://www.researchgate.net/post/Are-international-organization-of-scienctific-research-IOSR-and-Journal-of-ChemistryEducation-research-and-practice-predators-journals-or-real), so this is also not a serious support for any claim.

Jeff Sokoloff has articles in this topic.

An incommensurate intermediste layer will lower friction.

The concept of coordination of reflection and action, as well as network synchronicity for conscious states, aligns well with the Interactive Universe Theory (IU Theory). Here’s how I see it through the lens of IU Theory:Coordination of Reflection and ActionIn IU Theory, consciousness is viewed as the fundamental fabric of reality. This field processes and integrates information continuously, which allows for the coordination of reflection (awareness) and action (responses). The dynamic nature of this field ensures that conscious states are not just static phenomena but are continuously evolving and adapting based on interactions within this field.Network SynchronicityThe idea of network synchronicity is crucial for conscious states. IU Theory posits that everything in the universe is interconnected through the consciousness field. This interconnectedness ensures that information is synchronized across different scales, from the microscopic to the macroscopic. This scale-invariant nature of consciousness supports a universal information matrix, akin to what you described as the implicate order.Field-Receptive Resonant WorkspaceIU Theory suggests that the brain, while a crucial interface, is not the sole repository of consciousness. Instead, it interacts with the broader consciousness field. This resonates with the idea of a field-receptive resonant workspace, which is associated with, but not reducible to, the brain. This workspace allows for the integration of transpersonal conscious states, providing a framework for understanding phenomena that go beyond individual experiences.Deep Connection with the CosmosIU Theory emphasizes the deep connection between humanity and the cosmos. By seeing consciousness as the underlying fabric of reality, it highlights our intrinsic connection to the universe. This perspective underscores the importance of our actions and decisions, not just for individual well-being but for the future of our planet and the cosmos at large.Responsibility and Conscious EvolutionRecognizing this deep connection places a significant responsibility on humanity. Our conscious evolution and the choices we make are pivotal in shaping the future of our planet. By understanding and integrating these insights, we can align our actions with the broader consciousness field, promoting harmony and sustainability.I believe IU Theory provides a comprehensive framework that aligns with and expands on the concepts you've highlighted. It integrates physical phenomena with the metaphysical aspects of consciousness, offering a unified understanding of reality.

Hi. Use a command in a snippet.

Et,1,45

Jeevan Dhungel Measuring human perception towards the geometry and configuration of built structures involves a combination of quantitative and qualitative methodologies. Here are some common approaches:

1. Surveys and Questionnaires

2. Interviews and Focus Groups

3. Behavioral Observations

4. Psychophysiological Measures

5. Virtual Reality (VR) and Augmented Reality (AR)

6. Cognitive Mapping and Sketching

7. Photographic Surveys

8. Case Studies and Ethnography

9. Post-Occupancy Evaluations (POE)

Combining these methodologies can provide a comprehensive understanding of human perception towards the geometry and configuration of built structures. Each method has its strengths and can provide unique insights that contribute to a holistic view of how people experience and interpret their built environment.

Hi,

Yes, of course, this issue was discussed in section 4.2 of this paper:

Dear Nils Wagner

Thank you very much for your detailed explanation. I previously followed a process similar to your suggestion, and it worked very well. However, for my recent study, it is impractical to use more than two commercial software programs.

There are two main reasons for this:

However, I will keep your suggestion in mind as an alternative solution.

Once again, thank you for your time and response.

Warm regards,

Mirhan

another way ... construct an equilateral triangle ADE with side AD where point E is located outside the triangle ABC (on the right side of line AC) ... find 2 congruent triangles:

ABE and BAC

because AB is a common side, AE = BC, and the angle between these corresponding sides is 80 degrees, ... therefore BE=AC

next, triangle ADB is congruent to to triangle EDB

because both triangles have 3 equal sides,

thus, angle ABD = angle EBD = a half of 20 ... etc.

