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We study the ground-state properties of a system of identical classical Coulombic point particles, evenly distributed between two equivalently charged parallel plates at distance $d$; the system as a whole is electroneutral. It was previously shown that upon increasing d from 0 to infinity, five different structures of the bilayer Wigner crystal become energetically favored, starting from a hexagonal lattice (phase I, d=0) and ending at a staggered hexagonal lattice (phase V, d -> infinity). In this paper, we derive new series representations of the ground-state energy for all five bilayer structures. The derivation is based on a sequence of transformations for lattice sums of Coulomb two-particle potentials plus the neutralizing background, having their origin in the general theory of Jacobi theta functions. The new series provide convenient starting points for both analytical and numerical progress. Its convergence properties are indeed excellent: Truncation at the fourth term determines in general the energy correctly up to 17 decimal digits. The accurate series representations are used to improve the specification of transition points between the phases and to solve a controversy in previous studies. In particular, it is shown both analytically and numerically that the hexagonal phase I is stable only at d=0, and not in a finite interval of small distances between the plates as was anticipated before. The expansions of the structure energies around second-order transition points can be done analytically, which enables us to show that the critical behavior is of the Ginzburg-Landau type, with a mean-field critical index beta=1/2 for the growth of the order parameters.

We study Andreev bound states (ABS) and resulting charge transport of Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures is sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode similar to that in spinless chiral p-wave pairing in topological phase (TP). We clarify that two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether ABS exists at QCP or not. In the former type, ABS has a energy gap and does not cross at zero energy in non-topological phase (NTP). These complex properties can be detected by tunneling conductance between normal metal / RSC junctions.

We study time-dependent perturbations to a family of five-dimensional black hole spacetimes constructed as a holographic model of the QCD phase diagram. We use the results to calculate two transport coefficients, the bulk viscosity and conductivity, as well as the associated baryon diffusion constant, throughout the phase diagram. Near the critical point in the T-mu plane, the transport coefficients remain finite, although their derivatives diverge, and the diffusion goes to zero. This provides further evidence that large-N_c gauge theories suppress convective transport. We also find a divergence in the low-temperature bulk viscosity, outside the region expected to match QCD, and compare the results to the transport behavior of known R-charged black holes.

We consider the critical system with a point defect and study the variation of thermodynamic quantities, which are the differences between those with and without the defect. Within renormalization group theory, we show generally that the critical exponent of the internal energy variation is the specific heat exponent of a pure system, and the critical exponent of the heat capacity variation is that for the temperature derivative of specific heat of a pure system. This conclusion is valid for the isotropic systems with a short-range interaction. As an example we solve the two dimensional Ising model with a point defect numerically. The variations of the free energy, internal energy and specific heat are calculated with bond propagation algorithm. At the critical point, the internal energy variation diverges with the lattice size logarithmically and the heat capacity variation diverges with size linearly. Near the critical point, the internal energy variation behaves as $\ln |t|$ and the heat capacity variation behaves as $|t|^{-1}$, where $t$ is the reduced temperature.

Biochemical reaction networks in living cells usually involve reversible covalent modification of signaling molecules, such as protein phosphorylation. Under conditions of small molecule numbers, as is frequently the case in living cells, mass action theory fails to describe the dynamics of such systems. Instead, the biochemical reactions must be treated as stochastic processes that intrinsically generate concentration fluctuations of the chemicals. We investigate the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modeling and numerically exact Monte-Carlo simulation of the temporally fluctuating concentration. Depending on the parameter regime, we find for the probability density of the concentration qualitatively distinct classes of distribution functions, including power law distributions with a fractional and tunable exponent. These findings challenge the traditional view of biochemical control networks as deterministic computational systems and suggest that CMCs in cells can function as versatile and tunable noise generators.

We study the dynamic critical phenomena near the possible high-density QCD critical point inside the superfluid phase of nuclear and quark matter. We find that this critical point belongs to a new dynamic universality class beyond the conventional classification by Hohenberg and Halperin. We show that the speed of the superfluid phonon vanishes at the critical point and that the dynamic critical index is $z \approx 2$.

We study the dynamic critical phenomena near the possible high-density QCD critical point inside the superfluid phase of nuclear and quark matter. We find that this critical point belongs to a new dynamic universality class beyond the conventional classification by Hohenberg and Halperin. We show that the speed of the superfluid phonon vanishes at the critical point and that the dynamic critical index is $z \approx 2$.

