System Definition and 1000 Threads

The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...

Suppose the system of equations (coming from invariance of the wave equation) : $$B=-vE\\A^2-B^2/c^2=1\\E^2-c^2D^2=1\\AD=EB/c^2\\B=vA\\AE-BD=1$$ If one adds a lightspeed movement like $$A=a+f\\B=b-cf\\D=d+h\\E=e-ch$$ Then solving equ 1 for f gives $$f=(b+ve-vch)/c$$ Equ 4 for h implies...

Show that the nonlinear system $\dot{X_1}=2\cos X_2, X_1(0)=a$ $\dot{X_2}=3\sin X_1, X_2(0)=b$ has a unique solution for the arbitrary constants $a$ and $b$. how to solve this system? Thanks.

I have a doubt. It is said that antigens detected by macrophages and and Dendritic cells (by way of PAMPs and DAMPs) can initiate and mount an immune response, why antibodies need to be produced. Ok, antibodies opsonize the intruders. But then even without antibodies, the innate immune system...

I've marked correct answers above. Have a look at the solutions: How is the first equation justified? Shouldn't v2 and ωR be of opposite signs? What is v1? And how is it equal to v2? My biggest problem is the source of v1 since the ring is not having vertical displacement, then what is v1?

Good night! How do I find the values of a (real) so that the solution of this system is? (i) just an ordered pair? (ii) exactly two pairs. (iii) exactly 3? (iv) is there a place where you have more than 3 pairs as an answer?So... I thought like this: I developed the first part. I solved the...

1. How will the motion of M be? I assume wire S is inelastic so will M move downwards but not in straight line? (I mean M moves downwards but because the left side of pulley is connected to S, it will be static and the right side of pulley can go down along the extension of the spring so its...

Here is the picture on the system. I have to find the period (T). The masses, R and dX is given. The systam at first is at rest, then at t = 0 we pull the plank to dX distance from its originial position. In the thread...

I know that it will probably execute something similar to circular motion. I thought of conserving momentum but I think there is an external force being applied due to the impulse which will prevent me from doing so. I know that once I find the tension it would become very easy to find the...

I am writing a space opera, that is meant to be hard, except some alien magic. So far, i have the following points : asteroid belt is the most valuable for rare material mining, there they live in O Neil cylinders. Travel is done by fusion ships, that can maintain miliG-s of constant...

I have not clear how to solve this problem. Here it is my attempt at a solution: Let the charge at ##-a## be the number one and the one at ##+a## the number two. the potential energy of the punctual charge ##-Q## due to each charge +Q will be then ##E_{pi}=-k \frac{Q^2}{r_i}##, whit ##r_i## the...

can i solve this problem i didnt go university due to Covid-19

Suppose we have a system of particles being acted upon by a single external force ##\mathbf{F}^{e}##. Each individual particle feels a force of ##\mathbf{f}_i = \mathbf{f}_{i}^{int} + \mathbf{f}_{i}^{e}## such that ##\sum_i \mathbf{f}_{i}^{e} = \mathbf{F}^{e}##, and ##\mathbf{f}_{i}^{int}## are...

I understand how they might have got to these answers but I'm still kind of shaky on how the mass of the rope plays a role in the tension at point B, and how to mathematically represent the tension at any point along the rope; I know the tension varies because the rope has mass. If I was to...

My best guess right now is use Newton's version of Kepler's 3rd Law to maybe find a combined mass, as I'm under the impression that the smaller star's mass would still be too large to ignore, but I'm not confident. And I wouldn't be sure as where t go from their, either. Any guidance would be...

This is my attempt the system The 1 is the initial configuration where the 3 electron is at infinity. The 2 is the final configuration where the 3 electron is midway.U1 is the potential energy between e1 and e2 U1 = (q1*q2)/(4*π*ε0 * (0.02)^2); // q1, q2 charge of electrons K1 =...

Hi All, Anyone willing to help out in explaining what eigenfreuqncy for this oscilatory system, would be? Also if anybody knows the equation to calulate this stuff please, if you're willing to share I'd be greatful! Thanks, regards.

Hello, The question I have pertains to conservation of Angular momentum on a motorcycle. I know that the dynamic friction is less than the static friction, so when you are braking on a (say a motorcycle) and the wheels lock up, the bike is bound to fall over. This is the reason ABS (Anti-lock...

