arXiv subjects

Erwin Frey

Publications and source records attributed to Erwin Frey.

At least 199 records · Page 11Linked to original sources

arXiv2002

Domain wall roughening in dipolar films in the presence of disorder

We derive a low-energy Hamiltonian for the elastic energy of a Néel domain wall in a thin film with in-plane magnetization, where we consider the contribution of the long-range dipolar interaction beyond the quadratic approximation. We show that such a Hamiltonian is analogous to the Hamiltonian of a one-dimensional polaron in an external random potential. We use a replica variational method to compute the roughening exponent of the domain wall for the case of two-dimensional dipolar interactions.

cond-mat.stat-mech↗

arXiv2001

Relaxation kinetics of biological dimer adsorption models

We discuss the relaxation kinetics of a one-dimensional dimer adsorption model as recently proposed for the binding of biological dimers like kinesin on microtubules. The non-equilibrium dynamics shows several regimes: irreversible adsorption on short time scales, an intermediate plateau followed by a power-law regime and finally exponential relaxation towards equilibrium. In all four regimes we give analytical solutions. The algebraic decay and the scaling behaviour can be explained by mapping onto a simple reaction-diffusion model. We show that there are several possibilities to define the autocorrelation function and that they all asymptotically show exponential decay, however with different time constants. Our findings remain valid if there is an attractive interaction between bound dimers.

cond-mat.soft↗

arXiv2001

Dipolar Interactions in Superconductor-Ferromagnet Heterostructures

We consider a simple model for a superlattice composed of a thin magnetic film placed between two bulk superconductors. The magnetic film is modelled by a planar but otherwise arbitrary distribution of magnetic dipoles and the superconductors are treated in the London approximation. Due to the linearity of the problem, we are able to compute the magnetic energy of the film in the presence of the superconductors. We show that in the case of small wavenumbers compared to the inverse London penetration depth, the magnetic energy resembles the energy of a distribution of magnetisation in a two dimensional space. Possible experimental applications of these results are discussed.

cond-mat.supr-con↗

arXiv2000

Novel Phases and Reentrant Melting of Two Dimensional Colloidal Crystals

We investigate two-dimensional (2d) melting in the presence of a one-dimensional (1d) periodic potential as, for example, realized in recent experiments on 2d colloids subjected to two interfering laser beams. The topology of the phase diagram is found to depend primarily on two factors: the relative orientation of the 2d crystal and the periodic potential troughs, which select a set of Bragg planes running parallel to the troughs, and the commensurability ratio p= a'/d of the spacing a' between these Bragg planes to the period d of the periodic potential. The complexity of the phase diagram increases with the magnitude of the commensurabilty ratio p. Rich phase diagram, with ``modulated liquid'', ``floating'' and ``locked floating'' solid and smectic phases are found. Phase transitions between these phases fall into two broad universality classes, roughening and melting, driven by the proliferation of discommensuration walls and dislocations, respectively. We discuss correlation functions and the static structure factor in these phases and make detailed predictions of the universal features close to the phase boundaries. We predict that for charged systems with highly screened short-range interactions these melting transitions are generically reentrant as a function of the strength of the periodic potential, prediction that is in accord with recent 2d colloid experiments. Implications of our results for future experiments are also discussed.

cond-mat.soft↗

arXiv1999

Light Induced Melting of Colloidal Crystals in Two Dimensions

We demonstrate that particles confined to two dimensions (2d) and subjected to a one-dimensional (1d) periodic potential exhibit a rich phase diagram, with both ``locked floating solids'' and smectic phases. The resulting phases and phase transitions are studied as a function of temperature and potential strength. We find reentrant melting as a function of the potential strength. Our results lead to universal predictions consistent with recent experiments on 2d colloids in the presence of a laser-induced 1d periodic potential.

cond-mat.soft↗

arXiv1999

Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 ρ}) in Fourier space, as a function of ρand the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the critical and correction-to-scaling exponents at the roughening transition are determined to all orders in a (d - d_c) expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension d_c = 2 (1 + ρ) are genuinely different which could lead to a re-interpretation of results in the literature.

