10,554 research outputs found
Exact on-event expressions for discrete potential systems
The properties of systems composed of atoms interacting though discrete potentials are dictated by a series of events which occur between pairs of atoms. There are only four basic event types for pairwise discrete potentials and the square-well/shoulder systems studied here exhibit them all. Closed analytical expressions are derived for the on-event kinetic energy distribution functions for an atom, which are distinct from the Maxwell-Boltzmann distribution function. Exact expressions are derived that directly relate the pressure and temperature of equilibrium discrete potential systems to the rates of each type of event. The pressure can be determined from knowledge of only the rate of core and bounce events. The temperature is given by the ratio of the number of bounce events to the number of disassociation/association events. All these expressions are validated with event-driven molecular dynamics simulations and agree with the data within the statistical precision of the simulations
Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations
In this article, we study the self-similar solutions of the 2-component
Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho_{t}+u\rho_{x}+\rho u_{x}=0
m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation}
with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation
method, we can obtain a class of blowup or global solutions for or
. In particular, for the integrable system with , we have the
global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right)
}{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi}
0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right.
,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x
\overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}%
>0,\text{ }\overset{\cdot}{a}(0)=a_{1}
f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right)
^{2}}% \end{array} \right. \end{equation}
where with and are
arbitrary constants.\newline Our analytical solutions could provide concrete
examples for testing the validation and stabilities of numerical methods for
the systems.Comment: 5 more figures can be found in the corresponding journal paper (J.
Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm
Equations, Shallow Water System, Analytical Solutions, Blowup, Global,
Self-Similar, Separation Method, Construction of Solutions, Moving Boundar
Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass
The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon
potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues
and the corresponding eigenfunctions are computed. Results are also given for
the constant mass case.Comment: 13 page
Systematic perturbation calculation of integrals with applications to physics
In this paper we generalize and improve a method for calculating the period
of a classical oscillator and other integrals of physical interest, which was
recently developed by some of the authors. We derive analytical expressions
that prove to be more accurate than those commonly found in the literature, and
test the convergence of the series produced by the approach.Comment: 11 pages, 5 figure
Developing molecular genetic markers for grape breeding; using polymerase chain reaction procedures
Research Not
Exact Spin and Pseudo-Spin Symmetric Solutions of the Dirac-Kratzer Problem with a tensor potential via Laplace Transform Approach
Exact bound state solutions of the Dirac equation for the Kratzer potential
in the presence of a tensor potential are studied by using the Laplace
transform approach for the cases of spin- and pseudo-spin symmetry. The energy
spectra is obtained in the closed form for the relativistic as well as
non-relativistic cases including the Coulomb potential. It is seen that our
analytical results are in agrement with the ones given in literature. The
numerical results are also given in a table for different parameter values.Comment: 8 page
Diffusive transport in networks built of containers and tubes
We developed analytical and numerical methods to study a transport of
non-interacting particles in large networks consisting of M d-dimensional
containers C_1,...,C_M with radii R_i linked together by tubes of length l_{ij}
and radii a_{ij} where i,j=1,2,...,M. Tubes may join directly with each other
forming junctions. It is possible that some links are absent. Instead of
solving the diffusion equation for the full problem we formulated an approach
that is computationally more efficient. We derived a set of rate equations that
govern the time dependence of the number of particles in each container
N_1(t),N_2(t),...,N_M(t). In such a way the complicated transport problem is
reduced to a set of M first order integro-differential equations in time, which
can be solved efficiently by the algorithm presented here. The workings of the
method have been demonstrated on a couple of examples: networks involving
three, four and seven containers, and one network with a three-point junction.
Already simple networks with relatively few containers exhibit interesting
transport behavior. For example, we showed that it is possible to adjust the
geometry of the networks so that the particle concentration varies in time in a
wave-like manner. Such behavior deviates from simple exponential growth and
decay occurring in the two container system.Comment: 21 pages, 18 figures, REVTEX4; new figure added, reduced emphasis on
graph theory, additional discussion added (computational cost, one
dimensional tubes
Coarse-grained model of entropic allostery
Many signaling functions in molecular biology require proteins to bind to substrates such as DNA in response to environmental signals such as the simultaneous binding to a small molecule. Examples are repressor proteins which may transmit information via a conformational change in response to the ligand binding. An alternative entropic mechanism of "allostery" suggests that the inducer ligand changes the intramolecular vibrational entropy, not just the mean static structure. We present a quantitative, coarse-grained model of entropic allostery, which suggests design rules for internal cohesive potentials in proteins employing this effect. It also addresses the issue of how the signal information to bind or unbind is transmitted through the protein. The model may be applicable to a wide range of repressors and also to signaling in trans-membrane proteins
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