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For a number of mixtures of rate gases at high pressures, sound speed minima are experimentally observed depending on the concentration. This behavior has not yet been explained. We have studied the behavior of a mixture of argon and helium using computer simulation. Sound speed minima have been discovered at a certain concentration, which is in good agreement with experimental data. It is shown that this behavior is due to the fact that the P and T parameters for gas mixtures are near the Frenkel line, separating the states of "rigid" and quasi-gas fluid.

Two-dimensional systems are realized experimentally as thin layers on a substrate. The substrate can have some imperfections (defects of the crystalline structure, chemical impurities, etc.), which demonstrate stronger interaction with the particles of the two-dimensional layer than the rest of the system. Such randomly distributed centers of strong interactions are called "pinning centers". The presence of random pinning can substantially change the behavior of the system. It not only shifts the melting point of the system, but can also change the melting scenario itself. In the present paper the influence of Gaussian pinning on the melting scenario of a two-dimensional system of soft disks is studied by means of molecular dynamics simulation. We randomly introduce into the system of soft disks a set of "pinning centers" which attract the particles via the Gauss potential. We observe that increasing the depth of a Gaussian well leads to a change in the melting scenario of the system. The results demonstrate that simple kind of quenched disorder can significantly affect the melting scenario of two-dimensional systems, offering the possibility of its introduction in complex experiments and studying its influence on the self-assembly and phase diagram of two-dimensional systems in rotating external fields.

A molecular dynamics simulation of sublimation of silicene and silicon films of different thikness is performed. It is shown that thiner films sublimate at lower temperatures. The sublimation temperature comes to a saturated value of $T=1725$ K at the films thiker than $16$ atomc layers. These results are consistent with the surface mediated collaps of the crystal structure. At the same time this mechanism is different from the crystal structure collapse of graphite and graphene.

Here we present a computational study of the thermodynamic and structural properties of bulk and confined (1,1,1,3,3-pentafuorobutane) with different lengths of the carbon backbone. The DREIDING force field model has been used in the method of molecular dynamics. In order to study the effect of confinement we have placed (1,1,1,3,3-pentauorobutane) molecules between two graphene walls. In order to study the influence of pore loading on system behavior we have simulated systems of the same size, but with a different number of (1,1,1,3,3-pentauorobutane) molecules, from 200 to 2000. The equations of state at $T = 300$ K in a wide range of densities for all considered systems had a single peculiarity that is attributed to gas-liquid transition. From the two-dimensional radial distribution functions, density profile and angular distribution we have observed the systems split into layers with amorphization rather than crystallization in them.

The anomalous behavior of a two-dimensional system of Hertzian spheres with exponent $\alpha = 7/2 $ has been studied using the method of molecular dynamics. The phase diagram of this system is the melting line of a triangular crystal with several maxima and minima. Water-like density and diffusion anomalies have been found in the reentrant melting regions. Noteworthy, a density anomaly has been observed not only in the liquid and hexatic but also solid phase. The calculations of the phonon spectra of longitudinal and transverse modes have yielded negative dependence of the frequency of transverse modes on density along all directions in the regions with a density anomaly. This indicates an association of the density anomaly with transverse oscillations of the crystal lattice. The regions of density and diffusion anomalies have been drawn on the phase diagram. It has been found that the stability regions of anomalous diffusion extend to temperatures well above maximum melting point $T = 0.0058$ of the triangular crystal. From analysis of the translational order parameter, which decreases with increasing density in the reentrant melting regions, the presence of a structural anomaly in the system has been assumed., Comment: 8 pages, 5 figures

In the present paper we discuss the properties of Voronoi polygons in several monatomic glass-forming systems and compare them with those of the Kob-Andersen mixture. We show that two mechanisms of glass formation are possible: smearing of Voronoi polygons or formation of polygons of two different shapes. Both mechanisms lead to disturbance of the crystalline order in the system and glass transition., Comment: 13 pages, 14 figures

Using molecular dynamics simulation we have investigated the influence of random pinning on the phase diagram and melting scenarios of a two-dimensional (2D) system with the Hertz potential for $\alpha=5/2$. For the first time it has been shown that random pinning can cardinally change the mechanism of first-order transition between the different crystalline phases (triangular and square) by virtue of generating hexatic and tetratic phases: a triangular crystal to hexatic transition is of the continuous Berezinskii-Kosterlitz-Thouless (BKT) type, a hexatic to tetratic transition is of the first-order, and finally, a continuous BKT type transition from tetratic to the square crystal., Comment: 12 pages, 15 figures

We investigate a behavior of a core-softened system in a thin slit pore (the width of the pore is equil to three diameters of the particles). In previous studies it was shown that strongly confined systems form crystalline phases which consist of several triangular or square layers. These phases can be also considered as cuts of FCC or HCP structures. We show that the behavior of the core-softened system is more complex. We observe also a quasicrystalline phase. Moreover, the phase with two triangular layers appears at lower densities than the one with two square layers which is in contrast to the behavior of the systems studied before. These results demonstrate that the phase behavior of strongly confined systems can be even more complex than it was supposed before.

