1,932 research outputs found
A Quantum-Gravity Perspective on Semiclassical vs. Strong-Quantum Duality
It has been argued that, underlying M-theoretic dualities, there should exist
a symmetry relating the semiclassical and the strong-quantum regimes of a given
action integral. On the other hand, a field-theoretic exchange between long and
short distances (similar in nature to the T-duality of strings) has been shown
to provide a starting point for quantum gravity, in that this exchange enforces
the existence of a fundamental length scale on spacetime. In this letter we
prove that the above semiclassical vs. strong-quantum symmetry is equivalent to
the exchange of long and short distances. Hence the former symmetry, as much as
the latter, also enforces the existence of a length scale. We apply these facts
in order to classify all possible duality groups of a given action integral on
spacetime, regardless of its specific nature and of its degrees of freedom.Comment: 10 page
Invariant Regions and Global Asymptotic Stability in an Isothermal Catalyst
A well-known model for the evolution of the (space-dependent) concentration and (lumped) temperature in a porous catalyst is considered. A sequence of invariant regions of the phase space is given, which converges to a globally asymptotically stable region . Quantitative sufficient conditions are obtained for (the region to consist of only one point and) the problem to have a (unique) globally asymptotically stable steady state
High orders of Weyl series for the heat content
This article concerns the Weyl series of spectral functions associated with
the Dirichlet Laplacian in a -dimensional domain with a smooth boundary. In
the case of the heat kernel, Berry and Howls predicted the asymptotic form of
the Weyl series characterized by a set of parameters. Here, we concentrate on
another spectral function, the (normalized) heat content. We show on several
exactly solvable examples that, for even , the same asymptotic formula is
valid with different values of the parameters. The considered domains are
-dimensional balls and two limiting cases of the elliptic domain with
eccentricity : A slightly deformed disk () and an
extremely prolonged ellipse (). These cases include 2D domains
with circular symmetry and those with only one shortest periodic orbit for the
classical billiard. We analyse also the heat content for the balls in odd
dimensions for which the asymptotic form of the Weyl series changes
significantly.Comment: 20 pages, 1 figur
Linear and multiplicative 2-forms
We study the relationship between multiplicative 2-forms on Lie groupoids and
linear 2-forms on Lie algebroids, which leads to a new approach to the
infinitesimal description of multiplicative 2-forms and to the integration of
twisted Dirac manifolds.Comment: to appear in Letters in Mathematical Physic
A note on the wellposedness of scalar brane world cosmological perturbations
We discuss scalar brane world cosmological perturbations for a 3-brane world
in a maximally symmetric 5D bulk. We show that Mukoyama's master equations
leads, for adiabatic perturbations of a perfect fluid on the brane and for
scalar field matter on the brane, to a well posed problem despite the "non
local" aspect of the boundary condition on the brane. We discuss in relation to
the wellposedness the way to specify initial data in the bulk.Comment: 14 pages, one figure, v2 minor change
Electromagnetic Oscillations in a Driven Nonlinear Resonator: A New Description of Complex Nonlinear Dynamics
Many intriguing properties of driven nonlinear resonators, including the
appearance of chaos, are very important for understanding the universal
features of nonlinear dynamical systems and can have great practical
significance. We consider a cylindrical cavity resonator driven by an
alternating voltage and filled with a nonlinear nondispersive medium. It is
assumed that the medium lacks a center of inversion and the dependence of the
electric displacement on the electric field can be approximated by an
exponential function. We show that the Maxwell equations are integrated exactly
in this case and the field components in the cavity are represented in terms of
implicit functions of special form. The driven electromagnetic oscillations in
the cavity are found to display very interesting temporal behavior and their
Fourier spectra contain singular continuous components. To the best of our
knowledge, this is the first demonstration of the existence of a singular
continuous (fractal) spectrum in an exactly integrable system.Comment: 5 pages, 3 figure
Shear-driven size segregation of granular materials: modeling and experiment
Granular materials segregate by size under shear, and the ability to
quantitatively predict the time required to achieve complete segregation is a
key test of our understanding of the segregation process. In this paper, we
apply the Gray-Thornton model of segregation (developed for linear shear
profiles) to a granular flow with an exponential profile, and evaluate its
ability to describe the observed segregation dynamics. Our experiment is
conducted in an annular Couette cell with a moving lower boundary. The granular
material is initially prepared in an unstable configuration with a layer of
small particles above a layer of large particles. Under shear, the sample mixes
and then re-segregates so that the large particles are located in the top half
of the system in the final state. During this segregation process, we measure
the velocity profile and use the resulting exponential fit as input parameters
to the model. To make a direct comparison between the continuum model and the
observed segregation dynamics, we locally map the measured height of the
experimental sample (which indicates the degree of segregation) to the local
packing density. We observe that the model successfully captures the presence
of a fast mixing process and relatively slower re-segregation process, but the
model predicts a finite re-segregation time, while in the experiment
re-segregation occurs only exponentially in time
Initial boundary value problem for the spherically symmetric Einstein equations with fluids with tangential pressure
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.This work was supported by CMAT, Univ. Minho, through FEDER funds COMPETE and FCT Projects Est-OE/MAT/UI0013/2014 and PTDC/MAT-ANA/1275/2014.info:eu-repo/semantics/publishedVersio
Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions
In this paper, a supersymmetric extension of a system of hydrodynamic type
equations involving Riemann invariants is formulated in terms of a superspace
and superfield formalism. The symmetry properties of both the classical and
supersymmetric versions of this hydrodynamical model are analyzed through the
use of group-theoretical methods applied to partial differential equations
involving both bosonic and fermionic variables. More specifically, we compute
the Lie superalgebras of both models and perform classifications of their
respective subalgebras. A systematic use of the subalgebra structures allow us
to construct several classes of invariant solutions, including travelling
waves, centered waves and solutions involving monomials, exponentials and
radicals.Comment: 30 page
Incorporating Forcing Terms in Cascaded Lattice-Boltzmann Approach by Method of Central Moments
Cascaded lattice-Boltzmann method (Cascaded-LBM) employs a new class of
collision operators aiming to improve numerical stability. It achieves this and
distinguishes from other collision operators, such as in the standard single or
multiple relaxation time approaches, by performing relaxation process due to
collisions in terms of moments shifted by the local hydrodynamic fluid
velocity, i.e. central moments, in an ascending order-by-order at different
relaxation rates. In this paper, we propose and derive source terms in the
Cascaded-LBM to represent the effect of external or internal forces on the
dynamics of fluid motion. This is essentially achieved by matching the
continuous form of the central moments of the source or forcing terms with its
discrete version. Different forms of continuous central moments of sources,
including one that is obtained from a local Maxwellian, are considered in this
regard. As a result, the forcing terms obtained in this new formulation are
Galilean invariant by construction. The method of central moments along with
the associated orthogonal properties of the moment basis completely determines
the expressions for the source terms as a function of the force and macroscopic
velocity fields. In contrast to the existing forcing schemes, it is found that
they involve higher order terms in velocity space. It is shown that the
proposed approach implies "generalization" of both local equilibrium and source
terms in the usual lattice frame of reference, which depend on the ratio of the
relaxation times of moments of different orders. An analysis by means of the
Chapman-Enskog multiscale expansion shows that the Cascaded-LBM with forcing
terms is consistent with the Navier-Stokes equations. Computational experiments
with canonical problems involving different types of forces demonstrate its
accuracy.Comment: 55 pages, 4 figure
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