Paul Ehrenfest: The Genesis of the Adiabatic Hypothesis, 1911–1914
... EINSTEIN and STERN.4 Then, in another article of 1913 on a mechanical theorem of
BOLTZMANN,5 EHRENFEST already employed a primitive adiabatic hypothesis but
did not formulate it clearly. He used it instead to deduce a set of quantization rules that
differed from the usual ones and specifically obtai ...
x - UCSB ECE
... The equilibrium point xeq 2 Rn is (Lyapunov) stable if 9 a 2 K:
||x(t) – xeq|| · a(||x(t0) – xeq||) 8 t¸ t0¸ 0, ||x(t0) – xeq||· c
Suppose there exists a continuously differentiable, positive definite, radially
unbounded function V: Rn ! R such that
Then xeq is a Lyapunov stable ...
Statistical Significance and Univariate and Bivariate Tests
... A sampling distribution is the probability distribution of the
Is this the same thing as the probability distribution of the
NO! They may coincidentally have the same shape though.
BUS 230: Business and Economics Research and Communication Statistical Significance and Univariat ...
HQ-1: Conference on the History of Quantum Physics Max Planck
... the History of Quantum Physics. This conference, held at the Max Planck Institute for
the History of Science (July 2–6, 2007), has been sponsored by the Max Planck Society
in honor of Max Planck on the occasion of the sixtieth anniversary of his passing. It
is the first in a new series of conference ...
... • We can also determine the concentration of an ion
necessary for precipitation to begin.
• Assume that precipitation begins when Qsp = Ksp
• Example: If a solution contains 0.0020 mol CrO42per liter, what concentration of Ag+ ion must be added
as AgNO3 before Ag2CrO4 begins to precipitate.
... 11.3 Center of Gravity
Center of mass is often called center of gravity, the average
position of all the particles of weight that make up an object.
For almost all objects on and near Earth, these terms are
There can be a small difference between center of gravity and
center of mass ...
Remarks on the Donnan condenser in the sedimentation–diffusion
... the inflated gravitational length (1 + z)L in region III, see appendix B. The foregoing results for
the inhomogeneous Donnan equilibrium in the gravity field are easily extended to colloids in
a centrifuge. The main difference is that now the acceleration changes in the radial direction,
producing a ...
Examination of the crystal growth paths for racemic solutions
... F3D1 or F2D0 mechanism, the rung before last is made up of at least one ion of wrong absolute configuration,
so that the only solution is the desorption of this wrong pair.
In configuration M, there are two pairs containing the right carboxylic ion to be inserted; both lead to the
formation of one a ...
Funky Mechanics Concepts
... http://physics.ucsd.edu/~emichels for the latest versions of the Funky Series, and for contact information.
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Paper - College of the Redwoods
... down both sides of the hoop. The second example is the same but the velocity of the bead has
died down. When we increase the value of γ, the bead is restricted to one side of the hoop,
but the area in which it moves gets much smaller as the angular velocity increases. It gets to a
point where we can ...
Lesson - Port of Long Beach
... 1. When placing the skewer or pencil on your
finger, when was static equilibrium reached and
how do you know?
2. What did you learn about mass and distance
from the fulcrum in the gantry crane examples?
3. Using the information from question #2, how do
mass and distance relate to the pencil on yo ...
Statistical mechanics is a branch of theoretical physics that studies, using probability theory, the average behaviour of a mechanical system where the state of the system is uncertain.The classical view of the universe was that its fundamental laws are mechanical in nature, and that all physical systems are therefore governed by mechanical laws at a microscopic level. These laws are precise equations of motion that map any given initial state to a corresponding future state at a later time. There is however a disconnection between these laws and everyday life experiences, as we do not find it necessary (nor even theoretically possible) to know exactly at a microscopic level the simultaneous positions and velocities of each molecule while carrying out processes at the human scale (for example, when performing a chemical reaction). Statistical mechanics is a collection of mathematical tools that are used to fill this disconnection between the laws of mechanics and the practical experience of incomplete knowledge.A common use of statistical mechanics is in explaining the thermodynamic behaviour of large systems. Microscopic mechanical laws do not contain concepts such as temperature, heat, or entropy, however, statistical mechanics shows how these concepts arise from the natural uncertainty that arises about the state of a system when that system is prepared in practice. The benefit of using statistical mechanics is that it provides exact methods to connect thermodynamic quantities (such as heat capacity) to microscopic behaviour, whereas in classical thermodynamics the only available option would be to just measure and tabulate such quantities for various materials. Statistical mechanics also makes it possible to extend the laws of thermodynamics to cases which are not considered in classical thermodynamics, for example microscopic systems and other mechanical systems with few degrees of freedom. This branch of statistical mechanics which treats and extends classical thermodynamics is known as statistical thermodynamics or equilibrium statistical mechanics.Statistical mechanics also finds use outside equilibrium. An important subbranch known as non-equilibrium statistical mechanics deals with the issue of microscopically modelling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions, or flows of particles and heat. Unlike with equilibrium, there is no exact formalism that applies to non-equilibrium statistical mechanics in general and so this branch of statistical mechanics remains an active area of theoretical research.