Genetic algorithms based on natural selection and minimal fluctuations have been applied to model physical and biological systems. Critical exponents have been extracted via computational simulations of nucleation for colossal magnetoresistance, heavy ions liquid-gas phase transitions and HIV to AIDS transition.

We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse one have an analytic unstable mode. Since the homogeneous collapse solution is known to suffer the kink instability, the present result and recent numerical simulations strongly support a proposition that the Larson-Penston solution will be realized in astrophysical situations. It is also found that the Hunter (A) solution has a single unstable mode, which implies that it is a critical solution associated with some critical phenomena which are analogous to those in general relativity. The critical exponent $\gamma$ is calculated as $\gamma\simeq 0.10567$. In contrast to the general relativistic case, the order parameter will be the collapsed mass. In order to obtain a complete picture of the Newtonian critical phenomena, full numerical simulations will be needed.

The critical properties of the Frank model of spontaneous chiral synthesis are discussed by applying results from the field theoretic renormalization group (RG). The long time and long wavelength features of this microscopic reaction scheme belong to the same universality class as multi-colored directed percolation processes. Thus, the following RG fixed points (FP) govern the critical dynamics of the Frank model for d

Critical phenomena were discovered by Cagniard de la Tour in 1822, who died 150 years ago. In order to mark this anniversary, the context and the early history of his discovery is reviewed. We then follow with a brief sketch of the history of critical phenomena, indicating the main lines of development until the present date. Os fen\'omenos cr\'{\i}ticos foram descobertos pelo Cagniard de la Tour em Paris em 1822. Para comemorar os 150 anos da sua morte, o contexto e a hist\'oria initial da sua descoberta \'e contada. Conseguimos com uma descri\c{c}\~ao breve da hist\'oria dos fen\'emenos cr\'{\i}ticos, indicando as linhas principais do desenvolvimento at\'e o presente.

Critical phenomena were discovered by Cagniard de la Tour in 1822, who died 150 years ago. In order to mark this anniversary, the context and the early history of his discovery is reviewed. We then follow with a brief sketch of the history of critical phenomena, indicating the main lines of development until the present date. Os fen\'omenos cr\'{\i}ticos foram descobertos pelo Cagniard de la Tour em Paris em 1822. Para comemorar os 150 anos da sua morte, o contexto e a hist\'oria initial da sua descoberta \'e contada. Conseguimos com uma descri\c{c}\~ao breve da hist\'oria dos fen\'emenos cr\'{\i}ticos, indicando as linhas principais do desenvolvimento at\'e o presente.

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, 'weak' or 'strong', interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular $\beta_1 = 0.80 \pm 0.01$, are found to be robust against these perturbations.

This work establishes critical phenomena in the topological transition of black hole coalescence. We describe and validate a computational front tracking event horizon solver, developed for generic studies of the black hole coalescence problem. We then apply this to the Kastor - Traschen axisymmetric analytic solution of the extremal Maxwell - Einstein black hole merger with cosmological constant. The surprising result of this computational analysis is a power law scaling of the minimal throat proportional to time. The minimal throat connecting the two holes obeys this power law during a short time immediately at the beginning of merger. We also confirm the behavior analytically. Thus, at least in one axisymmetric situation a critical phenomenon exists. We give arguments for a broader universality class than the restricted requirements of the Kastor - Traschen solution.

We study the critical phenomena of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion by the Monte Carlo method. We get the critical exponents, $\beta / \nu$ = 0.313(9) and $\gamma / \nu$ = 2.37(2), where $\beta$ is the critical exponent for the staggered density, $\gamma$ for the staggered compressibility, and $\nu$ for the correlation length.

NAS 1.26:149665 Digitized from IA1177305-11-0046 , IA1177305-11-0047 .

158 p. : 21x27 cm

Includes index

The idea of biased symmetries to avoid or alleviate cosmological problems caused by the appearance of some topological defects is familiar in the context of domain walls, where the defect statistics lend themselves naturally to a percolation theory description, and for cosmic strings, where the proportion of infinite strings can be varied or disappear entirely depending on the bias in the symmetry. In this paper we measure the initial configurational statistics of a network of string defects after a symmetry-breaking phase transition with initial bias in the symmetry of the ground state. Using an improved algorithm, which is useful for a more general class of self-interacting walks on an infinite lattice, we extend the work in \cite{MHKS} to better statistics and a different ground state manifold, namely $\R P^2$, and explore various different discretisations. Within the statistical errors, the critical exponents of the Hagedorn transition are found to be quite possibly universal and identical to the critical exponents of three-dimensional bond or site percolation. This improves our understanding of the percolation theory description of defect statistics after a biased phase transition, as proposed in \cite{MHKS}. We also find strong evidence that the existence of infinite strings in the Vachaspati Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all discretisations thereof, and all regular three-dimensional lattices.

