Biomedical subjects

Nadav M Shnerb

Publications and source records attributed to Nadav M Shnerb.

4 recordsLinked to original sources

PubMed2006

Nonlocal competition and logistic growth: patterns, defects, and fronts.

Logistic growth of diffusing reactants on spatial domains with long-range competition is studied. The bifurcations cascade involved in the transition from the homogeneous state to a spatially modulated stable solution is presented, and a distinction is made between a modulated phase, dominated by single or few wave numbers, and the spiky phase, where localized colonies are separated by depleted region. The characteristic defects in the periodic structure are presented for each phase, together with the invasion dynamics in the case of local initiation. It is shown that the basic length scale that controls the bifurcation is the width of the Fisher front, and that the total population grows as this width decreases. A mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition.

Journal Article↗

PubMed2005

Inverse melting and inverse freezing: a spin model.

Systems of highly degenerate ordered or frozen state may exhibit inverse melting (reversible crystallization upon heating) or inverse freezing (reversible glass transition upon heating). This phenomenon is reviewed, and a list of experimental demonstrations and theoretical models is presented. A simple spin model for inverse melting is introduced and solved analytically for infinite range, constant paramagnetic exchange interaction. The random exchange analogue of this model yields inverse freezing, as implied by the analytic solution based on the replica trick. The qualitative features of this system (generalized Blume-Capel spin model) are shown to resemble a large class of inverse melting phenomena. The appearance of inverse melting is related to an exact rescaling of one of the interaction parameters that measures the entropy of the system. For the case of almost degenerate spin states, perturbative expansion is presented, and the first three terms correspond to the empiric formula for the Flory-Huggins chi parameter in the theory of polymer melts. The possible microscopic origin of this chi parameter and the limitations of the Flory-Huggins theory where the state degeneracy is associated with the different conformations of a single polymer or with the spatial structures of two interacting molecules are discussed.

Journal Article↗

PubMed2004

Spin model for inverse melting and inverse glass transition.

A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the "ferromagnetic" phase, while lower energy associated with the noninteracting states yields a "paramagnetic" phase as temperature decreases. An infinite range model is solved analytically for constant paramagnetic exchange interaction, while for its random exchange analogous results based on the replica symmetric solution are presented. The qualitative features of this model are shown to resemble a large class of inverse melting phenomena. First and second order transition regimes are identified.

Journal Article↗

PubMed2004

Pattern formation and nonlocal logistic growth.

Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and long-range interactions. Domain walls between regions of different order parameter are expressed as soliton solutions of the reduced dynamics for nearest-neighbor interactions. The analytic results are confirmed by numerical simulations.

Animals↗