Searcharxiv⌕ Search

arXiv subjects

A. Engel

Publications and source records attributed to A. Engel.

At least 37 records · Page 2Linked to original sources
arXiv2007

Jarzynski equation for a simple quantum system: Comparing two definitions of work

The validity of the Jarzynski equation for a very simple, exactly solvable quantum system is analyzed. The implications of two different definitions of work proposed in the literature are investigated. The first one derives from measurements of the system energy at the beginning and at the end of the process under consideration making the work a classical stochastic variable with transition probabilities derived from quantum mechanics. In the second definition an operator of work is introduced and the average in the Jarzynski equation is a quantum expectation value. For the first definition a general quantum mechanical version of the Jarzynski equation is known to hold. For the second one the Jarzynski equation fails to yield the free energy difference at low temperature.

cond-mat.stat-mech↗
arXiv2007

Replica mean-field theory for Levy spin-glasses

Infinite-range spin-glass models with Levy-distributed interactions show a freezing transition similar to disordered spin systems on finite connectivity random graphs. It is shown that despite diverging moments of the local field distribution this transition can be analyzed within the replica approach by working at imaginary temperature and using a variant of the replica method developed for diluted systems and optimization problems. The replica-symmetric self-consistent equation for the distribution of local fields illustrates how the long tail in the distribution of coupling strengths gives rise to a significant fraction of strong bonds per spin which form a percolating backbone at the transition temperature.

cond-mat.dis-nn↗
arXiv2006

Suppressing the Rayleigh-Taylor instability with a rotating magnetic field

The Rayleigh-Taylor instability of a magnetic fluid superimposed on a non-magnetic liquid of lower density may be suppressed with the help of a spatially homogeneous magnetic field rotating in the plane of the undisturbed interface. Starting from the complete set of Navier-Stokes equations for both liquids a Floquet analysis is performed which consistently takes into account the viscosities of the fluids. Using experimentally relevant values of the parameters we suggest to use this stabilization mechanism to provide controlled initial conditions for an experimental investigation of the Rayleigh-Taylor instability.

physics.flu-dyn↗
arXiv2006

Cylindrical Korteweg-de Vries solitons on a ferrofluid surface

Linear and non-linear surface waves on a ferrofluid cylinder surrounding a current-carrying wire are investigated. Suppressing the Rayleigh-Plateau instability of the fluid column by the magnetic field of a sufficiently large current in the wire axis-symmetric surface deformations are shown to propagate without dispersion in the long wavelength limit. Using multiple scale perturbation theory the weakly non-linear regime may be described by a Korteweg-de Vries equation with coefficients depending on the magnetic field strength. For different values for the current in the wire hence different solutions such as hump or hole solitons may be generated. The possibility to observe these structures in experiments is also elucidated.

physics.flu-dyn↗
arXiv2005

Fluctuation effects in superconducting nanostrips

Superconducting fluctuations in long and narrow strips made from ultrathin NbN films, have been investigated. For large bias currents close to the critical current fluctuations led to localized, temporary transitions into the normal conducting state, which were detected as voltage transients developing between the strip ends. We present models based on fluctuations in the Cooper pair density and current-assisted thermal-unbinding of vortex-antivortex pairs, which explain the current and temperature dependence of the experimental fluctuation rates.

cond-mat.supr-con↗
arXiv2001

Shape transformations in rotating ferrofluid drops

Floating drops of magnetic fluid can be brought into rotation by applying a rotating magnetic field. We report theoretical and experimental results on the transition from a spheroid equilibrium shape to non-axissymmetrical three-axes ellipsoids at certain values of the external field strength. The transitions are continuous for small values of the magnetic susceptibility and show hysteresis for larger ones. In the non-axissymmetric shape the rotational motion of the drop consists of a vortical flow inside the drop combined with a slow rotation of the shape. Nonlinear magnetization laws are crucial to obtain quantitative agreement between theory and experiment.

nlin.PS↗
arXiv2001

On the electromagnetic force on a polarizable body

The force on a macroscopic polarizable body in an inhomogenous electromagnetic field is calculated for three simple exactly solvable situations. Comparing different approaches we pinpoint possible pitfalls and resolve recent confusion about the force density in ferrofluids.

cond-mat.mtrl-sci↗
arXiv2001

Vortex dynamics in layered superconductors with correlated defects: influence of interlayer coupling

We report a detailed study of the vortex dynamics and vortex phase diagrams of two amorphous Ta_0.3Ge_0.7/Ge multilayered films with intrinsic coplanar defects, but different interlayer coupling. A pinned Bose-glass phase in the more weakly coupled sample exists only below a cross-over field H* in striking contrast to the strongly coupled film. Above H* the flux lines are thought to break up into pancake vortices and the cross-over field is significantly increased when the field is aligned along the extended defects. The two films show different vortex creep excitations in the Bose-glass phase.