Akhil Chakravarthy

Sure, I can help you with that. Here's a Python script that can read the GAMESS `frequencies.log` file and extract the distortion geometries along the frequency modes:

```python

import re

def read_gamess_frequencies(filename):

"""

Reads the GAMESS frequencies.log file and returns the distortion geometries

along the frequency modes.

Args:

filename (str): Path to the GAMESS frequencies.log file.

Returns:

dict: A dictionary where the keys are the frequency mode numbers and the

values are the corresponding distortion geometries.

"""

distortions = {}

with open(filename, 'r') as file:

lines = file.readlines()

# Find the start of the frequency modes section

start_index = None

for i, line in enumerate(lines):

if line.startswith(' FREQUENCY'):

start_index = i

break

if start_index is None:

return distortions

# Iterate through the frequency modes section

for i in range(start_index + 1, len(lines)):

line = lines[i]

# Check if the line starts with a mode number

match = re.match(r'^\s*(\d+)\s*$', line.strip())

if match:

mode_num = int(match.group(1))

distortion = []

# Read the distortion geometry for the current mode

i += 1

while i < len(lines) and lines[i].strip():

distortion.append(lines[i].strip())

i += 1

distortions[mode_num] = '\n'.join(distortion)

return distortions

```

You can use this function by providing the path to the `frequencies.log` file:

```python

distortions = read_gamess_frequencies('path/to/frequencies.log')

```

The function will return a dictionary where the keys are the frequency mode numbers and the values are the corresponding distortion geometries.

For example, if the `frequencies.log` file contains the following content:

```

FREQUENCY NO. 1 25.6356 CM(-1)

1 -0.1358 0.0095 -0.0285

2 0.0095 0.1268 -0.0169

3 -0.0285 -0.0169 0.0993

FREQUENCY NO. 2 39.1266 CM(-1)

1 0.0497 -0.0997 0.0169

2 -0.0997 -0.0896 -0.0216

3 0.0169 -0.0216 0.1892

```

The `read_gamess_frequencies` function will return the following dictionary:

```python

{

1: '-0.1358 0.0095 -0.0285\n0.0095 0.1268 -0.0169\n-0.0285 -0.0169 0.0993',

2: '0.0497 -0.0997 0.0169\n-0.0997 -0.0896 -0.0216\n0.0169 -0.0216 0.1892'

}

```

The keys are the frequency mode numbers, and the values are the corresponding distortion geometries.

Good luck; partial credit AI

R = short answer = AO_1 + AO_2

Let points D and E denote the common tangent points where the big circle touches the two small circles, and point C be the intersection point of the tangent lines at the points D and E.

First, there is a circle which passes through the points O, D, C, E, and A, because the line segment OC is seen from the points D, E, A under right angle.

Next, angle O_2AE = angle AEO_2 = say = a = angle ADO = angle DAO_1, thus angle OO_1A = angle OO_2A = 2a.

Second, angle OAO_2 = angle AOO_1 because

angle OAO_2 = is measured by the following arcs = -OA + OA + AEC + CD = -OA + pi/2 + CD,

and similarly,

angle AOO_1 = measured by the arc DCEA = DC + CEAO - AO = DC + pi/2 - AO.

Hence, triangles AOO_1 and AOO_2 are identical - they have a common side and 2 equal angles.

Thus, AO_1 = OO_2, so AO_1 + AO_2 = OO_2 + AO_2 = OO_2 + EO_2 = OE = R.

Apparently, both share same length OO1 = OO2 = 📷 = sqrt(R*R - R1*R2)

Cristhian, what version of the Anton Paar software are you using? It seems to me that is RheoPlus. Not RheoCompass, am I right on it? Usually, the software itself made all calculations, showing you Stribeck curves, with the friction coefficient as a function of sliding distance OR sliding speed. Look below. Vs in [m/s] as you want. Good luck, Antonio Bombard

Take a Cartesian coordinate: let C be the original, DM and DC be the x-axis and y-axis. Let AD=a, DB=b, CQ=x, then C=(0, 0), D=(0,-h), B=(b,-h),A=(-a,-h), etc.. From AC perpendicular to BC, we have h^2=ab; and from CN perpendicular to QM, we have -4ab+h^2+hx=0. Now we can see that

x=3h.

These self-similar patterns are the result of a simple equation or mathematical statement. You create fractals by repeating this equation through a feedback loop in a process called iteration, where the results of one iteration form the input value for the next.

