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B. Mehlig

Publications and source records attributed to B. Mehlig.

At least 127 records · Page 7Linked to original sources
arXiv2004

On the Aggregation of Inertial Particles in Random Flows

We describe a criterion for particles suspended in a randomly moving fluid to aggregate. Aggregation occurs when the expectation value of a random variable is negative. This random variable evolves under a stochastic differential equation. We analyse this equation in detail in the limit where the correlation time of the velocity field of the fluid is very short, such that the stochastic differential equation is a Langevin equation.

cond-mat.stat-mech↗
arXiv2004

Gene-history correlation and population structure

Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the correlation of gene histories in established demographic models for genetic evolution and show how to extend the analysis to more realistic (but more complicated) models of demographic structure. We identify two contributions to the correlation of gene histories in divergent populations: linkage disequilibrium, and differences in the demographic history of individuals in the sample. These two factors contribute to correlations at different length scales: the former at small, and the latter at large scales. We show that recent mixing events in divergent populations limit the range of correlations and compare our findings to empirical results on the correlation of gene histories in the human genome.

q-bio.GN↗
arXiv2004

Understanding of the phase transformation from fullerite to amorphous carbon at the microscopic level

We have studied the shock-induced phase transition from fullerite to a dense amorphous carbon phase by tight-binding molecular dynamics. For increasing hydrostatic pressures P, the C60-cages are found to polymerise at P<10 GPa, to break at P~40 GPa and to slowly collapse further at P>60 GPa. By contrast, in the presence of additional shear stresses, the cages are destroyed at much lower pressures (P<30 GPa). We explain this fact in terms of a continuum model, the snap-through instability of a spherical shell. Surprisingly, the relaxed high-density structures display no intermediate-range order.

cond-mat.mtrl-sci↗
arXiv2004

Fluctuations of the Shannon capacity in a Raleigh model of wireless communication

Using the fact that the Shannon capacity C of a Raleigh model of wireless channels is a linear statistic of the channel matrix, we calculate its variance var[C]. We find that the expected value of the Shannon capacity is typical in the model considered, that is the coefficient of variation (var[C])^(1/2)/ is small.

cond-mat.dis-nn↗
arXiv2004

The decay of photoexcited quantum systems: a description within the statistical scattering model

The decay of photoexcited quantum systems (examples are photodissociation of molecules and autoionization of atoms) can be viewed as a half-collision process (an incoming photon excites the system which subsequently decays by dissociation or autoionization). For this reason, the standard statistical approach to quantum scattering, originally developed to describe nuclear compound reactions, is not directly applicable. Using an alternative approach, correlations and fluctuations of observables characterizing this process were first derived in [Fyodorov YV and Alhassid Y 1998 Phys. Rev. A 58, R3375]. Here we show how the results cited above, and more recent results incorporating direct decay processes, can be obtained from the standard statistical scattering approach by introducing one additional channel.

cond-mat.dis-nn↗
arXiv2003

Path Coalescence in Spatially Correlated Random Walks

A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in many areas of science and engineering as well as other fields such as finance and the life sciences. This letter describes a phenomenon occurring in a natural extension of this model: we consider the motion of a large number of particles subject to successive random displacements which are correlated in space, but not in time. If these random displacements are smaller than their correlation length, the trajectories coalesce onto a decreasing number of trails. This surprising effect is explained and quantitative results are obtained. Various possible realisations are discussed, ranging from coalescence of the tracks of water droplets blown off a windshield to migration patterns of animals.

cond-mat.stat-mech↗
arXiv2003

The path-coalescence transition and its applications

We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the particle trajectories coalesce. We analyse this transition by mapping it to a Kramers problem which we solve exactly. In the limit of weak random force we characterise the dynamics by computing the rate at which caustics are crossed, and the statistics of the particle density in the coalescing phase. Last but not least we describe possible realisations of the effect, ranging from trajectories of raindrops on glass surfaces to animal migration patterns.

cond-mat.dis-nn↗
arXiv2003

Coagulation by Random Velocity Fields as a Kramers Problem

We analyse the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and non-coagulating phases. We show that the phase transition is related to a Kramers problem, and use this to determine the phase diagram, as a function of the dimensionless inertia of the particles, epsilon, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Gamma. We find that the phase line is described by a function which is non-analytic at epsilon=0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realisations of this phase transition.

cond-mat.dis-nn↗
arXiv2003

Fano interference and cross-section fluctuations in molecular photodissociation

We derive an expression for the total photodissociation cross section of a molecule incorporating both indirect processes that proceed through excited resonances, and direct processes. We show that this cross section exhibits generalized Beutler-Fano line shapes in the limit of isolated resonances. Assuming that the closed system can be modeled by random matrix theory, we derive the statistical properties of the photodissociation cross section and find that they are significantly affected by the direct processes. We identify a unique signature of the direct processes in the cross-section distribution in the limit of isolated resonances.