This is the problem's picture: My problem is that what I got for one acceleration (m3's) via Newton's equations is not the same as via D'Alembert's principle (I've checked on my PC if they are the same expression). I can't find the mistake. Any suggestion is welcome. I attach pictures of what...

I know that from the given problem, I need to find the expression for Kinetic energy, KE = 1/2 m [r(dot)]^2 and Potential energy, PE = 1/2 k r^2 So L = 1/2 m [r(dot)]^2 - 1/2 k r^2 Hence H = 1/2 m [r(dot)]^2 + 1/2 k r^2 I assume that the fixed length r0 is provided to find the value of end...

So I started by checking the options.I substituted the value of friction in the equations I got by making free body diagrams.I got different value of Tensions.For 1 and 3 Tension came to be 38 N.For 2 Tension came out to be 42N and for 4 Tension came out to be 40 N. Now I think that I will take...

I use the following script and function in MatLab, but get three errors. I shall first write down the code and after that the errors that I get. function yprime = lorenz_de(t,y) %LORENZ_DE Lorenz equations. % yprime = lorenz_de(t,y). yprime = [10*(y(2)-y(1))...

Equal masses of ice at –10ºC and water at 80ºC are placed in an insulated container and allowed to reach thermal equilibrium. Calculate the equilibrium temperature Data: Water(ice): 37,65 J/mol.K Agua (l): 75,29 J/mol.K ## Lf = 6011 J/mol ## I solved it this way: ## -Q_{l} = Q_{ice} ## ##...

Let a mass m charged with q, attached to a spring with constant factor k = mω ^2 in an electric field E(t) = E0(t/τ) x since t=0. (Equilibrium position is x0 and the deformation obeys ξ = x - x0) What would the hamiltonian and motion equations be in t ≥ 0, in terms of m and ω?? Despise magnetic...

(I hope this is not a double posting) I want to solve this system of equations, containing logarithmic terms: ##7\ln(a/b)+A = 7\ln(d/e)+D = 7\ln(g/h)+G## ##7\ln(a/c)+B = 7\ln(d/f)+E = 7\ln(g/i)+H## ##7\ln(b/c)+C = 7\ln(e/f)+F = 7\ln(h/i)+I## ##a\phi_1+d\phi_2+g\phi_3=X##...

I was solving a Physics problem, and for it to be consistent there should exist a function f(t) in real numbers and a time T, such that: $$\int_{0}^{T} f(t) dt=0 $$ $$\int_{0}^{T} \int_{0}^{t} f(t') dt' dt=0$$ $$\int_{0}^{T} f(t) (\int_{0}^{t} f(t') dt') dt>0$$ i.e. the integral is zero, the...

I don't know how to calclute error in derivative for daming ratio of 0.5

Hey! :o We have the matrix $A=\begin{pmatrix}1 & -1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1\end{pmatrix}$ and the vectors $b_1=\begin{pmatrix}1 \\ 0 \\1\end{pmatrix}$ and $b_2=\begin{pmatrix}-1 \\ 1 \\2\end{pmatrix}$. Check if the system $Ax=b_i$ for $i\in \{1,2\}$ has a solution. If the system is...

See the picture I am stuck at 12(1+2k)=0 So k=-1/2 for stability k must have value greater the - 1/2 which means there will no sign changes in rooth array and equation represents a stable system

I want to solve the following system of equations ##M_{1} = f_1+f_2+m_1+m_2\ \ ;\ \ M_{7} = f_1+f_2+s_1+s_2\ \ ;\ \ M_{13} = m_1+m_2+s_1+s_2## ##M_{2} = f_1+f_3+m_1+m_3\ \ ;\ \ M_{8} = f_1+f_3+s_1+s_3\ \ ;\ \ M_{14} = m_1+m_3+s_1+s_3## ##M_{3} = f_1+f_4+m_1+m_4\ \ ;\ \ M_{9} = f_1+f_4+s_1+s_4\...

If 1kg make a displacement of 1unit upward then A make a 1/2unit down because 1/sin 30.after that i have no idea what do I will really need help. Thanks!

I would like to design a system that is capable of generating frictional heat through its servo motor to heat up an enclosed chamber to 500 'Celsius . The challenge is that external heating source such as heating element, heat chamber etc. shall not be included in the design setup. Assuming that...

