24,391 research outputs found
An exact solution of linearized flow of an emitting, absorbing and scattering grey gas
The governing equations for the problem of linearized flow through a normal shock wave in an emitting, absorbing, and scattering grey gas are reduced to two linear coupled integro-differential equations. By separation of variables, these equations are further reduced to an integral equation similar to that which arises in neutron-transport theory. It is shown that this integral equation admits both regular (associated with discrete eigenfunctions) and singular (associated with continuum eigenfunctions) solutions to form a complete set. The exact closed-form solution is obtained by superposition of these eigen-functions. If the gas downstream of a strong shock is absorption–emission dominated, the discrete mode of the solution disappears downstream. The effects of isotropic scattering are discussed. Quantitative comparison between the numerical results based on the exact solution and on the differential approximation are presented
Solid quantization for non-point particles
In quantum field theory, elemental particles are assumed to be point
particles. As a result, the loop integrals are divergent in many cases.
Regularization and renormalization are necessary in order to get the physical
finite results from the infinite, divergent loop integrations. We propose new
quantization conditions for non-point particles. With this solid quantization,
divergence could be treated systematically. This method is useful for effective
field theory which is on hadron degrees of freedom. The elemental particles
could also be non-point ones. They can be studied in this approach as well.Comment: 7 page
Integrable Systems in n-dimensional Riemannian Geometry
In this paper we show that if one writes down the structure equations for the
evolution of a curve embedded in an (n)-dimensional Riemannian manifold with
constant curvature this leads to a symplectic, a Hamiltonian and an hereditary
operator. This gives us a natural connection between finite dimensional
geometry, infinite dimensional geometry and integrable systems. Moreover one
finds a Lax pair in (\orth{n+1}) with the vector modified Korteweg-De Vries
equation (vmKDV) \vk{t}=
\vk{xxx}+\fr32 ||\vk{}||^2 \vk{x} as integrability condition. We indicate
that other integrable vector evolution equations can be found by using a
different Ansatz on the form of the Lax pair. We obtain these results by using
the {\em natural} or {\em parallel} frame and we show how this can be gauged by
a generalized Hasimoto transformation to the (usual) {\em Fren{\^e}t} frame. If
one chooses the curvature to be zero, as is usual in the context of integrable
systems, then one loses information unless one works in the natural frame
Hydrodynamic slip boundary condition at chemically patterned surfaces: A continuum deduction from molecular dynamics
We investigate the slip boundary condition for single-phase flow past a
chemically patterned surface. Molecular dynamics (MD) simulations show that
modulation of fluid-solid interaction along a chemically patterned surface
induces a lateral structure in the fluid molecular organization near the
surface. Consequently, various forces and stresses in the fluid vary along the
patterned surface. Given the presence of these lateral variations, a general
scheme is developed to extract hydrodynamic information from MD data. With the
help of this scheme, the validity of the Navier slip boundary condition is
verified for the chemically patterned surface, where a local slip length can be
defined. Based on the MD results, a continuum hydrodynamic model is formulated
using the Navier-Stokes equation and the Navier boundary condition, with a slip
length varying along the patterned surface. Steady-state velocity fields from
continuum calculations are in quantitative agreement with those from MD
simulations. It is shown that, when the pattern period is sufficiently small,
the solid surface appears to be homogeneous, with an effective slip length that
can be controlled by surface patterning. Such a tunable slip length may have
important applications in nanofluidics.Comment: 41 pages, 17 figure
Quantum bit string sealing
Though it was proven that secure quantum sealing of a single classical bit is
impossible in principle, here we propose an unconditionally secure quantum
sealing protocol which seals a classical bit string. Any reader can obtain each
bit of the sealed string with an arbitrarily small error rate, while reading
the string is detectable. The protocol is simple and easy to be implemented.