cond-mat.stat-mech↗

arXiv1998

Statistical Mechanics of Semiflexible Polymers: Theory and Experiment

We review the physical properties of macromolecular networks, consisting of semiflexible polymers such as actin. We start by giving a theoretical analysis of the conformational statistics and mechanical response of single filaments. Experimentally relevant quantities such as the end-to-end distribution function and the force-extension relation are discussed. The results are used to analyze the elastic modulus of an entangled solution of such objects. We also discuss the short time and long time (terminal regime) dynamics and compare our results with recent dynamic light scattering and viscoelastic measurements. Furthermore, we analyze the elasticity transition in stochastic models of crosslinked networks.

cond-mat.soft↗

arXiv1998

Physics of Solutions and Networks of Semiflexible Macromolecules and the Control of Cell Function

Living cells are soft bodies of a characteristic form, but endowed with a capacity for a steady turnover of their structures. Both of these material properties, i.e. recovery of the shape after an external stress has been imposed and dynamic structural reorganization, are essential for many cellular phenomena. Examples are mechanical properties of tissue, cell motility, cell growth and division, and active intracellular transport. Numerous experiments in vivo and in vitro have shown that the structural element responsible for the extraordinary mechanical and dynamical properties of eukaryotic cells is the cytoskeleton, a three-dimensional assembly of protein fibers such as actin filaments and microtubules. In addition to those biopolymers various proteins with structural and regulatory functions have a major influence on the mechanical properties. At the relevant length-scales (a few microns at most) the building blocks of these biomaterials are very different from conventional polymeric material. In contrast to flexible polymers the persistence length is of the same order of magnitude as their total contour length or even larger. This implies that the physics of such a system is determined by a subtle interplay between energetic and entropic contributions. We review our present understanding of the physics of biopolymers using concepts from macromolecular and statistical physics complemented by computer simulation. These systems open up a new field of soft condensed matter research, which to date is only poorly understood but has a great potential for interesting new physical phenomena.

cond-mat.soft↗

arXiv1998

Elastically coupled molecular motors

We study the influence of filament elasticity on the motion of collective molecular motors. It is found that for a backbone flexibility exceeding a characteristic value (motor stiffness divided through the mean displacement between attached motors), the ability of motors to produce force reduces as compared to rigidly coupled motors, while the maximum velocity remains unchanged. The force-velocity-relation in two different analytic approximations is calculated and compared with Monte-Carlo simulations. Finally, we extend our model by introducing motors with a strain-dependent detachment rate. A remarkable crossover from the nearly hyperbolic shape of the Hill curve for stiff backbones to a linear force-velocity relation for very elastic backbones is found. With realistic model parameters we show that the backbone flexibility plays no role under physiological conditions in muscles, but it should be observable in certain in vitro assays.

cond-mat.soft↗

arXiv1998

Force-Velocity Relations of a Two-State Crossbridge Model for Molecular Motors

We discuss the force-velocity relations obtained in a two-state crossbridge model for molecular motors. They can be calculated analytically in two limiting cases: for a large number and for one pair of motors. The effect of the strain-dependent detachment rate on the motor characteristics is studied. It can lead to linear, myosin-like, kinesin-like and anomalous curves. In particular, we specify the conditions under which oscillatory behavior may be found.

cond-mat.soft↗

arXiv1998

Screened and Unscreened Phases in Sedimenting Suspensions

A coarse-grained stochastic hydrodynamical description of velocity and concentration fluctuations in steadily sedimenting suspensions is constructed, and analyzed using self-consistent and renormalization group methods. We find that there exists a dynamical, non-equilibrium phase transition from an "unscreened" phase in which we recover the Caflisch-Luke (R.E. Caflisch and J.H.C. Luke, Phys. Fluids 28, 759 (1985)) divergence of the velocity variance to a "screened" phase where the velocity fluctuations have a finite correlation length growing as $ϕ^{-1/3}$ where $ϕ$ is the particle volume fraction, in agreement with Segrè et. al. (Phys. Rev. Lett. 79, 2574 (1997)) and the velocity variance is independent of system size. Detailed predictions are made for the correlation function in both phases and at the transition.

