2,652 research outputs found
Morphometric approach to many-body correlations in hard spheres
We model the thermodynamics of local structures within the hard sphere liquid
at arbitrary volume fractions through the \textit{morphometric} calculation of
-body correlations. We calculate absolute free energies of local geometric
motifs in excellent quantitative agreement with molecular dynamics simulations
across the liquid and supercooled liquid regimes. We find a bimodality in the
density library of states where five-fold symmetric structures appear lower in
free energy than four-fold symmetric structures, and from a single reaction
path predict a relaxation barrier which scales linearly in the compressibility
factor. The method provides a new route to assess changes in the free energy
landscape at volume fractions dynamically inaccessible to conventional
techniques.Comment: 6+17 pages, 3 figure
Transformation elastodynamics and active exterior acoustic cloaking
This chapter consists of three parts. In the first part we recall the
elastodynamic equations under coordinate transformations. The idea is to use
coordinate transformations to manipulate waves propagating in an elastic
material. Then we study the effect of transformations on a mass-spring network
model. The transformed networks can be realized with "torque springs", which
are introduced here and are springs with a force proportional to the
displacement in a direction other than the direction of the spring terminals.
Possible homogenizations of the transformed networks are presented, with
potential applications to cloaking. In the second and third parts we present
cloaking methods that are based on cancelling an incident field using active
devices which are exterior to the cloaked region and that do not generate
significant fields far away from the devices. In the second part, the exterior
cloaking problem for the Laplace equation is reformulated as the problem of
polynomial approximation of analytic functions. An explicit solution is given
that allows to cloak larger objects at a fixed distance from the cloaking
device, compared to previous explicit solutions. In the third part we consider
the active exterior cloaking problem for the Helmholtz equation in 3D. Our
method uses the Green's formula and an addition theorem for spherical outgoing
waves to design devices that mimic the effect of the single and double layer
potentials in Green's formula.Comment: Submitted as a chapter for the volume "Acoustic metamaterials:
Negative refraction, imaging, lensing and cloaking", Craster and Guenneau
ed., Springe
Vector magnetometer design study: Analysis of a triaxial fluxgate sensor design demonstrates that all MAGSAT Vector Magnetometer specifications can be met
The design of the vector magnetometer selected for analysis is capable of exceeding the required accuracy of 5 gamma per vector field component. The principal elements that assure this performance level are very low power dissipation triaxial feedback coils surrounding ring core flux-gates and temperature control of the critical components of two-loop feedback electronics. An analysis of the calibration problem points to the need for improved test facilities
Spherical single-roll dynamos at large magnetic Reynolds numbers
This paper concerns kinematic helical dynamos in a spherical fluid body
surrounded by an insulator. In particular, we examine their behaviour in the
regime of large magnetic Reynolds number \Rm, for which dynamo action is
usually concentrated upon a simple resonant stream-surface. The dynamo
eigensolutions are computed numerically for two representative single-roll
flows using a compact spherical harmonic decomposition and fourth-order
finite-differences in radius. These solutions are then compared with the growth
rates and eigenfunctions of the Gilbert and Ponty (2000) large \Rm asymptotic
theory. We find good agreement between the growth rates when \Rm>10^4, and
between the eigenfunctions when \Rm>10^5.Comment: 36 pages, 8 figures. V2: incorrect labels in Fig3 corrected. The
article appears in Physics of Fluids, 22, 066601, and may be found at
http://pof.aip.org/phfle6/v22/i6/p066601_s1 . (Copyright 2010 American
Institute of Physics. This article may be downloaded for personal use only.
Any other use requires prior permission of the author and the American
Institute of Physics
Classical and quantum shortcuts to adiabaticity for scale-invariant driving
A shortcut to adiabaticity is a driving protocol that reproduces in a short
time the same final state that would result from an adiabatic, infinitely slow
process. A powerful technique to engineer such shortcuts relies on the use of
auxiliary counterdiabatic fields. Determining the explicit form of the required
fields has generally proven to be complicated. We present explicit
counterdiabatic driving protocols for scale-invariant dynamical processes,
which describe for instance expansion and transport. To this end, we use the
formalism of generating functions, and unify previous approaches independently
developed in classical and quantum studies. The resulting framework is applied
to the design of shortcuts to adiabaticity for a large class of classical and
quantum, single-particle, non-linear, and many-body systems.Comment: 17 pages, 5 figure
Fourth order real space solver for the time-dependent Schr\"odinger equation with singular Coulomb potential
We present a novel numerical method and algorithm for the solution of the 3D
axially symmetric time-dependent Schr\"odinger equation in cylindrical
coordinates, involving singular Coulomb potential terms besides a smooth
time-dependent potential. We use fourth order finite difference real space
discretization, with special formulae for the arising Neumann and Robin
boundary conditions along the symmetry axis. Our propagation algorithm is based
on merging the method of the split-operator approximation of the exponential
operator with the implicit equations of second order cylindrical 2D
Crank-Nicolson scheme. We call this method hybrid splitting scheme because it
inherits both the speed of the split step finite difference schemes and the
robustness of the full Crank-Nicolson scheme. Based on a thorough error
analysis, we verified both the fourth order accuracy of the spatial
discretization in the optimal spatial step size range, and the fourth order
scaling with the time step in the case of proper high order expressions of the
split-operator. We demonstrate the performance and high accuracy of our hybrid
splitting scheme by simulating optical tunneling from a hydrogen atom due to a
few-cycle laser pulse with linear polarization
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