Biomedical subjects

Per Arne Rikvold

Publications and source records attributed to Per Arne Rikvold.

11 recordsLinked to original sources

PubMed2006

Effects of preference for attachment to low-degree nodes on the degree distributions of a growing directed network and a simple food-web model.

We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a preferential-attachment scheme, in which a new node attaches to an existing node i with probability II(k(i)) approximately k(-1), where k(i) is the number of outgoing links at i. We calculate the degree distribution for the outgoing links in the asymptotic regime t --> infinity, n(k) both analytically and by Monte Carlo simulations. The distribution decays like kmu(k)/Tau(k) for large k, where is a constant. We investigate the effect of this preferential-attachment scheme, by comparing the results to an equivalent growth model with a degree-independent probability of attachment, which gives an exponential outdegree distribution. Also, we relate this mechanism to simple food-web models by implementing it in the cascade model. We show that the low-degree preferential-attachment mechanism breaks the symmetry between in- and outdegree distributions in the cascade model. It also causes a faster decay in the tails of the outdegree distributions for both our network growth model and the cascade model.

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PubMed2005

Decay of metastable phases in a model for the catalytic oxidation of CO.

We study by kinetic Monte Carlo simulations the dynamic behavior of a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O-->CO(2) on a catalytic surface. Finite-size scaling analysis of the fluctuations and the fourth-order order-parameter cumulant show that below a critical CO desorption rate, the model exhibits a nonequilibrium first-order phase transition between low and high CO coverage phases. We calculate several points on the coexistence curve. We also measure the metastable lifetimes associated with the transition from the low CO coverage phase to the high CO coverage phase, and vice versa. Our results indicate that the transition process follows a mechanism very similar to the decay of metastable phases associated with equilibrium first-order phase transitions and can be described by the classic Kolmogorov-Johnson-Mehl-Avrami theory of phase transformation by nucleation and growth. In the present case, the desorption parameter plays the role of temperature, and the distance to the coexistence curve plays the role of an external field or supersaturation. We identify two distinct regimes, depending on whether the system is far from or close to the coexistence curve, in which the statistical properties and the system-size dependence of the lifetimes are different, corresponding to multidroplet or single-droplet decay, respectively. The crossover between the two regimes approaches the coexistence curve logarithmically with system size, analogous to the behavior of the crossover between multidroplet and single-droplet metastable decay near an equilibrium first-order phase transition.

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PubMed2005

Effects of lateral diffusion on morphology and dynamics of a microscopic lattice-gas model of pulsed electrodeposition.

The influence of nearest-neighbor diffusion on the decay of a metastable low-coverage phase (monolayer adsorption) in a square lattice-gas model of electrochemical metal deposition is investigated by kinetic Monte Carlo simulations. The phase-transformation dynamics are compared to the well-established Kolmogorov-Johnson-Mehl-Avrami theory. The phase transformation is accelerated by diffusion, but remains in accord with the theory for continuous nucleation up to moderate diffusion rates. At very high diffusion rates the phase-transformation kinetic shows a crossover to instantaneous nucleation. Then, the probability of medium-sized clusters is reduced in favor of large clusters. Upon reversal of the supersaturation, the adsorbate desorbs, but large clusters still tend to grow during the initial stages of desorption. Calculation of the free energy of subcritical clusters by enumeration of lattice animals yields a quasiequilibrium distribution which is in reasonable agreement with the simulation results. This is an improvement relative to classical droplet theory, which fails to describe the distributions, since the macroscopic surface tension is a bad approximation for small clusters.

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PubMed2005

Response of a catalytic reaction to periodic variation of the CO pressure: increased CO2 production and dynamic phase transition.

We present a kinetic Monte Carlo study of the dynamical response of a Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic variation of the CO pressure. We use a square-wave periodic pressure variation with parameters that can be tuned to enhance the catalytic activity. We produce evidence that, below a critical value of the desorption rate, the driven system undergoes a dynamic phase transition between a CO2 productive phase and a nonproductive one at a critical value of the period and waveform of the pressure oscillation. At the dynamic phase transition the period-averaged CO2 production rate is significantly increased and can be used as a dynamic order parameter. We perform a finite-size scaling analysis that indicates the existence of power-law singularities for the order parameter and its fluctuations, yielding estimated critical exponent ratios beta/nu approximately 0.12 and gamma/nu approximately 1.77. These exponent ratios, together with theoretical symmetry arguments and numerical data for the fourth-order cumulant associated with the transition, give reasonable support for the hypothesis that the observed nonequilibrium dynamic phase transition is in the same universality class as the two-dimensional equilibrium Ising model.

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PubMed2004

Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers.

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.

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PubMed2004

Low-temperature nucleation in a kinetic Ising model with soft stochastic dynamics.

