Properties Definition and 1000 Threads

I recall seeing briefing notes dating from about the 1970's that advocated doing stratified sampling of the outputs of simulations by using strata based on properties of the random number streams. However, I don't recall how the strata were to be defined. Is this type of stratified sampling a...

We know that when a magnet is exposed to high temperatures, it loses its magnetic properties. Why then does the Earth's magnetic field behave differently? That is, why doesn't the Earth lose its magnetic properties? According to BBC News Brasil, the core temperature is around 6000 ° C, higher...

This is probably a long shot but it's worth trying. My question is the following: What properties of dark matter can we derive from each of the available methods for probing the physics of dark matter? To elaborate a bit, my understanding is that the evidence for dark matter comes from its...

I am a First Year Undergraduate Physics student. Which will be the best textbook for me to study properties of matter (Elasticity) and fluid mechanics? I prefer a better theoretical understanding.

Is any way to get Rodrigues' rotation formula from matrix exponential \begin{equation} e^{i\phi (\star\vec{n}) } = e^{i\phi (\vec{n}\cdot\hat{\vec{S}}) } = \hat{I} + (\star\vec{n})\sin\phi + (\star\vec{n})^2( 1 - \cos\phi ). \end{equation} using SO(3) groups comutators properties ONLY...

I appreciate some helps with this question. I understand that soft noodles is not as strong as calamari squid and breaks easily . I also know that that calamari squid does not have elastic behaviour since behaves like rubber band and it goes back to it's original shape after reloading. But I'm...

a)plastic deformation because of permanent deformation b) the other parts that have been destroyed have stored the energy and this saved the passenger compartment. C) the alloy crash barrier is stronger than the car body and and saves more of the energy by deforming shape. I'm not sure about my...

Does scale factor must be continuous(Con.) and differentiable (Diff.) ? Or can it be one of them or neither ? Physically one expects it to be Con. and Diff. but is there a more rigorous proof. And as a separate question, if ##\dot{a}## is not continuous/differentiable in some case, does that...

I can't seem to figure out which chemical properties govern the physical property that is young's modulus. For example, any linear (or with a low degree of branching) polyethylene with no crosslinking is still a somewhat rigid and solid substance (higher ym), whereas the most linear possible...

Summary:: Please help me to determine the thickness of the material of the bicycle given, i need a step by step procedure. I know the formula required but can figure out the forces acting and reactions on the bicycle. The weight of the person riding the cycle is estimated to be 70-80kg Help me

In the solid state physics by Ashcroft & Mermin, in chapter 9 there is a paragraph that I would be grateful if anyone could explain it more for me. The paragraph is: As it said in chapter 12 it will be seen. I read chapter 12 but unfortunately I can't understand what exactly it want to say...

print ('Calculate threshold, power, slope efficiency for different lengths of SC Laser') g = 510 # The gain of the laser, arbitrary value of 510 m^-1 was picked I = np.linspace(0, 0.03,5) #DRIVE CURRENT; 100 values of current, 'I', between 0A and 0.03AV = 1.8 #INPUT VOLTAGE; arbitrary value of...

Hello everyone, Is there a straightforward way to determine the electrical properties, such as the dielectric constant (or function), of a molecule (for instance, a metal oxide)? I understand a simple weight-average model wouldn't work for various reasons. Thanks so much!

Hi, I have been having some trouble in finding the determinant of matrix A in this Q Which relevant determinant property should I make use of to help me find the determinant of matrix A and maybe matrix B also This is what I have tried for matrix A so far but it's not much help really Any...

screenshot to avoid typos I picked B just could see the others as definite insights?

I'm looking for a book series tabulating various mechanical and material properties for metals and alloys. There is a book series called "Thermophysical Properties of Matter" and it details the thermophysical properties of hundreds of elements and compounds (even including some obscure uranium...

So let's say that we have som unitary matrix, ##S##. Let that unitary matrix be the scattering matrix in quantum mechanics or the "S-matrix". Now we all know that it can be defined in the following way: $$\psi(x) = Ae^{ipx} + Be^{-ipx}, x<<0$$ and $$ \psi(x) = Ce^{ipx} + De^{-ipx}$$. Now, A and...

I'm not very sure whether a predicate can be neither true or false, and I haven't seen any example so far. The second choice is false because it is the truth set that is the set of all values which make the predicate true. A predicate has finite variables, so the third choice is false too. I...

Is it true that ##\frac{|a|}{|b|} = |\frac{a}{b}|## and ##|a| < |b| = a^2 < b^2##?