cond-mat↗
arXiv2003

On random symmetric matrices with a constraint: the spectral density of random impedance networks

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found recently for the average density of resonances in random impedance networks [Y.V. Fyodorov, J. Phys. A: Math. Gen. 32, 7429 (1999)]. In the case of banded matrices, the analytical results are compared with those extracted from the numerical solution of Kirchhoff equations for quasi one-dimensional random impedance networks.

cond-mat.dis-nn↗
arXiv2002

On the spatial structure of anomalously localised states in disordered conductors

We study the spatial structure of wave functions with exceptionally high local amplitudes in the Anderson model of localisation. By means of exact diagonalisations of finite systems, we obtain and analyse images of these wave functions: we compare the spatial structure of such anomalously localised states in quasi-one-dimensional samples to that in three-dimensional samples. In both cases the average wave-function intensity exhibits a very narrow peak. The background intensity, however, is found to be very different in these two cases: in three dimensions, it is constant, independent of the distance to the localisation centre (as expected for extended states). In quasi-one dimensional samples, on the other hand, it is redistributed towards the localisation centre and approaches a characteristic form predicted in [A. D. Mirlin, Phys. Rep. 326, 249 (2000)].

cond-mat.dis-nn↗
arXiv2002

Optical response of two-dimensional electron fluids beyond the Kohn regime: strong non-parabolic confinement and intense laser light

We investigate the linear and non-linear optical response of two-dimensional (2D) interacting electron fluids confined by a strong non-parabolic potential. We show that such fluids may exhibit higher-harmonic spectra under realistic experimental conditions. Higher harmonics arise as the electrons explore anharmonicities of the confinement potential (electron-electron interactions reduce this non-linear effect). This opens the possibility of controlling the optical functionality of such systems by engineering the confinement potential. Our results were obtained within time-dependent density-functional theory, employing the adiabatic local-density approximation. A classical hydrodynamical model is in good agreement with the quantum-mechanical results.

cond-mat↗
arXiv2002

Clustering of SNPs along a chromosome: can the neutral model be rejected?

Single nucleotide polymorphisms (SNPs) often appear in clusters along the length of a chromosome. This is due to variation in local coalescent times caused by,for example, selection or recombination. Here we investigate whether recombination alone (within a neutral model) can cause statistically significant SNP clustering. We measure the extent of SNP clustering as the ratio between the variance of SNPs found in bins of length $l$, and the mean number of SNPs in such bins, $σ^2_l/μ_l$. For a uniform SNP distribution $σ^2_l/μ_l=1$, for clustered SNPs $σ^2_l/μ_l > 1$. Apart from the bin length, three length scales are important when accounting for SNP clustering: The mean distance between neighboring SNPs, $Δ$, the mean length of chromosome segments with constant time to the most recent common ancestor, $\el$, and the total length of the chromosome, $L$. We show that SNP clustering is observed if $Δ< \el \ll L$. Moreover, if $l\ll \el \ll L$, clustering becomes independent of the rate of recombination. We apply our results to the analysis of SNP data sets from mice, and human chromosomes 6 and X. Of the three data sets investigated, the human X chromosome displays the most significant deviation from neutrality.

physics.bio-ph↗
arXiv2001

Statistics of selectively neutral genetic variation

Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties of empirical observables (such as the local homozygosity for instance). Previous work relies on numerical results or assumes Gaussian approximations for the corresponding distributions. In this paper we give an analytical derivation of the statistical properties of the local homozygosity and other empirical observables assuming selective neutrality. We find that such distributions can be very non-Gaussian.

physics.bio-ph↗
arXiv2000

Semiclassical trace formulae using coherent states

We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum-mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.

cond-mat.mes-hall↗
arXiv2000

Universal eigenvector statistics in a quantum scattering ensemble

We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector correlations corresponding to eigenvalues in the center of the support of the density of states in the complex plane are described by an expression recently derived for Ginibre's ensemble of random non-Hermitian matrices.

cond-mat.mes-hall↗
arXiv2000

Collective versus single-particle effects in the optical spectra of finite electronic quantum systems

We study optical spectra of finite electronic quantum systems at frequencies smaller than the plasma frequency using a quasi-classical approach. This approach includes collective effects and enables us to analyze how the nature of the (single-particle) electron dynamics influences the optical spectra in finite electronic quantum systems. We derive an analytical expression for the low-frequency absorption coefficient of electro-magnetic radiation in a finite quantum system with ballistic electron dynamics and specular reflection at the boundaries: a two-dimensional electron gas confined to a strip of width a (the approach can be applied to systems of any shape and electron dynamics -- diffusive or ballistic, regular or irregular motion). By comparing with results of numerical computations using the random-phase approximation we show that our analytical approach provides a qualitative and quantitative understanding of the optical spectrum.

cond-mat.mes-hall↗