The first part is actually fine. You just note that since r=r1+r2 that means r1=r+r2 and r2=r1-r and you substitute that into the center of mass, R, and simplify to get r1=R+(μ/m1)r, and r2=R-(μ/m2)r But the next part is where I'm very confused. The general idea is that you want to prove ∇1 =...

<work done a system> a) w=5N*(0.4m)=2J I think this is right, but b) center of mass initial = ((0.5kg)(0.05m)+0.5kg(0.65m))/1kg = 0.35m center of mass final = ((0.5kg)(0.45m)+0.5kg(0.4+0.1+0.3+0.25))/1kg = 0.75m I'm not sure for this one... How can I calculate the displacement of the...

I'm finding it slightly tricky to just get a hold of where to start. I try $$\text{m}\text{s}^{-1} = \frac{c}{3\times 10^8}$$ If we then set ##c = 1##, that would seem to imply $$3\times 10^8 = \text{s}\text{m}^{-1}$$For ##G = 1##, I might also write $$\text{kg}\text{m}^{-3}\text{s}^{2} =...

So for the 1D infinite well with the states above, I have ## \psi_{symmetric} = \frac{2}{L} [sin[\frac{\pi x_1}{L}]sin[\frac{2\pi x_2}{L}] + sin[\frac{2\pi x_1}{L}]sin[\frac{\pi x_2}{L}]] ## ## \psi_{antisymmetric} = \frac{2}{L} [sin[\frac{\pi x_1}{L}]sin[\frac{2\pi x_2}{L}] - sin[\frac{2\pi...

I got the correct answer for the first part but I'm not sure why the answer for (b) is the same for (a). Wouldn't the rings falling off mean that I_f = \frac{1}{12}M_L L^2 only where I_F, M_L, L are the final moment of inertia, mass of the rod and length of the rod as opposed to I_f =...

If we have the following relations between x, y, and z: M_{xy}=\frac{2xy}{x+y} M_{xz}=\frac{2xz}{x+z} M_{yz}=\frac{2yz}{y+z} where M_{xy}, M_{xz}, and M_{yz} are known constants, what technique can be used to determine the values of x, y, and z?

What is nonlocality? How could a quantum system (like a superposition - is that right?) "know" an interaction will take place? Source...

Good Morning I have a very vague memory of having read (about 40 years ago) that there are only 11 coordinate systems in which the field equations of physics can be separated. I can no longer be sure if my memory has failed me. But this issue has been in my head for all these years. (Gotta do...

Hi, I am getting following error message: I have written the following code which should display the system information of a simple program which I am running as a function: import psutil import osclass Counting_SysInfo: def __init__(self, i): self.i = i def...

Hi guys, First of all I'm sorry for my bad english I'll try to be as clear as possible. I have tried to solve this problem to understand the First Law of Thermodinamics: Q+L=ΔE_t In fact I know L (in the current convention) is the work which the envirorment does on the system but I don't...

Attempt at a Solution: Heat Absorbed By The System By the first law of thermodynamics, dU = dQ + dW The system is of fixed volume and therefore mechanically isolated. dW = 0 Therefore dQ = dU The change of energy of the system equals the change of energy of the gas plus the change of energy...

My attempt: According to the implicit function theorem as long as the determinant of the jacobian given by ∂(F,G)/∂(y,z) is not equal to 0, the parametrization is possible. ∂(F,G)/∂(y,z)=4yzMeaning that all points where z and y are not equal to 0 are possible parametrizations. My friend's...

Lets say we have a system of two point particles (1. and 2.) which are rotating around an axis. What is written next in my physics course book is: The torque of a 2.body on the 1. body is M21=r1xF21 and the torque of the 1.body on the 2.body is M12=r2xF12. Understandable. But how? There is no...

I know that our laws are as far as the logic goes Universal? Now, can we use other ancient number systems and come up with the same results, or is the success of all the recent science dependent on the efficiency of Hindu Numerals ? Is the logic of all mathematics based on Hindu numerals , and...

1. Draw Free body Diagram for each weight. 2. Solve for Tension in Rope. 3. Find Spring Constant. 4. Find omega (w, or angular velocity)

Let´ s call ##N_x## the magnitud of the force between the rod and the box and ## N_y## the magnitud of the force between the rod and the surface. ##N_x = ma_c## ##N_x= ma_r## ##mg-N_y=ma_y## The following I think is to find a relation between ##a_r## and ##a_y## and that can be found by...