[Throughout we're considering the intrinsic version of the covariant derivative. The extrinsic version isn't of any concern.] I'm having trouble reconciling different versions of the properties to be satisfied by the covariant derivative. Essentially ##\nabla## sends ##(p,q)##-tensors to...

The following exercise was proposed by samalkhaiat here. The given Lorentz identities were proven here. We first note that ##d^4 k = d^3 \vec k dk_0##, the ##k_0## integration is over ##-\infty < k_0 < \infty## and ##\epsilon (k_0)## is the sign function, which is defined as $$\epsilon...

Hello all! I would like to know what chemical/physical properties influencies the specific heat. For example, why are specific heat of metals smaller than the specific heat of water, and why do ice and steam have a smaller specific heat than liquid water do.

I am trying to understand but without a succes why symmetric magnetic field around ##Z## axis make that ##\hat \phi## magnetic field is zero I can't understand why it physically happens and also how can I derive it mathematically? What does the word symmetric means when talking about magnetic...

My questions are as follows: 1. How do we find them and why do we need them? 2. What are the meanings of the mean and the median of a PDF? Are the formulae below correct? $$\int_{a}^{median} f(x) \mathrm{d}x = \int_{median}^{b} f(x) \mathrm{d}x$$ $$\int_{a}^{mean} f(x) \cdot x \mathrm{d}x =...

I have tried to write down the boundary conditions in this case and looked into them. As conditions i) and ii) were trivial, i looked into iii) and iv) for information that I could use. But all I got was that for the transmitted wave to have an angle, the reflective wave should also have an...

Hey! Let $1\leq n\in \mathbb{N}$, $V=\mathbb{R}^n$ and $\cdot$ the standard scalar multiplication. Let $b_1, \ldots , b_k\in V$ such that $$b_i\cdot b_j=\delta_{ij}$$ Let $\lambda_1, \ldots , \lambda_k\in \mathbb{R}$. Determine $\displaystyle{\left (\sum_{i=1}^k\lambda_i b_i\right )\cdot...

Hey! 😊 Let $G$ be a permutation group of a set $X\neq \emptyset$ and let $x,y\in X$. We define: \begin{align*}&G_x:=\{g\in G\mid g(x)=x\} \\ &G_{x\rightarrow y}:=\{g\in G\mid g(x)=y\} \\ &B:=\{y\in X\mid \exists g\in G: g(x)=y\}\end{align*} Show the following: $G_x$ is a subgroup of $G$. The...

Hello Everyone in the forum: I have a theoretical question about Worm Holes. So for the sake of this question let's just assume we have the technology and the power source to fire up a small human size worm hole. My question would be regarding the edge of the worm hole. Would you be able to...

To elaborate a little on what I think I do understand / accept: 1. I don't think I have a problem accepting the "weirdness" of quantum concepts. So, for example, I am willing to accept the concept that a quantum system can "exist" in a large number of different states simultaneously. 2. I...

I know the hyperbola of the form x^2/a^2-y^2/b^2=1 and xy=c; but coming across this question I'm put in a dilemma of how to proceed with calculating anything of it - say eccentricity or latus rectum or transverse axis as said. How to generalize a hyperbola (but i don't want a complex derivation...

I see this question in PSE and it seemed interesting. The Question is like this, Consider a semi-Riemannian manifold which of these statements is false: 1) All vectors on the light-cone are light-like, all vectors in the interior of the light-cone are time-like and all vectors in the exterior...

Hey! :o We have the matrix $A=\frac{1}{3}\begin{pmatrix}1 & 2 & 2 \\ 2 & 1 & -2 \\ 2 & -2 & 1\end{pmatrix}$. Show that there is an unit vector $v_1$, such that $A=I-2v_1v_1^T$. We consider an orthogonal matrix $Q=\begin{pmatrix}v_1 & v_2 & v_3\end{pmatrix}$. Show that...

I'm trying to delve into the reason why this is so. It seems that there are 5 fundamental properties: P - Pressure V - Volume (specific) T - Temperature S - Entropy (specific) U - Internal Energy (Yes, there are other types of energy, but they are fully determinable from these 5 - e.g...

I would like to know about the hypothetical properties of hypothetical negative energy--most especially the properties that would be useful for a science fiction writer to know. If such energy existed, could it be used in a drive for space craft? An FTL drive? For a weapon? A safety...

Hey! :o Could you give me a hint how to prove the following statements? (Wondering) Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be differentiable (or twice differentiable). $\left.\begin{matrix} \displaystyle{\lim_{x\rightarrow +\infty}f(x)=\ell} \ (\text{or } \displaystyle{\lim_{x\rightarrow...