A priori I would say that you would need to optimise again the structure. While you might get something better than the initial configuration you might need to optimise again your structure. Indeed, this comes from the fact that the forces are evaluated starting from the electronic ground state.

The presence of a spin-polarisation changes that ground state and the occupation of the atomic orbitals thus producing forces different from the un-polarised case. (This would be a problem with any optimisation step, irregardless if you are using a DFT or more sophisticated methods.)

If you calculation is particularly heavy, you might try and evaluate the forces again when you perform the polarised calculation. Clearly, the assumption is that the relaxed structure you have obtained from the un-polarised case is close enough to the polarised case and that they belong somehow to similar structures.

Regards,

Roberto

Relaxation NMR.

En cualquier caso, la velocidad de rotacion del rotor debe resultar elemento predominante para el emulsionamiento

In any case, the rotation speed of the rotor must be the predominant element

Liudmyla Hetmanenko , Steftcho P. Dokov Not necessarly to consider two pairs of similar triangles, because:

quadrilaterals CFKE_1 and BFKE_2 are inscriptible, so

1. angle FKE_1=angle FKE_2 (= 180-C=180-B)

2. angle FE_1K=angle FCK=1/2 arc KB=angle KBE_2=angle KFE_2,

then triangles E_1KF and FKE_2 are similar, and from here KE_1/KF=KF/KE_2 which implies KF = 12

NOTE: Trying to understand Yosef M. Yoely's answer I have some doubts! First, I thought Yosef quickly saw the similarity of triangles E_1KF and FKE_2! If not, maybe Yosef told himself that quadrilaterals CFKE_1 and BFKE_2 are similar because they have equal angles......=>conclusion.....which is not correct, two quadrilaterals with all equal angles are not necessarily similar (for example a square and a rectangle that is not a square !!).

Yes, using Time-Dependent Density Functional Theory (TD-DFT) combined with Molecular Dynamics (MD) simulations can be a viable approach to find conical intersections.

After all, what can general relativity say about the geometry of the Universe if it is a foliation on a seven-dimensional sphere with a typical layer R^3×S^3? And quantum mechanics says that this is so.

Farnaz Hosseini thank you madame for your interaction

This is what i thought too, can you describe the steps to calculate the parameters needed to calculate the nusselt.

There's two temperatures: the wall temperature and the mean(or mixing) temperature, i wanna make sure what i did is correct(i used the report definitions option to do this).

There's something confusing me: to calculate the nusselt number we need the heat flux exchanged betweeen the wall and the fluid can you tell me how to calculate it in fluent cuz i'm not sure about what i did.

Thank you again for your feedback madame.

Does a body fall in a gravitational field without passing time?

Original text (in French) see here:

Olivier Hakizimana

Theories which imply a violation of conservation laws are irrelevant by default. There is no specific proof necessary.

Dear Ajay Jayswal ,

When you are simulating quasi-static compression using ANSYS Workbench Explicit Dynamics, it's important to set up the simulation parameters properly to ensure accurate results such as:

If Automatic Mass Scaling is not working as expected, you may need to troubleshoot the issue or manually adjust the mass scaling settings. Additionally, consulting ANSYS documentation, forums, or seeking assistance from experienced users may help in resolving specific issues or optimizing simulation settings for your particular case.

I hope this helps you to achieve better results in your quasi-static compression analysis using ANSYS Workbench Explicit Dynamics. If you have any further questions, feel free to ask!

Dear Dr. Hafez,

This is a good theoretical work describing turbulent motion of fluid in pipes. In references of this article you can find experimental data. Best wishes, Oleh Shvydkyi.

Thank you for you answer Belyazid Abdellatif , if I understand it correctly, are you talking about the curvature of the earth, or the curvature of the cylinder? As I am wondering how big the cylinder need to be for you to not notice the curvature of the cylinder, not the curvature of the earth being obscured by the cylinder. Or are you meaning that the curvature of the cylinder can only be obscured by the inherent curvature of the earth? I thought that the curvature of the cylinder would be unnoticable at a smaller distance than caused by the curvature of the earth?