2,623 research outputs found
The converse problem for the multipotentialisation of evolution equations and systems
We propose a method to identify and classify evolution equations and systems
that can be multipotentialised in given target equations or target systems. We
refer to this as the {\it converse problem}. Although we mainly study a method
for -dimensional equations/system, we do also propose an extension of
the methodology to higher-dimensional evolution equations. An important point
is that the proposed converse method allows one to identify certain types of
auto-B\"acklund transformations for the equations/systems. In this respect we
define the {\it triangular-auto-B\"acklund transformation} and derive its
connections to the converse problem. Several explicit examples are given. In
particular we investigate a class of linearisable third-order evolution
equations, a fifth-order symmetry-integrable evolution equation as well as
linearisable systems.Comment: 31 Pages, 7 diagrams, submitted for consideratio
AK-cut crystal resonators
Calculations have predicted the existence of crystallographically doubly rotated quartz orientations with turnover temperatures which are considerably less sensitive to angular misorientation then comparable AT- or BT-cuts. These crystals are arbitrarily designated as the AK-cut. Experimental data is given for seven orientations, phi-angle variations between 30-46 deg and theta-angle variations between 21-28 deg measured on 3.3-3.4 MHz fundamental mode resonators vibrating in the thickness shear c-mode. The experimental turnover temperatures of these resonators are between 80 C and 150 C, in general agreement with calculated values. The normalized frequency change as a function of temperature has been fitted with a cubic equation
3+1D hydrodynamic simulation of relativistic heavy-ion collisions
We present MUSIC, an implementation of the Kurganov-Tadmor algorithm for
relativistic 3+1 dimensional fluid dynamics in heavy-ion collision scenarios.
This Riemann-solver-free, second-order, high-resolution scheme is characterized
by a very small numerical viscosity and its ability to treat shocks and
discontinuities very well. We also incorporate a sophisticated algorithm for
the determination of the freeze-out surface using a three dimensional
triangulation of the hyper-surface. Implementing a recent lattice based
equation of state, we compute p_T-spectra and pseudorapidity distributions for
Au+Au collisions at root s = 200 GeV and present results for the anisotropic
flow coefficients v_2 and v_4 as a function of both p_T and pseudorapidity. We
were able to determine v_4 with high numerical precision, finding that it does
not strongly depend on the choice of initial condition or equation of state.Comment: 16 pages, 11 figures, version accepted for publication in PRC,
references added, minor typos corrected, more detailed discussion of
freeze-out routine adde
A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
We explore a nonlocal connection between certain linear and nonlinear
ordinary differential equations (ODEs), representing physically important
oscillator systems, and identify a class of integrable nonlinear ODEs of any
order. We also devise a method to derive explicit general solutions of the
nonlinear ODEs. Interestingly, many well known integrable models can be
accommodated into our scheme and our procedure thereby provides further
understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres
Effective action for Einstein-Maxwell theory at order RF**4
We use a recently derived integral representation of the one-loop effective
action in Einstein-Maxwell theory for an explicit calculation of the part of
the effective action containing the information on the low energy limit of the
five-point amplitudes involving one graviton, four photons and either a scalar
or spinor loop. All available identities are used to get the result into a
relatively compact form.Comment: 13 pages, no figure
Polarizations and differential calculus in affine spaces
Within the framework of mappings between affine spaces, the notion of -th
polarization of a function will lead to an intrinsic characterization of
polynomial functions. We prove that the characteristic features of derivations,
such as linearity, iterability, Leibniz and chain rules, are shared -- at the
finite level -- by the polarization operators. We give these results by means
of explicit general formulae, which are valid at any order , and are based
on combinatorial identities. The infinitesimal limits of the -th
polarizations of a function will yield its -th derivatives (without
resorting to the usual recursive definition), and the above mentioned
properties will be recovered directly in the limit. Polynomial functions will
allow us to produce a coordinate free version of Taylor's formula
On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations
We discuss nonlocal symmetries and nonlocal conservation laws that follow
from the systematic potentialisation of evolution equations. Those are the Lie
point symmetries of the auxiliary systems, also known as potential symmetries.
We define higher-degree potential symmetries which then lead to nonlocal
conservation laws and nonlocal transformations for the equations. We
demonstrate our approach by the Burgers' hierarchy and the
Calogero-Degasperis-Ibragimov-Shabat hierarchy
Towards a direct measurement of vacuum magnetic birefringence: PVLAS achievements
Nonlinear effects in vacuum have been predicted but never observed yet
directly. The PVLAS collaboration has long been working on an apparatus aimed
at detecting such effects by measuring vacuum magnetic birefringence.
Unfortunately the sensitivity has been affected by unaccounted noise and
systematics since the beginning. A new small prototype ellipsometer has been
designed and characterized at the Department of Physics of the University of
Ferrara, Italy entirely mounted on a single seismically isolated optical bench.
With a finesse F = 414000 and a cavity length L = 0.5 m we have reached the
predicted sensitivity of psi = 2x10^-8 1/sqrt(Hz) given the laser power at the
output of the ellipsomenter of P = 24 mW. This record result demonstrates the
feasibility of reaching such sensitivities and opens the way to designing a
dedicated apparatus for a first detection of vacuum magnetic birefringence
Supergoop Dynamics
We initiate a systematic study of the dynamics of multi-particle systems with
supersymmetric Van der Waals and electron-monopole type interactions. The
static interaction allows a complex continuum of ground state configurations,
while the Lorentz interaction tends to counteract this configurational fluidity
by magnetic trapping, thus producing an exotic low temperature phase of matter
aptly named supergoop. Such systems arise naturally in gauge
theories as monopole-dyon mixtures, and in string theory as collections of
particles or black holes obtained by wrapping D-branes on internal space
cycles. After discussing the general system and its relation to quiver quantum
mechanics, we focus on the case of three particles. We give an exhaustive
enumeration of the classical and quantum ground states of a probe in an
arbitrary background with two fixed centers. We uncover a hidden conserved
charge and show that the dynamics of the probe is classically integrable. In
contrast, the dynamics of one heavy and two light particles moving on a line
shows a nontrivial transition to chaos, which we exhibit by studying the
Poincar\'e sections. Finally we explore the complex dynamics of a probe
particle in a background with a large number of centers, observing hints of
ergodicity breaking. We conclude by discussing possible implications in a
holographic context.Comment: 35 pages,11 figures. v2: updated references to include a previous
proof of classical integrability, exchanged a figure for a prettier versio
Quantum effects in the evolution of vortices in the electromagnetic field
We analyze the influence of electron-positron pairs creation on the motion of
vortex lines in electromagnetic field. In our approach the electric and
magnetic fields satisfy nonlinear equations derived from the Euler-Heisenberg
effective Lagrangian. We show that these nonlinearities may change the
evolution of vortices.Comment: REVTEX4 and 5 EPS figure
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