Biomedical subjects

David Hochberg

Publications and source records attributed to David Hochberg.

7 recordsLinked to original sources

PubMed2006

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 spatiotemporal 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.

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PubMed2006

A review of the contributions of Albert Einstein to earth sciences--in commemoration of the World Year of Physics.

The World Year of Physics (2005) is an international celebration to commemorate the 100th anniversary of Einstein's "Annus Mirabilis." The United Nations has officially declared 2005 as 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 accessible, 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. Regarding geodynamics, Einstein essentially supported Hapgood's very controversial theory called Earth Crust Displacement. With respect to geological (planetary) catastrophism, it is shown how the ideas of Einstein about Velikovsky's proposals evolved from 1946 to 1955. Finally, in relation to fluvial geodynamics, the review incorporates the elegant work in which Einstein explains the formation of meandering rivers. A general analysis of his contributions is also carried out from today's perspective. Given the interdisciplinarity and implications of Einstein's achievements to multiple fields of knowledge, we propose that the year 2005 serve, rather than to confine his universal figure within a specific scientific area, to broaden it for a better appreciation of this brilliant scientist in all of his dimensions.

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PubMed2005

Galilean invariance and homogeneous anisotropic randomly stirred flows.

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

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PubMed2005

Spatiotemporal patterns driven by autocatalytic internal reaction noise.

The influence that intrinsic local-density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the presence of strong internal reaction noise. The dynamics of the Gray-Scott (GS) model [P. Gray and S. K. Scott, Chem. Eng. Sci. 38, 29 (1983); and ibid.39, 1087 (1984); and J. Phys. Chem. 89, 22 (1985)] with a constant external source is first cast in terms of a continuum field theory representing the corresponding master equation. We then derive a Langevin description of the field theory and use these stochastic differential equations in our simulations. The nature of the multiplicative noise is specified exactly without recourse to assumptions and turns out to be of the same order as the reaction itself, and thus cannot be treated as a small perturbation. Many of the complex patterns obtained in the absence of noise for the GS model are completely obliterated by these strong internal fluctuations, but we find novel spatial patterns induced by this reaction noise in the regions of parameter space that otherwise correspond to homogeneous solutions when fluctuations are not included.

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PubMed2003

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

The nonequilibrium 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.

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PubMed2003

Noise-controlled self-replicating patterns.

We present novel numerical evidence of spot self-replication controlled by noise in a simple autocatalytic reaction-diffusion system. The system dynamics exhibits a noise controlled transition from stripe growth to spot replication. The growth kinetics is also controlled by noise, and there is an optimal noise intensity for which the multiplication rate of spots is maximal. For larger noise intensities, the spots become unstable and the system is attracted by the trivial steady state. Some of the effects are reminiscent of both polymer chain and cell colony formation in random environments.

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PubMed2003

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 nondissipative 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.

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