Mass limiting flow characteristics for a 55 L/D tube with a Borda type inlet were assessed over large ranges of temperature and pressure, using fluid nitrogen. Under certain conditions, separation and pressure drop at the inlet was sufficiently strong to permit partial vaporization and the remaining fluid flowed through the tube as if it were a free jet. An empirical relation was determined which defines conditions under which this type of flow can occur. A flow coefficient is presented which enables estimations of flow rates over the experimental range. A flow rate stagnation pressure map for selected stagnation isotherms and pressure profiles document these flow phenomena.

Mass limiting flow characteristics for a 55 L/D tube with a Borda type inlet were assessed over large ranges of temperature and pressure, using fluid nitrogen. Under certain conditions, separation and pressure drop at the inlet was sufficiently strong to permit partial vaporization and the remaining fluid flowed through the tube as if it were a free jet. An empirical relation was determined which defines conditions under which this type of flow can occur. A flow coefficient is presented which enables estimations of flow rates over the experimental range. A flow rate stagnation pressure map for selected stagnation isotherms and pressure profiles document these flow phenomena.

Mass limiting flow characteristics for a 55 L/D tube with a Borda type inlet were assessed over large ranges of temperature and pressure, using fluid nitrogen. Under certain conditions, separation and pressure drop at the inlet was sufficiently strong to permit partial vaporization and the remaining fluid flowed through the tube as if it were a free jet. An empirical relation was determined which defines conditions under which this type of flow can occur. A flow coefficient is presented which enables estimations of flow rates over the experimental range. A flow rate stagnation pressure map for selected stagnation isotherms and pressure profiles document these flow phenomena.

We consider solutions to the nonlinear sigma model (wave maps) with target space S^3 and base space 3+1 Minkowski space, and we find critical behavior separating singular solutions from nonsingular solutions. For families of solutions with localized spatial support a self-similar solution is found at the boundary. For other families, we find that a static solution appears to sit at the boundary. This behavior is compared to the black hole critical phenomena found by Choptuik.

The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^\alpha. Using a scaling argument, 1/C is shown to be a marginal variable when \alpha=\nu_\perp/\nu_\parallel=1/2, i.e., on a parabola. As a consequence the directed walk may display varying local exponents. Such a behaviour is indeed observed for restricted walks. This generalizes a result of Cardy showing that nonuniversal behaviour occurs at corners for isotropic systems.

Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments.

As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with time-- dependent viscosity in epochs of dissipation. As a consequence of the Dynamical Critical Scaling induced by noise and fluctuations, these equations describe the fractal behavior (with a scale dependent fractal dimension) observed at the smaller scales for the galaxy--to--galaxy correlation function and $also$ the Harrison--Zel'dovich spectrum at decoupling. By a Renormalization Group calculation of the two--point correlation function between galaxies in the presence of (i) the expansion of the Universe and (ii) non--equilibrium, we can account, from first principles, for the main features of the observed shape of the power spectrum.

The experimental results on the relation between the processes of total disintegration of nuclei (or the cases with central collisions) and the critical phenomena which can occur in the region of high degree of nuclear disintegration or of collision centrality are discussed.

The theory of current transport in a narrow superconducting channel accounting for thermal fluctuations is developed. These fluctuations result in the appearance of small but finite dissipation in the sample. The value of corresponding voltage is found as the function of temperature (close to transition temperature) and arbitrary bias current. It is demonstrated that the value of the activation energy (exponential factor in the Arrenius law) when current approaches to the critical one is proportional to (1-J/Jc)^(5/4). This result is in concordance with the one for the affine phenomenon of the Josephson current decay due to the thermal phase fluctuations, where the activation energy proportional (1-J/J_c)^(3/2)(the difference in the exponents is related to the additional current dependence of the order parameter). Found dependence of the activation energy on current explains the enormous discrepancy between the theoretically predicted before and the experimentally observed broadening of the resistive transition.

Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo (MQMC) method introduced by us in Ref. [1], we investigate the quantum critical phenomena of {\it spinless} Dirac fermions at their charge-density-wave (CDW) phase transitions on the honeycomb lattice having $N_s=2L^2$ sites with largest $L=24$. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of {\it two} (two-component) Dirac fermions in 2+1D: $\eta=0.45(2)$, $\nu=0.77(3)$, and $\beta=0.60(3)$, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.

Ubiquity of unconventional phenomena observed in a series of heavy fermion metals is discussed on the basis of an idea of critical valence fluctuations. After surveying experimental aspects of these unconventional behaviors in prototypical compounds, CeCu_2(Si,Ge)_2, under pressure, we propose that sharp valence crossover phenomena are realized in CeCu_6, CeRhIn_5, and Ce(Ir,Rh)Si_3 by tuning the pressure and the magnetic field simultaneously, on the basis of previous results for an extended Anderson lattice model with the Coulomb repulsion U_fc between localized f-electron and itinerant conduction electrons.

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, Nc, based on the QCD inequalities and the large-Nc orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential \mu for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential \mu_B = Nc\mu is ruled out, if the coordinate (T, \mu) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential \mu_I = 2\mu.

By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given physical system. In particular, we show how the constraints due to the Ward identities, which implement the conservation laws associated with the various symmetries, help to minimize the number of independent running variables. This use of the Ward identities is examined both in the case of a stable phase and of a critical phenomenon. In the first case we consider the problems of interacting fermions and bosons. In one dimension general and specific Ward identities are sufficient to show the non-Fermi-liquid character of the interacting fermion system, and also allow to describe the crossover to a Fermi liquid above one dimension. This crossover is examined both in the absence and presence of singular interaction. On the other hand, in the case of interacting bosons in the superfluid phase, the implementation of the Ward identities provides the asymptotically exact description of the acoustic low-energy excitation spectrum, and clarifies the subtle mechanism of how this is realized below and above three dimensions. As a critical phenomenon, we discuss the disorder-driven metal-insulator transition in a disordered interacting Fermi system. In this case, through the use of Ward identities, one is able to associate all the disorder effects to renormalizations of the Landau parameters. As a consequence, the occurrence of a metal-insulator transition is described as a critical breakdown of a Fermi liquid.

Development and analysis of schemes for suppression of the startup overvoltage transient in the AEDC High Performance Demonstration Experiment (HPDE), analysis of performance enhancement due to electrode voltage drop reduction by use of pyrolytic graphites in the HPDE, prediction of optimal loading schemes for the HPDE, prediction of PHDE performance with a diagonal electrical connection, and predictions of the likelihood and effects of axial current leakage between adjacent electrodes in the HPDE are reviewed. Simulations of tests at the AEDC/HPDE with STD Research Corporation multidimensional and time dependent computer codes provided additional validation for the computer codes and shed light on physical mechanisms which govern performance and durability of MHD power generators. The magnetoaerothermal effect was predicted by STD Research Corporation to have a significant effect on the HPDE/MHD generator performance at high interaction.

In this paper, we deal with the following singular perturbed fractional elliptic problem $ \epsilon^{} (-\Delta)^{1/2}{u}+V(z)u=f(u)\,\,\, \mbox{in} \,\,\, \mathbb{R}, $ where $ (-\Delta)^{1/2}u$ is the square root of the Laplacian and $f(s)$ has exponential critical growth. Under suitable conditions on $f(s)$, we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of $V$ as $\epsilon$ goes to $0.$

In this paper, we deal with the following singular perturbed fractional elliptic problem $ \epsilon^{} (-\Delta)^{1/2}{u}+V(z)u=f(u)\,\,\, \mbox{in} \,\,\, \mathbb{R}, $ where $ (-\Delta)^{1/2}u$ is the square root of the Laplacian and $f(s)$ has exponential critical growth. Under suitable conditions on $f(s)$, we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of $V$ as $\epsilon$ goes to $0.$

