LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques.

Magnetic behavior of 10 nm-magnetite particles diluted in lyotropic liquid crystals

A magnetic study of 10 nm magnetite nanoparticles diluted in lyotropic liquid crystal and common liquids was carried out. In the liquid crystal the ZFC-FC curves showed a clear irreversible behavior, and it was possible to distinguish the nematic from the isotropic phase since the magnetization followed the dependence of the nematic order parameter with the temperature. This behavior could be mimicked by Monte Carlo simulation. (C) 2011 American Institute of Physics. [doi:10.1063/1.3549616]

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution. (C) 2009 American Institute of Physics. [doi:10.1063/1.3253297]

Coexistence of interacting opinions in a generalized Sznajd model

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.

Power-law creep behavior of a semiflexible chain

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Frustration and anomalous behavior in the Bell-Lavis model of liquid water

We have reconsidered the Bell-Lavis model of liquid water and investigated its relation to its isotropic version, the antiferromagnetic Blume-Emery-Griffiths model on the triangular lattice. Our study was carried out by means of an exact solution on the sequential Husimi cactus. We show that the ground states of both models share the same topology and that fluid phases (gas and low- and high-density liquids) can be mapped onto magnetic phases (paramagnetic, antiferromagnetic, and dense paramagnetic, respectively). Both models present liquid-liquid coexistence and several thermodynamic anomalies. This result suggests that anisotropy introduced through orientational variables play no specific role in producing the density anomaly, in agreement with a similar conclusion discussed previously following results for continuous soft core,models. We propose that the presence of liquid anomalies may be related to energetic frustration, a feature common to both models.

Perturbations of black p-branes

We consider black p-brane solutions of the low-energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a AdSd((p+2)) x Sd((8-p)) space which, in the framework of Maldacena's conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a (p+1)-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.

Piezomagnetic behavior of Co-doped ZnO nanoribbons

Using ab initio total energy calculations, we show that bilayer systems of ZnO nanoribbons, (ZnO)(2)NR, doped with Co atoms exhibit a piezomagnetic behavior. We find the formation of energetically stable zigzag chains of Co atoms along the edge sites of (ZnO)(2)NR's, Co(Zn(chain))-(ZnO)(2)NR. At the ground state, the antiferromagnetic and the ferromagnetic states are very close in energy, whereas upon longitudinal stretch, parallel to the nanoribbon growth direction, it becomes ferromagnetic. Further electronic structure calculations indicate that not only the magnetic state but also the electronic structure of CoZn(chain)-(ZnO)(2)NR can be tuned by the mechanical stretch. In this case, we find that stretched NR's exhibit dispersive unpaired electronic states within the (ZnO)(2)NR band gap.

Mimicking nanoribbon behavior using a graphene layer on SiC

We propose a natural way to create quantum-confined regions in graphene in a system that allows large-scale device integration. We show, using first-principles calculations, that a single graphene layer on a trenched region of [000 (1) over bar] SiC mimics (i) the energy bands around the Fermi level and (ii) the magnetic properties of free-standing graphene nanoribbons. Depending on the trench direction, either zigzag or armchair nanoribbons are mimicked. This behavior occurs because a single graphene layer over a SiC surface loses the graphenelike properties, which are restored solely over the trenches, providing in this way a confined strip region.

Critical behavior of the magnetization in the spin-gapped system NiCl(2)-4SC (NH(2))(2)

We report accurate magnetization measurements on the spin-gap compound NiCl(2)-4SC (NH(2))(2) around the low portion of the magnetic induced phase ordering. The critical density of the magnetization at the phase boundary is analyzed in terms of a Bose-Einstein condensation (BEC) of bosonic particles, and the boson interaction strength is obtained as upsilon(0)=0.61 meV. The detailed analysis of the magnetization data across the transition leads to the conclusion for the preservation of the U(1) symmetry, as required for BEC. (c) 2009 American Institute of Physics. [DOI: 10.1063/1.3055265]

Understanding the ""Antikick"" in the Merger of Binary Black Holes

The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the ""antikick,"" namely, the sudden deceleration after the merger, has not yet found a simple explanation. We show that the antikick can be understood in terms of the radiation from a deformed black hole where the anisotropic curvature distribution on the horizon correlates with the direction and intensity of the recoil. Our analysis is focused on Robinson-Trautman spacetimes and allows us to measure both the energies and momenta radiated in a gauge-invariant manner. At the same time, this simpler setup provides the qualitative and quantitative features of merging black holes, opening the way to a deeper understanding of the nonlinear dynamics of black-hole spacetimes.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton

Stavskaya's model is a one-dimensional probabilistic cellular automaton (PCA) introduced in the end of the 1960s as an example of a model displaying a nonequilibrium phase transition. Although its absorbing state phase transition is well understood nowadays, the model never received a full numerical treatment to investigate its critical behavior. In this Brief Report we characterize the critical behavior of Stavskaya's PCA by means of Monte Carlo simulations and finite-size scaling analysis. The critical exponents of the model are calculated and indicate that its phase transition belongs to the directed percolation universality class of critical behavior, as would be expected on the basis of the directed percolation conjecture. We also explicitly establish the relationship of the model with the Domany-Kinzel PCA on its directed site percolation line, a connection that seems to have gone unnoticed in the literature so far.

Influence of temperature and excitation procedure on the athermal behavior of Nd(3+)-doped phosphate glass: Thermal lens, interferometric, and calorimetric measurements

In this work, thermal and optical properties of the commercial Q-98 neodymium-doped phosphate glass have been measured at low temperature, from 50 to 300 K. The time-resolved thermal lens spectrometry together with the optical interferometry and the thermal relaxation calorimetry methods were used to investigate the glass athermal characteristics described by the temperature coefficient of the optical path length change, ds/dT. The thermal diffusivity was also determined, and the temperature coefficients of electronic polarizability, linear thermal expansion, and refractive index were calculated and used to explain ds/dT behavior. ds/dT measured via thermal lens method was found to be zero at 225 K. The results provided a complete characterization of the thermo-optical properties of the Q-98 glass, which may be useful for those using this material for diode-pumped solid-state lasers. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3234396]