Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs.

Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven by the heat-bath dynamics, their stationary characteristics, such as magnetization, are correctly reproduced by MFA as confirmed by Monte Carlo simulations. It turns out that MFA reproduces the same result as the generating functional analysis that is expected to provide the exact description of such models. We argue that on directed regular random graphs, the neighbors of a given vertex are typically uncorrelated, and that is why MFA for models with heat-bath dynamics provides their exact description. For models with Metropolis dynamics, certain additional correlations become relevant, and MFA, which neglects these correlations, is less accurate. Models with heat-bath dynamics undergo continuous phase transition, and at the critical point, the power-law time decay of the order parameter exhibits the behavior of the Ising mean-field universality class. Analogous phase transitions for models with Metropolis dynamics are discontinuous.

Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds.

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.

The central role of peripheral nodes in directed network dynamics.

Many social, technological, and biological systems with asymmetric interactions display a variety of collective phenomena, such as opinion formation and synchronization. This has motivated much research on the dynamical impact of local and mesoscopic structure in directed networks. However, the unique constraints imposed by the global organization of directed networks remain largely undiscussed. Here, we control the global organization of directed Erdos-Rényi networks, and study its impact on the emergence of synchronization and ferromagnetic ordering, using Kuramoto and Ising dynamics. In doing so, we demonstrate that source nodes - peripheral nodes without incoming links - can disrupt or entirely suppress the emergence of collective states in directed networks. This effect is imposed by the bow-tie organization of directed networks, where a large connected core does not uniquely ensure the emergence of collective states, as it does for undirected networks.

In vitro hemodynamic evaluation of ventricular suction conditions of the EVAHEART ventricular assist pump.

PURPOSE: Mismatches between pump output and venous return in a continuous-flow ventricular assist device may elicit episodes of ventricular suction. This research describes a series of in vitro experiments to characterize the operating conditions under which the EVAHEART centrifugal blood pump (Sun Medical Technology Research Corp., Nagano, Japan) can be operated with minimal concern regarding left ventricular (LV) suction. METHODS: The pump was interposed into a pneumatically driven pulsatile mock circulatory system (MCS) in the ventricular apex to aorta configuration. Under varying conditions of preload, afterload, and systolic pressure, the speed of the pump was increased step-wise until suction was observed. Identification of suction was based on pump inlet pressure. RESULTS: In the case of reduced LV systolic pressure, reduced preload (=10 mmHg), and afterload (=60 mmHg), suction was observed for speeds=2,200 rpm. However, suction did not occur at any speed (up to a maximum speed of 2,400 rpm) when preload was kept within 10-14 mmHg and afterload=80 mmHg. Although in vitro experiments cannot replace in vivo models, the results indicated that ventricular suction can be avoided if sufficient preload and afterload are maintained. CONCLUSION: Conditions of hypovolemia and/or hypotension may increase the risk of suction at the highest speeds, irrespective of the native ventricular systolic pressure. However, in vitro guidelines are not directly transferrable to the clinical situation; therefore, patient-specific evaluation is recommended, which can be aided by ultrasonography at various points in the course of support.

Assessment of cardiac function during mechanical circulatory support: the quest for a suitable clinical index.

A new index to assess left ventricular (LV) function in patients implanted with continuous flow left-ventricular assist devices (LVADs) is proposed. Derived from the pump flow signal, this index is defined as the coefficient (k) of the semilogarithmic relationship between "pseudo-ejection" fraction (pEF) and the volume discharged by the pump in diastole, (V d). pEF is defined as the ratio of the "pseudo-stroke volume" (pSV) to V d. The pseudo-stroke volume is the difference between V d and the volume discharged by the pump in systole (V s), both obtained by integrating pump flow with respect to time in a cardiac cycle. k was compared in-vivo with others two indices: the LV pressure-based index, M(TP), and the pump flow-based index, I(Q). M(TP) is the slope of the linear regression between the "triple-product" and end-diastolic pressure, EDP. The triple-product, TP = LV SP.dP/dt(max). HR, is the product of LV systolic pressure, maximum time-derivative of LV pressure, and heart rate. I(Q) is the slope of the linear regression between maximum time-derivative of pump flow, dQ/dt(max), and pump flow peak-to-peak amplitude variation, Q(P2P). To test the response of k to contractile state changes, contractility was altered through pharmacological interventions. The absolute value of k decreased from 1.354 ± 0.25 (baseline) to 0.685 ± 0.21 after esmolol infusion. The proposed index is sensitive to changes in inotropic state, and has the potential to be used clinically to assess contractile function of patients implanted with VAD.

Molecular dynamics simulations of ballistic annihilation.

Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents xi and gamma, which describe the long-time decay of the number of particles [n(t) approximately t-xi] and of their typical velocity [v(t) approximately t-gamma]. To a good accuracy our results confirm the scaling relation xi+gamma=1. In the two-dimensional case our results are in good agreement with those obtained from Boltzmann kinetic theory.

Splitting the voter Potts model critical point.

Recently some two-dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class. We show that, for an absorbing-states Potts model with finite but further than nearest-neighbor range of interactions, the critical point is split into two critical points: one of the Ising type and the other of the directed percolation universality class. Similar splitting takes place in the three-dimensional nearest-neighbor model.

Oscillations and dynamics in a two-dimensional prey-predator system.

Using Monte Carlo simulations we study two-dimensional prey-predator systems. Measuring the variance of densities of prey and predators on the triangular lattice and on the lattice with eight neighbors, we conclude that temporal oscillations of these densities vanish in the thermodynamic limit. This result suggests that such oscillations do not exist in two-dimensional models, at least when driven by local dynamics. Depending on the control parameter, the model could be either in an active or in an absorbing phase, which are separated by the critical point. The critical behavior of this model is studied using the dynamical Monte Carlo method. This model has two dynamically nonsymmetric absorbing states. In principle both absorbing states can be used for the analysis of the critical point. However, dynamical simulations which start from the unstable absorbing state suffer from metastablelike effects, which sometimes renders the method inefficient.