The elastic interaction, induced by the lattice distortion due to the difference of the molecular size, causes an effective long-range interaction. In spin-crossover (SC) compounds, local bistable states, i.e., high-spin and low-spin states have different molecular sizes, and the elastic interaction is important. In bipartite lattices, e.g., the square lattice, the ground state can be two types of phases: ferromagnetic-like (FM) and antiferromagnetic-like (AFM) phases. In systems like SC compounds, the former phase consists of all small or large molecules, and the latter phase has the configuration of alternating small and large molecules. In fact, both cases are observed in SC systems. In this paper, we have studied the effect of the short-range interaction in the elastic system on the properties of those order-disorder phase transitions. We have obtained a phase diagram in the coordinates of the temperature and the strength of the short-range interaction, including the metastable structures. We show that effects of the short-range interaction are essentially different for FM and AFM phase transitions. In the FM transition, the long-range interaction of elasticity is relevant, and the system exhibits a phase transition in the mean-filed universality class. In this case, the long-range interaction strongly enhances the FM order, and it works cooperatively with the short-range interaction. In contrast, in the AFM transition, the elastic interaction slightly enhances the AFM order, but essentially it does not contribute to the ordering, and the system shows a transition in the Ising universality class. We have found that in the border region between FM and AFM phases, the AFM phase has an advantage at finite temperatures. We discuss the critical properties of two-step SC transitions with comparison between the elastic interaction model and conventional SC models (Ising-like models).

We study the superfluid-insulator transition of a particle-hole symmetric system of long-range interacting bosons in a time-dependent random potential in two dimensions, using the momentum-shell renormalization-group method. We find a new stable fixed point with non-zero values of the parameters representing the short- and long-range interactions and disorder when the interaction is asymptotically logarithmic. This is contrasted to the non-random case with a logarithmic interaction, where the transition is argued to be first-order, and to the $1/r$ Coulomb interaction case, where either a first-order transition or an XY-like transition is possible depending on the parameters. We propose that our model may be relevant in studying the vortex liquid-vortex glass transition of interacting vortex lines in point-disordered type-II superconductors.

A generic classification of critical behavior is provided in systems for which the renormalization group equations are parameter dependent. It describes phase transitions in a wide class of networks with a hierarchical structure but also applies, for instance, to conformal field theories. Although these transitions generally do not exhibit universality, three distinct regimes of characteristic critical behavior can be discerned that combine an unusual mixture of second-order, infinite-order, and discontinuous transitions. In the spirit of Landau, the problem can be reduced to the local analysis of a cubic recursion equation, here, for the renormalization group flow of some generalized coupling. Among other insights, this theory explains the often noted prevalence of so-called inverted Berezinskii-Kosterlitz-Thouless transitions in complex networks. As a demonstration, a one-parameter family of Ising models on hierarchical networks is considered.

We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interactions. In order to check for the effect of leading bulk corrections we have also simulated the spin-1/2 Ising model on the simple cubic lattice. We have accurately estimated the surface enhancement coupling at the special point of these models. We find $y_{t_s}=0.718(2)$ and $y_{h_s}=1.6465(6)$ for the surface renormalization group exponents of the special transitions. These results are compared with previous ones obtained by using field theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore we study the behaviour of the surface transition near the special point and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.

The first-year progress for the project of precise measurements of the density and critical phenomena of helium near phase transitions is summarized below: (1) completion of a cryogenic sample probe for the proposed measurements, and the rehabilitation of a designated laboratory at Caltech for this project; (2) construction and testing of a superconducting niobium cavity; (3) acquisition of one phase-locked-loop system for high-resolution frequency control and read- out; (4) setting up high-resolution thermometry (HRT) for temperature readout and control; (5) developing new approaches for calibrating the coefficient between the resonant frequency shift (delta f) and the helium density (rho), as well as for measuring the effect of gravity on T(sub lambda) to a much better precision; (6) programming of the interface control of all instruments for automatic data acquisition; and (7) improving data analyses and fitting procedures.

We show that given an initial vorticity which is bounded and $m$-fold rotationally symmetric for $m \ge 3$, there is a unique global solution to the 2D Euler equation on the whole plane. That is, in the well-known $L^1 \cap L^\infty$ theory of Yudovich, the $L^1$ assumption can be dropped upon having an appropriate symmetry condition. This contains a class of radially homogeneous solutions to the 2D Euler equation, which gives rise to a new 1D fluid model. We discuss several interesting properties of this 1D system. Using this framework, we construct time quasi-periodic solutions to the 2D Euler equation exhibiting pendulum-like behavior. We also exhibit solutions with compact support for which angular derivatives grow linearly in time or exponential in time (the latter being in the presence of a boundary). A similar study can be done for the surface quasi-geostrophic (SQG) equation. Using the same symmetry condition, we prove local existence and uniqueness of solutions which are merely Lipschitz continuous near the origin - though, without the symmetry, Lipschitz initial data is expected to lose its Lipschitz continuity immediately. Once more, a special class of radially homogeneous solutions is considered and we extract a 1D model which bears great resemblance to the so-called De Gregorio model. We then show that finite-time singularity formation for the 1D model implies finite-time singularity formation in the class of Lipschitz solutions to the SQG equation which are compact support. While the study of special infinite energy solutions to fluid models is classical, this appears to be the first case where they can be embedded into a natural existence/uniqueness class for the equation. Moreover, these special solutions approximate finite-energy solutions for long time and have a direct bearing on the global regularity problem for finite-energy solutions.

