arXiv subjects

David Hochberg

Publications and source records attributed to David Hochberg.

At least 37 records · Page 2Linked to original sources

arXiv2009

Large scale emergent properties of an autocatalytic reaction-diffusion model subject to noise

The non-equilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable fixed point at one-loop order, and the asymptotic scaling of the correlation functions is predicted for both spatial and temporally correlated noise sources. New effective three-body reaction terms, not present in the original GS model, are induced by the combined interplay of the fluctuations and nonlinearities.

cond-mat.stat-mech↗

arXiv2008

Stability of racemic and chiral steady states in open and closed chemical systems

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived.

q-bio.PE↗

arXiv2007

Mirror symmetry breaking as a problem in dynamical critical phenomena

The critical properties of the Frank model of spontaneous chiral synthesis are discussed by applying results from the field theoretic renormalization group (RG). The long time and long wavelength features of this microscopic reaction scheme belong to the same universality class as multi-colored directed percolation processes. Thus, the following RG fixed points (FP) govern the critical dynamics of the Frank model for d<4: one unstable FP that corresponds to complete decoupling between the two enantiomers, a saddle-point that corresponds to symmetric interspecies coupling, and two stable FPs that individually correspond to unidirectional couplings between the two chiral molecules. These latter two FPs are associated with the breakdown of mirror or chiral symmetry. In this simplified model of molecular synthesis, homochirality is a natural consequence of the intrinsic reaction noise in the critical regime, which corresponds to extremely dilute chemical systems.

q-bio.PE↗

arXiv2007

Reaction-noise induced homochirality

Starting from the chemical master equation, we employ field theoretic techniques to derive Langevin-type equations that exactly describe the stochastic dynamics of the Frank chiral amplification model with spatial diffusion. The intrinsic multiplicative noise properties are completely and rigorously derived by this procedure. We carry out numerical simulations in two spatial dimensions. When the inherent spatio-temporal fluctuations are properly included, then complete chiral amplification results from a purely racemic initial configuration. Phase separation can also arise in which the enantiomers coexist in spatially segregated domains separated by a sharp racemic interface or boundary.

q-bio.PE↗

arXiv2006

Complex noise in diffusion-limited reactions of replicating and competing species

We derive exact Langevin-type equations governing quasispecies dynamics. The inherent multiplicative noise has both real and imaginary parts. The numerical simulation of the underlying complex stochastic partial differential equations is carried out employing the Cholesky decomposition for the noise covariance matrix. This noise produces unavoidable spatio-temporal density fluctuations about the mean field value. In two dimensions, the fluctuations are suppressed only when the diffusion time scale is much smaller than the amplification time scale for the master species.

cond-mat.stat-mech↗

arXiv2006

Complex reaction noise in molecular quasispecies model

We have derived exact Langevin equations for a model of quasispecies dynamics. The inherent multiplicative reaction noise is complex and its statistical properties are specified completely. The numerical simulation of the complex Langevin equations is carried out using the Cholesky decomposition for the noise covariance matrix. This internal noise, which is due to diffusion-limited reactions, produces unavoidable spatio-temporal density fluctuations about the mean field value. In two dimensions, this noise strictly vanishes only in the perfectly mixed limit, a situation difficult to attain in practice.

q-bio.PE↗

arXiv2005

Contributions of Albert Einstein to Earth Sciences: A review in Commemoration of the World Year of Physics

The World Year of Physics (2005) is an international celebration to commemorate the one hundredth anniversary of Einstein's "Annus Mirabilis". The United Nations has officially declared 2005 the International Year of Physics. However, the impact of Einstein's ideas was not restricted to physics. Among numerous other disciplines, Einstein also made significant and specific contributions to Earth Sciences. His geosciences-related letters, comments, and scientific articles, are dispersed, not easily accesible and are poorly known. The present review attempts to integrate them, as a tribute to Einstein in commemoration of this centenary. These contributions can be classified into three basic areas: geodynamics, geological (planetary) catastrophism and fluvial geomorphology.

physics.hist-ph↗

arXiv2005

Path integral evaluation of the one-loop effective potential in field theory of diffusion-limited reactions

The well-established effective action and effective potential framework from the quantum field theory domain is adapted and successfully applied to classical field theories of the Doi and Peliti type for diffusion controlled reactions. Through a number of benchmark examples, we show that the direct calculation of the effective potential in fixed space dimension $d=2$ to one-loop order reduces to a small set of simple elementary functions, irrespective of the microscopic details of the specific model. Thus the technique, which allows one to obtain with little additional effort, the potentials for a wide variety of different models, represents an important alternative to the standard model dependent diagram-based calculations. The renormalized effective potential, effective equations of motion and the associated renormalization group equations are computed in $d=2$ spatial dimensions for a number of single species field theories of increasing complexity.

