2,666 research outputs found
Longitudinal and transversal flow over a cavity containing a second immiscible fluid
An analytical solution for the flow field of a shear flow over a rectangular
cavity containing a second immiscible fluid is derived. While flow of a
single-phase fluid over a cavity is a standard case investigated in fluid
dynamics, flow over a cavity which is filled with a second immiscible fluid,
has received little attention. The flow filed inside the cavity is considered
to define a boundary condition for the outer flow which takes the form of a
Navier slip condition with locally varying slip length. The slip-length
function is determined from the related problem of lid-driven cavity flow.
Based on the Stokes equations and complex analysis it is then possible to
derive a closed analytical expression for the flow field over the cavity for
both the transversal and the longitudinal case. The result is a comparatively
simple function, which displays the dependence of the flow field on the cavity
geometry and the medium filling the cavity. The analytically computed flow
field agrees well with results obtained from a numerical solution of the
Navier-Stokes equations. The studies presented in this article are of
considerable practical relevance, for example for the flow over
superhydrophobic surfaces.Comment: http://journals.cambridge.or
Universal Markovian reduction of Brownian particle dynamics
Non-Markovian processes can often be turned Markovian by enlarging the set of
variables. Here we show, by an explicit construction, how this can be done for
the dynamics of a Brownian particle obeying the generalized Langevin equation.
Given an arbitrary bath spectral density , we introduce an orthogonal
transformation of the bath variables into effective modes, leading stepwise to
a semi-infinite chain with nearest-neighbor interactions. The transformation is
uniquely determined by and defines a sequence
of residual spectral densities describing the
interaction of the terminal chain mode, at each step, with the remaining bath.
We derive a simple, one-term recurrence relation for this sequence, and show
that its limit is the quasi-Ohmic expression provided by the Rubin model of
dissipation. Numerical calculations show that, irrespective of the details of
, convergence is fast enough to be useful in practice for an effective
Markovian reduction of quantum dissipative dynamics
P-wave pi pi amplitude from dispersion relations
We solve the dispersion relation for the P-wave pi pi amplitude.We discuss
the role of the left hand cut vs Castillejo-Dalitz-Dyson (CDD), pole
contribution and compare the solution with a generic quark model description.
We review the the generic properties of analytical partial wave scattering and
production amplitudes and discuses their applicability and fits of experimental
data.Comment: 10 pages, 7 figures, typos corrected, reference adde
The explicit expression of the fugacity for weakly interacting Bose and Fermi gases
In this paper, we calculate the explicit expression for the fugacity for two-
and three-dimensional weakly interacting Bose and Fermi gases from their
equations of state in isochoric and isobaric processes, respectively, based on
the mathematical result of the boundary problem of analytic functions --- the
homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein
condensation phase transition of three-dimensional hard-sphere Bose gases.Comment: 24 pages, 9 figure
The role of P-wave inelasticity in J/psi to pi+pi-pi0
We discuss the importance of inelasticity in the P-wave pi pi amplitude on
the Dalitz distribution of 3pi events in J/psi decay. The inelasticity, which
becomes sizable for pi pi masses above 1.4 GeV, is attributed to
KK to pi pi rescattering. We construct an analytical model for the
two-channel scattering amplitude and use it to solve the dispersion relation
for the isobar amplitudes that parametrize the J/psi decay. We present
comparisons between theoretical predictions for the Dalitz distribution of 3pi
events with available experimental data.Comment: 10 pages, 10 figure
The X-ray edge singularity in Quantum Dots
In this work we investigate the X-ray edge singularity problem realized in
noninteracting quantum dots. We analytically calculate the exponent of the
singularity in the absorption spectrum near the threshold and extend known
analytical results to the whole parameter regime of local level detunings.
Additionally, we highlight the connections to work distributions and to the
Loschmidt echo.Comment: 7 pages, 2 figures; version as publishe
Integral equations of a cohesive zone model for history-dependent materials and their numerical solution
A nonlinear history-dependent cohesive zone (CZ) model of quasi-static crack propagation in
linear elastic and viscoelastic materials is presented. The viscoelasticity is described by a linear
Volterra integral operator in time. The normal stress on the CZ satisfies the history-dependent yield
condition, given by a nonlinear Abel-type integral operator. The crack starts propagating, breaking
the CZ, when the crack tip opening reaches a prescribed critical value. A numerical algorithm for
computing the evolution of the crack and CZ in time is discussed along with some numerical
results
Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at non-zero temperatures
We provide an exact finite temperature extension to the recently developed
Riemann-Hilbert approach for the calculation of response functions in
nonadiabatically perturbed (multi-channel) Fermi gases. We give a precise
definition of the finite temperature Riemann-Hilbert problem and show that it
is equivalent to a zero temperature problem. Using this equivalence, we discuss
the solution of the nonequilibrium Fermi-edge singularity problem at finite
temperatures.Comment: 10 pages, 2 figures; 2 appendices added, a few modifications in the
text, typos corrected; published in Phys. Rev.
Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models
We study the variance and the Laplace transform of the probability law of
linear eigenvalue statistics of unitary invariant Matrix Models of
n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test
function of statistics is smooth enough and using the asymptotic formulas by
Deift et al for orthogonal polynomials with varying weights, we show first that
if the support of the Density of States of the model consists of two or more
intervals, then in the global regime the variance of statistics is a
quasiperiodic function of n generically in the potential, determining the
model. We show next that the exponent of the Laplace transform of the
probability law is not in general 1/2variance, as it should be if the Central
Limit Theorem would be valid, and we find the asymptotic form of the Laplace
transform of the probability law in certain cases
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