In this work we studied the critical behavior of the critical point as function of the number of nearest neighbors on two dimensional regular lattices. We performed numerical simulations on triangular, hexagonal and bilayer square lattices. Using standard finite size scaling theory we found that all cases fall in the two dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.

According to the agreement between WL/FIV and Soreq NC, through the auspices of EOARD London, a simple explosive charge was designed so as to achieve the goals set forth by the agreement, both in writing and verbally.

Understanding the effects of gravity is essential if the behavior of fluids is to be predicted in spacecraft and orbital stations, and, more generally, to give a better understanding of the hydrodynamics in these systems. An understanding is sought of the behavior of fluids in space. What should emerge from the International Microgravity Lab (IML-1) mission is a better understanding of the kinetics of growth in off-critical conditions, in both liquid mixtures and pure fluids. This complex phenomenon is the object of intensive study in physics and materials sciences area. It is also expected that the IML-1 flight will procure key results to provide a better understanding of how a pure fluid can be homogenized without gravity induced convections, and to what extent the 'Piston Effect' is effective in thermalizing the compressible fluids.

In this paper we have studied the critical phenomena in higher curvature charged black holes in the anti-de Sitter (AdS) space-time. As an example we have considered the third order Lovelock-Born-Infeld black holes in AdS space-time. We have analytically derived the thermodynamic quantities of the system. Our analysis revealed the onset of a higher order phase transition in the black hole leading to an infinite discontinuity in the specific heat at constant charge at the critical points. Our entire analysis is based on the canonical framework where we have fixed the charge of the black hole. In an attempt to study the behavior of the thermodynamic quantities near the critical points we have derived the critical exponents of the system explicitly. Although the values of the critical points have been determined numerically, the critical exponents are calculated analytically. Our results fit well with the thermodynamic scaling laws. The scaling hypothesis is also seen to be consistent with these scaling laws. We find that all types of AdS black holes, studied so far, indeed belong to the same universality class. Moreover these results are consistent with the mean field theory approximation. We have derived the suggestive values of the other two critical exponents associated with the correlation function and correlation length on the critical surface.

We investigate critical phenomena in colloids by means of the renormalization-group based hierarchical reference theory of fluids (HRT). We focus on three experimentally relevant model systems: namely, the Asakura-Oosawa model of a colloidal dispersion under the influence of polymer-induced attractive depletion forces; fluids with competing short-range attractive and longer-range repulsive interactions; solutions of star-polymers whose pair potential presents both an attractive well and an ultrasoft repulsion at shorter distance. Our results show that the ability to tune the effective interactions between colloidal particles allows one to generate a variety of crossovers to the asymptotic critical behavior, which are not observed in atomic fluids.

We study the critical behavior of a random field O($N$) spin model with a second-rank random anisotropy term in spatial dimensions $4

The paper contains materials of the discussion concerning phase transitions and critical phenomena which took place during the Workshop on modern problems of soft matter theory (Aug. 27 -- Aug. 31, 2000, Lviv, Ukraine).

We give a physical interpretation of the entries of the reflection $K$-matrices of Baxter's eight-vertex model in terms of an Ising interaction at an open boundary. Although the model still defies an exact solution we nevertheless obtain the exact surface free energy from a crossing-unitarity relation. The singular part of the surface energy is described by the critical exponents $\alpha_s = 2 - \frac{\pi}{2\mu}$ and $\alpha_1 = 1 - \frac{\pi}{\mu}$, where $\mu$ controls the strength of the four-spin interaction. These values reduce to the known Ising exponents at the decoupling point $\mu=\pi/2$ and confirm the scaling relations $\alpha_s = \alpha_b + \nu$ and $\alpha_1 = \alpha_b -1$.

An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.