The possibility of using this protocol to seal a single bit in practical is
also discussed.Comment: Add a discussion on the possibility of sealing a single bit in
practica
A sequential formula for electronic coupling in long range bridge-assisted electron transfer: Formulation of theory and application to alkanethiol monolayers
A recursion relation is formulated for the Green's function for calculating the effective electron coupling in bridge-assisted electronic transfer systems, within the framework of the tight-binding Hamiltonian. The recursion expression relates the Green's function of a chain bridge to that of the bridge that is one unit less. It is applicable regardless of the number of orbitals per unit. This method is applied to the system of a ferrocenylcarboxy-terminated alkanethiol on the Au(111) surface. At larger numbers of bridge units, the effective coupling strength shows an exponential decay as the number of methylene(–CH2–) units increases. This sequential formalism shows numerical stability even for a very long chain bridge and, since it uses only small matrices, requires much less computer time for the calculation. Identical bridge units are not a requirement, and so the method can be applied to more complicated systems
Theory of random packings
We review a recently proposed theory of random packings. We describe the
volume fluctuations in jammed matter through a volume function, amenable to
analytical and numerical calculations. We combine an extended statistical
mechanics approach 'a la Edwards' (where the role traditionally played by the
energy and temperature in thermal systems is substituted by the volume and
compactivity) with a constraint on mechanical stability imposed by the
isostatic condition. We show how such approaches can bring results that can be
compared to experiments and allow for an exploitation of the statistical
mechanics framework. The key result is the use of a relation between the local
Voronoi volume of the constituent grains and the number of neighbors in contact
that permits a simple combination of the two approaches to develop a theory of
random packings. We predict the density of random loose packing (RLP) and
random close packing (RCP) in close agreement with experiments and develop a
phase diagram of jammed matter that provides a unifying view of the disordered
hard sphere packing problem and further shedding light on a diverse spectrum of
data, including the RLP state. Theoretical results are well reproduced by
numerical simulations that confirm the essential role played by friction in
determining both the RLP and RCP limits. Finally we present an extended
discussion on the existence of geometrical and mechanical coordination numbers
and how to measure both quantities in experiments and computer simulations.Comment: 9 pages, 5 figures. arXiv admin note: text overlap with
arXiv:0808.219
Non-linear supersymmetric Sigma-Model for Diffusive Scattering of Classical Waves with Resonance Enhancement
We derive a non-linear sigma-model for the transport of light (classical
waves) through a disordered medium. We compare this extension of the model with
the well-established non-linear sigma-model for the transport of electrons
(Schroedinger waves) and display similarities of and differences between both
cases. Motivated by experimental work (M. van Albada et al., Phys. Rev. Lett.
66 (1991) 3132), we then generalize the non-linear sigma-model further to
include resonance scattering. We find that the form of the effective action is
unchanged but that a parameter of the effective action, the mean level density,
is modified in a manner which correctly accounts for the data.Comment: 4 pages, 1 Figure, to be published in Europhysics Letter
Monte Carlo Protein Folding: Simulations of Met-Enkephalin with Solvent-Accessible Area Parameterizations
Treating realistically the ambient water is one of the main difficulties in
applying Monte Carlo methods to protein folding. The solvent-accessible area
method, a popular method for treating water implicitly, is investigated by
means of Metropolis simulations of the brain peptide Met-Enkephalin. For the
phenomenological energy function ECEPP/2 nine atomic solvation parameter (ASP)
sets are studied that had been proposed by previous authors. The simulations
are compared with each other, with simulations with a distance dependent
electrostatic permittivity , and with vacuum simulations
(). Parallel tempering and a recently proposed biased Metropolis
technique are employed and their performances are evaluated. The measured
observables include energy and dihedral probability densities (pds), integrated
autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be
unsuitable for these simulations. For all other sets, selected configurations
are minimized in search of the global energy minima. Unique minima are found
for the vacuum and the system, but for none of the ASP models.
Other observables show a remarkable dependence on the ASPs. In particular,
autocorrelation times vary dramatically with the ASP parameters. Three ASP sets
have much smaller autocorrelations at 300 K than the vacuum simulations,
opening the possibility that simulations can be speeded up vastly by
judiciously chosing details of the forceComment: 10 pages; published in "NIC Symposium 2004", eds. D. Wolf at el.
(NIC, Juelich, 2004
- …