3,166 research outputs found
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
In this paper we develop the Lagrangian and multisymplectic structures of the
Heisenberg magnet (HM) model which are then used as the basis for geometric
discretizations of HM. Despite a topological obstruction to the existence of a
global Lagrangian density, a local variational formulation allows one to derive
local conservation laws using a version of N\"other's theorem from the formal
variational calculus of Gelfand-Dikii. Using the local Lagrangian form we
extend the method of Marsden, Patrick and Schkoller to derive local
multisymplectic discretizations directly from the variational principle. We
employ a version of the finite element method to discretize the space of
sections of the trivial magnetic spin bundle over an
appropriate space-time . Since sections do not form a vector space, the
usual FEM bases can be used only locally with coordinate transformations
intervening on element boundaries, and conservation properties are guaranteed
only within an element. We discuss possible ways of circumventing this problem,
including the use of a local version of the method of characteristics,
non-polynomial FEM bases and Lie-group discretization methods.Comment: 12 pages, accepted Math. and Comp. Simul., May 200
Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs
Several recently developed multisymplectic schemes for Hamiltonian PDEs have
been shown to preserve associated local conservation laws and constraints very
well in long time numerical simulations. Backward error analysis for PDEs, or
the method of modified equations, is a useful technique for studying the
qualitative behavior of a discretization and provides insight into the
preservation properties of the scheme. In this paper we initiate a backward
error analysis for PDE discretizations, in particular of multisymplectic box
schemes for the nonlinear Schrodinger equation. We show that the associated
modified differential equations are also multisymplectic and derive the
modified conservation laws which are satisfied to higher order by the numerical
solution. Higher order preservation of the modified local conservation laws is
verified numerically.Comment: 12 pages, 6 figures, accepted Math. and Comp. Simul., May 200
On the heterogeneous character of water's amorphous polymorphism
In this letter we report {\it in situ} small--angle neutron scattering
results on the high--density (HDA) and low-density amorphous (LDA) ice
structures and on intermediate structures as found during the temperature
induced transformation of HDA into LDA. We show that the small--angle signal is
characterised by two regimes featuring different properties ( is the
modulus of the scattering vector defined as with being half the scattering
angle and the incident neutron wavelength). The very low--
regime ( \AA ) is dominated by a Porod--limit
scattering. Its intensity reduces in the course of the HDA to LDA
transformation following a kinetics reminiscent of that observed in wide--angle
diffraction experiments. The small--angle neutron scattering formfactor in the
intermediate regime of \AA HDA and LDA
features a rather flat plateau. However, the HDA signal shows an ascending
intensity towards smaller marking this amorphous structure as
heterogeneous. When following the HDA to LDA transition the formfactor shows a
pronounced transient excess in intensity marking all intermediate structures as
strongly heterogeneous on a length scale of some nano--meters
Functional renormalization and mean-field approach to multiband systems with spin-orbit coupling: Application to the Rashba model with attractive interaction
The functional renormalization group (RG) in combination with Fermi surface
patching is a well-established method for studying Fermi liquid instabilities
of correlated electron systems. In this article, we further develop this method
and combine it with mean-field theory to approach multiband systems with
spin-orbit coupling, and we apply this to a tight-binding Rashba model with an
attractive, local interaction. The spin dependence of the interaction vertex is
fully implemented in a RG flow without SU(2) symmetry, and its momentum
dependence is approximated in a refined projection scheme. In particular, we
discuss the necessity of including in the RG flow contributions from both bands
of the model, even if they are not intersected by the Fermi level. As the
leading instability of the Rashba model, we find a superconducting phase with a
singlet-type interaction between electrons with opposite momenta. While the gap
function has a singlet spin structure, the order parameter indicates an
unconventional superconducting phase, with the ratio between singlet and
triplet amplitudes being plus or minus one on the Fermi lines of the upper or
lower band, respectively. We expect our combined functional RG and mean-field
approach to be useful for an unbiased theoretical description of the
low-temperature properties of spin-based materials.Comment: consistent with published version in Physical Review B (2016
Scalable and Energy-Efficient Millimeter Massive MIMO Architectures: Reflect-Array and Transmit-Array Antennas
Hybrid analog-digital architectures are considered as promising candidates
for implementing millimeter wave (mmWave) massive multiple-input
multiple-output (MIMO) systems since they enable a considerable reduction of
the required number of costly radio frequency (RF) chains by moving some of the
signal processing operations into the analog domain. However, the analog feed
network, comprising RF dividers, combiners, phase shifters, and line
connections, of hybrid MIMO architectures is not scalable due to its
prohibitively high power consumption for large numbers of transmit antennas.
Motivated by this limitation, in this paper, we study novel massive MIMO
architectures, namely reflect-array (RA) and transmit-array (TA) antennas. We
show that the precoders for RA and TA antennas have to meet different
constraints compared to those for conventional MIMO architectures. Taking these
constraints into account and exploiting the sparsity of mmWave channels, we
design an efficient precoder for RA and TA antennas based on the orthogonal
matching pursuit algorithm. Furthermore, in order to fairly compare the
performance of RA and TA antennas with conventional fully-digital and hybrid
MIMO architectures, we develop a unified power consumption model. Our
simulation results show that unlike conventional MIMO architectures, RA and TA
antennas are highly energy efficient and fully scalable in terms of the number
of transmit antennas.Comment: submitted to IEEE ICC 201
Vibrational instability, two-level systems and Boson peak in glasses
We show that the same physical mechanism is fundamental for two seemingly
different phenomena such as the formation of two-level systems in glasses and
the Boson peak in the reduced density of low-frequency vibrational states
g(w)/w^2. This mechanism is the vibrational instability of weakly interacting
harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of
Debye frequency) the instability, controlled by the anharmonicity, creates a
new stable universal spectrum of harmonic vibrations with a Boson peak feature
as well as double-well potentials with a wide distribution of barrier heights.
Both are determined by the strength of the interaction I ~ w_c between the
oscillators. Our theory predicts in a natural way a small value for the
important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses.
We show that C ~ I^{-3} and decreases with increasing of the interaction
strength I. We show that the number of active two-level systems is very small,
less than one per ten million of oscillators, in a good agreement with
experiment. Within the unified approach developed in the present paper the
density of the tunneling states and the density of vibrational states at the
Boson peak frequency are interrelated.Comment: 28 pages, 3 figure
Diffusion and jump-length distribution in liquid and amorphous CuZr
Using molecular dynamics simulation, we calculate the distribution of atomic
jum ps in CuZr in the liquid and glassy states. In both states
the distribution of jump lengths can be described by a temperature independent
exponential of the length and an effective activation energy plus a
contribution of elastic displacements at short distances. Upon cooling the
contribution of shorter jumps dominates. No indication of an enhanced
probability to jump over a nearest neighbor distance was found. We find a
smooth transition from flow in the liquid to jumps in the g lass. The
correlation factor of the diffusion constant decreases with decreasing
temperature, causing a drop of diffusion below the Arrhenius value, despite an
apparent Arrhenius law for the jump probability
- …