Having read many times that there is no theory of quantum gravity, yet physicists at Physics Forums must have some ideas of what a theory of quantum gravity will contain. Is it allowed to discuss these questions at Physics Forums? Wikipedia does allow some current theoretical work to be...

I need to find the properties such as specific heat capacity, thermal conductivity, density and others.

In a recent paper about borophene it shows promise for detecting hydrogen cyanide gas [1903.11304 - Review of Borophene and it's Potential Applications]. My question may seem rather simpleminded but I'm under no illusions regarding my physics knowledge so please bear with me: Did anyone...

Hi All, I have review my thermodynamic notes (~35 year ago..), and I could not able to restore how to get thermodynamic properties (u,h,s,v ..) for compressed liquids. I have found properties tables for compressed liquids ( for water..) but unfortunately the data starts at 5MPa. What if I look...

Hey! :o Let $1\leq n\in \mathbb{N}$. For $0_{\mathbb{R}^n}\neq x\in \mathbb{R}^n$ we define the map $$\sigma_x:\mathbb{R}^n\rightarrow \mathbb{R}^n, \ v\mapsto v-2\frac{x\cdot v}{x\cdot x}x$$ Show that: The map is linear. It holds that $\sigma_x\in \text{Sym}(\mathbb{R}^n)$ and...

Hey! :o Let $v_1:\begin{pmatrix}1 \\ 1\\ 1\end{pmatrix}, \ \ v_2:\begin{pmatrix}1 \\ 0\\ 1\end{pmatrix}\in \mathbb{R}^3$. Let $w=\begin{pmatrix}1 \\ 0 \\2\end{pmatrix}\in \mathbb{R}^3$. If possible, give a linear map $\phi:\mathbb{R}^3\rightarrow \mathbb{R}^2$ such that $\phi...

Hey! :o Let $a\in \mathbb{R}$. We define the map $\text{cost}_a:\mathbb{R}\rightarrow \mathbb{R}$, $x\mapsto a$. We define also $-f:=(-1)f$ for a map $f:\mathbb{R}\rightarrow \mathbb{R}$. Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a map and $\lambda\in \mathbb{R}$. Show that: for...

Hey! :o I want to prove the following properties: $\left (e^x\right )^y=e^{xy}$ $\ln (1)=0$ $\ln \left (x^y\right )=y\ln (x)$ $a^x\cdot a^y=a^{x+y}$ and $\frac{a^x}{a^y}=a^{x-y}$ $a^x\cdot b^x=\left (ab\right )^x$ and $\frac{a^x}{b^x}=\left (\frac{a}{b}\right )^x$ $\left (a^x\right...

Two four-vectors have the property that ##A^\mu B_\mu = 0## (a) Suppose ##A^\mu A_\mu > 0##. Show that ##B^\mu B_\mu \leq 0## (b) Suppose ##A^\mu A_\mu = 0##. Show that ##B^\mu## is either proportional to ##A^\mu## (that is, ##B^\mu = k A^\mu##) or else ##B^\mu B_\mu < 0##. Part (a) is...

Hello everyone, First of all a very happy new year to everyone! And a big thank you to all the people who contribute to this forum, I have learned so much from here. I am prototyping a design for a part that will be used in a consumer product. I am in the early stages of researching...

Hey! :o I am looking at the following: There are the terms reflexive, symmetric, antisymmetric and transitive. Give for each combination of the properties (if possible) a set $M$ and a relation $R$ on $M$, such that $R$ satisfies these properties. What is meant exactly? Every possible...

Hey! Let $v, w\in \mathbb{R} ^n$ and let $V, W\subseteq \mathbb{R} ^n$. I want to show the following properties : $d(u.,w)=0\iff u=v$ $d(V, W) =0\iff V\cap W\neq \emptyset$ I have done the following: $d(u, w) =0\iff |u-w|=0\iff u-w=0\iff u=w$ Or do we have to do more steps? $$$$...

Dear Member, I am doing my research in plyurethane mateiral and planned to do simulation in Abaqus software for which i need some parameters. I browsed soo many sites and journal, unable to get. Please help me. 1. Inelastic Heat Fraction 2. Johnson Cook parameter 3. Plasticity 4. Film...

Back when the world was experimenting with radio it took significant advances in technology to gain the benefits. As we are just getting into the Quantum world I wonder if we can ever see something with our own eyes. I wonder where the line must be drawn and how technology can move that line. We...

1) How do we determine a Lie group's global properties when the manifold that it represents is not immediately obvious? Allow me to give the definitions I am working with. A Lie group G is a differentiable manifold G which is also a group, such that the group...