cond-mat.soft↗

arXiv1997

Dynamic Scattering from Solutions of Semiflexible Polymers

The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to the hydrodynamic interactions. For the cases of dilute and semidilute solutions exact expressions for the initial slope are obtained. When the hydrodynamic interaction is treated on the level of a renormalized friction coefficient, the decay of the structure factor due to the structural relaxation obeys a stretched exponential law in agreement with experiments on actin. We show how the characteristic parameters of the system (the persistence length \ell_p, the lateral diameter a of the molecules and the mesh size ξ_m of the network) are readily determined by a single scattering experiment with scattering wavelength λobeying a << λ<<\ell_p and λ<ξ_m. We also find an exact explicit expression for the effective (wave vector dependent) dynamic exponent z(k)<3 for semiflexible polymers and thus an enlightening explanation for a longstanding puzzle in polymer physics.

cond-mat.soft↗

arXiv1996

Radial distribution function of semiflexible polymers

We calculate the distribution function of the end--to--end distance of a semiflexible polymer with large bending rigidity. This quantity is directly observable in experiments on single semiflexible polymers (e.g., DNA, actin) and relevant to their interpretation. It is also an important starting point for analyzing the behavior of more complex systems such as networks and solutions of semiflexible polymers. To estimate the validity of the obtained analytical expressions, we also determine the distribution function numerically using Monte Carlo simulation and find good quantitative agreement.

cond-mat↗

arXiv1996

Critical Behavior of the Supersolid transition in Bose-Hubbard Models

We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF--CSS transition is in the three-dimensional XY universality class. The SF--XSS transition exhibits non-trivial new critical behavior, and appears, within a $d=3-ε$ expansion to be driven generically first order by fluctuations. However, within a one--loop calculation directly in $d=2$ a strong coupling fixed point with striking ``non-Bose liquid'' behavior is found. At special isolated multi-critical points of particle-hole symmetry, the system falls into the 3d Ising universality class.

cond-mat↗

arXiv1996

Force-Extension Relation and Plateau Modulus for Wormlike Chains

We derive the linear force-extension relation for a wormlike chain of arbitrary stiffness including entropy elasticity, bending and thermodynamic buckling. From this we infer the plateau modulus $G^0$ of an isotropic entangled solution of wormlike chains. The entanglement length $L_e$ is expressed in terms of the characteristic network parameters for three different scaling regimes in the entangled phase. The entanglement transition and the concentration dependence of $G^0$ are analyzed. Finally we compare our findings with experimental data.

cond-mat↗

arXiv1996

Mode coupling and renormalization group results for the noisy Burgers equation

We investigate the noisy Burgers equation (Kardar--Parisi--Zhang equation in 1+1 dimensions) using the dynamical renormalization group (to two--loop order) and mode--coupling techniques. The roughness and dynamic exponent are fixed by Galilean invariance and a fluctuation--dissipation theorem. The fact that there are no singular two--loop contributions to the two--point vertex functions supports the mode--coupling approach, which can be understood as a self--consistent one--loop theory where vertex corrections are neglected. Therefore, the numerical solution of the mode coupling equations yields very accurate results for the scaling functions. In addition, finite--size effects can be studied. Furthermore, the results from exact Ward identities, as well as from second--order perturbation theory permit the quantitative evaluation of the vertex corrections, and thus provide a quantitative test for the mode--coupling approach. It is found that the vertex corrections themselves are of the order one. Surprisingly, however, their effect on the correlation function is substantially smaller.

cond-mat↗

arXiv1995

Critical Dynamics of Magnets

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole--dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin wave theories. A detailed comparison is made of the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon--spin--resonance, electron--spin--resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three--dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin--wave spectrum in two--dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.

cond-mat↗

arXiv1995

Crossover scaling functions and an extended minimal subtraction scheme

A field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension. The method leads to flow functions for the parameters and coupling constants of the model which depend on the set of parameters which characterize the fixed point landscape of the underlying problem. Similar to Nelson's trajectory integral method any vertex function can be expressed as a line integral along a renormalization group trajectory, which in the field theoretic formulation are given by the characteristics of the corresponding Callan-Symanzik equation. The field theoretic renormalization automatically leads to a separation of the regular and singular parts of all crossover scaling functions. The method is exemplified for the crossover problem in magnetic phase transitions, percolation problems and quantum phase transitions. The broad applicability of the method is emphasized.

cond-mat↗