cond-mat.supr-con↗
arXiv2000

Planform selection in two-layer Benard-Marangoni convection

Benard-Marangoni convection in a system of two superimposed liquids is investigated theoretically. Extending previous studies the complete hydrodynamics of both layers is treated and buoyancy is consistently taken into account. The planform selection problem between rolls, squares and hexagons is investigated by explicitly calculating the coefficients of an appropriate amplitude equation from the parameters of the fluids. The results are compared with recent experiments on two-layer systems in which squares at onset have been reported.

patt-sol↗
arXiv1999

Correlations between hidden units in multilayer neural networks and replica symmetry breaking

We consider feed-forward neural networks with one hidden layer, tree architecture and a fixed hidden-to-output Boolean function. Focusing on the saturation limit of the storage problem the influence of replica symmetry breaking on the distribution of local fields at the hidden units is investigated. These field distributions determine the probability for finding a specific activation pattern of the hidden units as well as the corresponding correlation coefficients and therefore quantify the division of labor among the hidden units. We find that although modifying the storage capacity and the distribution of local fields markedly replica symmetry breaking has only a minor effect on the correlation coefficients. Detailed numerical results are provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and nonoverlapping receptive fields.

cond-mat.dis-nn↗
arXiv1998

Fingering Instability in a Water-Sand Mixture

The temporal evolution of a water-sand interface driven by gravity is experimentally investigated. By means of a Fourier analysis of the evolving interface the growth rates are determined for the different modes appearing in the developing front. To model the observed behavior we apply the idea of the Rayleigh-Taylor instability for two stratified fluids. Carrying out a linear stability analysis we calculate the growth rates from the corresponding dispersion relations for finite and infinite cell sizes. Based on the theoretical results the viscosity of the suspension is estimated to be approximately 100 times higher than that of pure water, in agreement with other experimental findings.

patt-sol↗
arXiv1998

Matrix Games, Mixed Strategies, and Statistical Mechanics

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices and derive analytical expressions for the value of the game and the distribution of strategy strengths. In particular the fraction of pure strategies not contributing to the optimal mixed strategy of a player is calculated. Both independently distributed as well as correlated elements of the payoff matrix are considered and the results compared with numerical simulations.

cond-mat.dis-nn↗
arXiv1998

A multifractal phase-space analysis of perceptrons with biased patterns

We calculate the multifractal spectrum of the partition of the coupling space of a perceptron induced by random input-output pairs with non-zero mean. From the results we infer the influence of the input and output bias respectively on both the storage and generalization properties of the network. It turns out that the value of the input bias is irrelevant as long as it is different from zero. The generalization problem with output bias is new and shows an interesting two-level scenario. To compare our analytical results with simulations we introduce a simple and efficient algorithm to implement Gibbs learning.

cond-mat.dis-nn↗
arXiv1997

Multifractality and percolation in the coupling space of perceptrons

The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=γN$ random input patterns. The multifractal spectrum $f(α)$ can be calculated analytically using the replica formalism. The storage capacity and the generalization behaviour of the perceptron are shown to be related to properties of $f(α)$ which are correctly described within the replica symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a transition from percolating to non-percolating cells. The existence of empty cells gives rise to singularities in the multifractal spectrum. The analytical results for binary couplings are corroborated by numerical studies.

cond-mat.dis-nn↗
arXiv1996

Storage capacity of correlated perceptrons

We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A general formalism is introduced using a multi-perceptron costfunction that allows to determine the maximal number of random inputs as a function of the desired values of the correlations. Replica-symmetric results for $K=2$ and $K=3$ are compared with properties of two-layer networks of tree-structure and fixed Boolean function between hidden units and output. The results show which correlations in the hidden layer of multi-layer neural networks are crucial for the value of the storage capacity.

cond-mat.dis-nn↗
arXiv1996

On the VC-dimension of neural networks with binary weights

We investigate the VC-dimension of the perceptron and simple two-layer networks like the committee- and the parity-machine with weights restricted to values $\pm1$. For binary inputs, the VC-dimension is determined by atypical pattern sets, i.e. it cannot be found by replica analysis or numerical Monte Carlo sampling. For small systems, exhaustive enumerations yield exact results. For systems that are too large for enumerations, number theoretic arguments give lower bounds for the VC-dimension. For the Ising perceptron, the VC-dimension is probably larger than $N/2$.

cond-mat↗
arXiv1996

K^+ momentum spectrum from (K^-,K^+) reactions in intranuclear cascade model

In a framework of intranuclear cascade (INC) type calculation, we study a momentum spectrum in reactions \KK at a beam momentum of 1.65 GeV/c. INC model calculations are compared with the relativistic impulse approximation (RIA) calculations to perform the detailed study of the reaction mechanism. We find that the INC model can reproduce the experimental data on various targets. Especially, in the low-momentum region, the forward-angle cross sections of the $(K^-,K^+)$ reaction on from light to heavy targets are consistently explained with the two-step strangeness exchange and production processes with various intermediate mesons, and $ϕ$, $a_0$ and $f_0$ productions and their decay into $K^+K^-$. In the two-step processes, inclusion of meson and hyperon resonances is found to be essential.

nucl-th↗