cond-mat.stat-mech↗

arXiv2005

Galilean invariance and homogeneous anisotropic randomly stirred flows

The Ward-Takahashi (WT) identities for incompressible flow implied by Galilean invariance are derived for the randomly forced Navier-Stokes equation (NSE), in which both the mean and fluctuating velocity components are explicitly present. The consequences of Galilean invariance for the vertex renormalization are drawn from this identity.

cond-mat.stat-mech↗

arXiv2003

Large Scale Features of Rotating Forced Turbulence

Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of modifications to the fluid equation of motion. The first correction transforms the molecular shear viscosity into a (rotation independent) effective viscosity. The second perturbative correction leads to a new large scale non-dissipative force proportional to the fluid angular velocity in the slow rotation regime. This effective force does no net work and alters the dispersion relation of inertial waves propagating in the fluid. Both dynamically generated corrections can be identified with certain components of the most general axisymmetric ``viscosity tensor'' for a Newtonian fluid.

physics.flu-dyn↗

arXiv2002

The renormalization group and fractional Brownian motion

We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the Renormalization Group as a tool to improve perturbative calculations, and check that beyond the classical regime of the field theory (i. e., when no fluctuations are present) the non--linearities drive the probability distribution function of the system away from classical Brownian Motion and into a regime which to the lowest order is that of fBM. Our results can be applied to systems away from equilibrium and to dynamical critical phenomena. We illustrate our results with two selected examples: a particle in a heat bath, and the KPZ equation.

cond-mat.stat-mech↗

arXiv2002

Asymptotic properties of turbulent magnetohydrodynamics

The dynamic renormalization group (RG) is used to study the large-distance and long-time limits of viscous and resistive incompressible magnetohydrodynamics subject to random forces and currents. The scale-dependent viscosity and magnetic resistivity are derived and used for carrying out RG-improved perturbation theory. This is applied to derive both the asymptotic scaling and the overall proportionality coefficients for both the velocity and magnetic field correlation functions as well as the kinetic and magnetic energy density spectral functions. The Kolmogorov, Iroshnikov-Kraichnan, as well as other energy spectra, formally can be obtained by suitable choice of injected noise, although the method limits the validity of these energy spectra only to the asymptotic regime . Injection of a random magnetic helicity is considered, its RG-improved spectral density derived, and its contribution to the velocity and magnetic field correlation functions determined. The RG scaling solutions are used to determine information at asymptotic scales about energy and helicity cascade directions and mixing between magnetic and kinetic energy. Some of the results found here also are shown to be valid for the Navier-Stokes hydrodynamic equation. The results have applicability to geomagnetism as well as cosmic magnetic fields at astrophysical and cosmological scales.

cond-mat.stat-mech↗

arXiv2000

Effective potential for classical field theories subject to stochastic noise

Classical field theories coupled to stochastic noise provide an extremely powerful tool for modeling phenomena as diverse as turbulence, pattern-formation, and the structural development of the universe itself. In this Letter we sketch a general formalism that maps such systems into a field theory language, and demonstrate how to extract the one-loop physics for an arbitrary classical field theory coupled to Gaussian noise. The amplitude of the noise two-point function serves as the loop-counting parameter and is the analog of Planck's constant hbar in quantum field theory. We define the effective action and the effective potential, and derive a general formula for the one-loop effective potential of a classical field theory coupled to translation-invariant Gaussian noise.

cond-mat.stat-mech↗

arXiv2000

Small-scale properties of the KPZ equation and dynamical symmetry breaking

A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or higher space dimensions. This potential is intimately related to the probability distribution function (PDF) for the spacetime averaged field. For the restricted class of field configurations considered here, the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman-Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions.

cond-mat.stat-mech↗

arXiv2000

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.

cond-mat.stat-mech↗

arXiv2000

Renormalization Group Analysis of a Quivering String Model of Posture Control

Scaling concepts and renormalization group (RG) methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various non-trivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak non-linearities is confirmed. Correlations in posture fluctuations are obtained in both the time and space domain. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both the large-separation (along the string) and long-time regimes of posture control.

cond-mat↗

arXiv1999

Effective potential for the reaction-diffusion-decay system

In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.

cond-mat.stat-mech↗

arXiv1999

Effective action for stochastic partial differential equations

Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. In this paper we set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these non-quantum field theories are fully interacting. Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues, and furthermore offers marked technical advantages: We can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the BRST formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ``direct approach'' is the SPDE analog of canonical quantization using physical fields.) We show how to define the effective action to all loops, and then focus on the one-loop effective action, and its specialization to constant fields: the effective potential. An important result is that the amplitude of the two-point function governing the noise acts as the loop-counting parameter and is the analog of Planck's constant hbar in this SPDE context. We derive a general expression for the one-loop effective potential of an arbitrary SPDE subject to translation-invariant Gaussian noise, and compare this with the one-loop potential for QFT.

cond-mat.stat-mech↗