We study low-temperature nucleation in kinetic Ising models by analytical and simulational methods, confirming the general result for the average metastable lifetime, =Aexp((betagamma) (beta=1/k(B)T) [Commun. Math. Phys. 137, 209 (1991)]]. Contrary to common belief, we find that both A and Gamma depend significantly on the stochastic dynamic. In particular, for a "soft" dynamic, in which the effects of the interactions and the applied field factorize in the transition rates, Gamma does not simply equal the energy barrier against nucleation, as it does for the standard Glauber dynamic, which does not have this factorization property.

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PubMed2003

Update statistics in conservative parallel-discrete-event simulations of asynchronous systems.

We model the performance of an ideal closed chain of L processing elements that work in parallel in an asynchronous manner. Their state updates follow a generic conservative algorithm. The conservative update rule determines the growth of a virtual time surface. The physics of this growth is reflected in the utilization (the fraction of working processors) and in the interface width. We show that it is possible to make an explicit connection between the utilization and the microscopic structure of the virtual time interface. We exploit this connection to derive the theoretical probability distribution of updates in the system within an approximate model. It follows that the theoretical lower bound for the computational speedup is s=(L+1)/4 for L> or =4. Our approach uses simple statistics to count distinct surface-configuration classes consistent with the model growth rule. It enables one to compute analytically microscopic properties of an interface, which are unavailable by continuum methods.

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PubMed2003

Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics.

We present a study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution. Selection is provided through a reproduction probability that contains quenched, random interspecies interactions, while genetic variation is provided through a low mutation rate. Both selection and mutation act on individual organisms. Consistent with some current theories of macroevolutionary dynamics, the model displays intermittent, statistically self-similar behavior with punctuated equilibria. The probability density for the lifetimes of ecological communities is well approximated by a power law with exponent near -2, and the corresponding power spectral densities show 1/f noise (flicker noise) over several decades. The long-lived communities (quasisteady states) consist of a relatively small number of mutualistically interacting species, and they are surrounded by a "protection zone" of closely related genotypes that have a very low probability of invading the resident community. The extent of the protection zone affects the stability of the community in a way analogous to the height of the free-energy barrier surrounding a metastable state in a physical system. Measures of biological diversity are on average stationary with no discernible trends, even over our very long simulation runs of approximately 3.4 x 10(7) generations.

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PubMed2003

Microstructure and velocity of field-driven Ising interfaces moving under a soft stochastic dynamic.

We present theoretical and dynamic Monte Carlo simulation results for the mobility and microscopic structure of (1+1)-dimensional Ising interfaces moving far from equilibrium in an applied field under a single-spin-flip "soft" stochastic dynamic. The soft dynamic is characterized by the property that the effects of changes in field energy and interaction energy factorize in the transition rate, in contrast to the nonfactorizing nature of the traditional Glauber and Metropolis rates "hard" dynamics). This work extends our previous studies of the Ising model with a hard dynamic and the unrestricted solid-on-solid (SOS) model with soft and hard dynamics. [P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000); J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116 (2002).] The Ising model with soft dynamics is found to have closely similar properties to the SOS model with the same dynamic. In particular, the local interface width does not diverge with increasing field as it does for hard dynamics. The skewness of the interface at nonzero field is very weak and has the opposite sign of that obtained with hard dynamics.

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PubMed2002

Microstructure and velocity of field-driven solid-on-solid interfaces: analytic approximations and numerical results.

The local structure of a solid-on-solid interface in a two-dimensional kinetic Ising ferromagnet or attractive lattice-gas model with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field or chemical potential, is studied by an analytic mean-field, nonlinear-response theory [P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)], and by dynamic Monte Carlo simulations. The probability density of the height of an individual step in the surface is obtained, both analytically and by simulation. The width of the probability density is found to increase dramatically with the magnitude of the applied field, with close agreement between the theoretical predictions and the simulation results. Excellent agreement between theory and simulations is also found for the field dependence and anisotropy of the interface velocity. The joint distribution of nearest-neighbor step heights is obtained by simulation. It shows increasing correlations with increasing field, similar to the skewness observed in other examples of growing surfaces.

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PubMed2002

Numerical confirmation of late-time t(1/2) growth in three-dimensional phase ordering.

Results for the late-time regime of phase ordering in three dimensions are reported, based on numerical integration of the time-dependent Ginzburg-Landau equation with nonconserved order parameter at zero temperature. For very large systems (700(3)) at late times, t> or =150, the characteristic length grows as a power law, R(t) approximately t(n), with the measured n in agreement with the theoretically expected result n=1/2 to within statistical errors. In this time regime R(t) is found to be in excellent agreement with the analytical result of Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. 49, 1223 (1982)]. At early times, good agreement is found between the simulations and the linearized theory with corrections due to the lattice anisotropy.

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