Two-length-scale pair potentials arise ubiquitously in condensed matter theory as effective interparticle interactions in molecular, metallic and soft matter systems. The existence of two different bond lengths generated by the shape of potential causes complex behavior in even one-component systems: polymorphism in solid and liquid states, water-like anomalies, the formation of quasicrystals and high stability against crystallization. Here we address general properties of freezing in one-component two-length-scale systems and argue that the formation of solid phases during cooling a liquid is essentially determined by the radial distribution function (RDF) of the liquid. We show that different two-length-scale systems having similar RDF freeze into the same solid phases. In most cases, the similarity between RDFs can be expressed by the proximity of two dimensionless effective parameters: the ratio between effective bond lengths, $\lambda$, and the fraction of short-bonded particles $\phi$. We validate this idea by studying the formation of different solid phases in different two-length-scale systems. The method proposed allows predicting effectively the formation of solid phases in both numerical simulations and self-assembling experiments in soft matter systems with tunable interactions., Comment: 7 pages, 4 figures

When the cooling rate $v$ is smaller than a certain material-dependent threshold, the glass transition temperature $T_g$ becomes to a certain degree the "material parameter" being nearly independent on the cooling rate. The common method to determine $T_g$ is to extrapolate viscosity $\nu$ of the liquid state at temperatures not far above the freezing conditions to lower temperatures where liquid freezes and viscosity is hardly measurable. It is generally accepted that the glass transition occurs when viscosity drops by $13\leq n\leq17$ orders of magnitude. The accuracy of $T_g$ depends on the extrapolation quality. We propose here an algorithm for a unique determining of $T_g$. The idea is to unambiguously extrapolate $\nu(T)$ to low temperatures without relying upon a specific model. It can be done using the numerical analytical continuation of $\nu(T)$-function from above $T_g$ where it is measurable, to $T\gtrsim T_g$. For numerical analytical continuation, we use the Pade approximant method., Comment: 5 pages, 5 figures

We present a molecular dynamics simulation study of the phase diagram and melting scenarios of two-dimensional Hertzian spheres with exponent 7/2. We have found multiple re-entrant melting of a single crystal with a triangular lattice in a wide range of densities from 0.5 to 10.0. Depending on the position on the phase diagram, the triangular crystal has been shown to melt through both two-stage melting with a first-order hexatic - isotropic liquid transition and a continuous solid - hexatic transition as well as in accordance with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario (two continuous transitions with an intermediate hexatic phase). We studied the behavior of heat capacity and have shown that despite two-stage melting, the heat capacity has one peak which seems to correspond to a solid-hexatic transition.

We present a computer simulation study of influence of the confinement on the density anomaly in the system with isotropic core-softened potential which is used for a qualitative description of the anomalous behavior of water and some other liquids. We have found that a maximum temperature of the density anomaly region along an isochor $\rho=0.5$ does not depend on the pore width. We have shown that a decrease in the width of the confining slit pore leads to an increase in the crystallization temperature and as a result the local density distribution is mostly controlled by the particle-wall interaction, which leads to the depression of the density anomaly.

We present a comparative computer simulation study of the phase diagrams and anomalous behavior of two-dimensional ($2D$) and quasi-two-dimensional ($q2D$) classical particles interacting with each other through isotropic core-softened potential which is used for a qualitative description of the anomalous behavior of water and some other liquids. We have shown that at the low density part of the phase diagram an increase in the width of the confining slit pore leads to a considerable decrease in the melting temperature while at high densities the melting temperature is almost unchanged.

We study the dependence of the excitation frequency of water along an isochore and an isotherm crossing the region of density anomaly. We have shown that the frequency of the longitudinal excitations demonstrated anomalous dependence on temperature along the isochore. At the same time the dependence for both longitudinal and transverse excitation frequencies on density along the isotherm are very modest or even negligible in rather wide range of densities. This kind of behavior also seems anomalous in comparison with the ordinary liquids.

Interaction of particles of many systems can be effectively approximated by multiscale interaction potentials. Such potentials are widely used for investigation of colloidal systems and colloid-polymer mixtures, complex liquids (for instance, water) and other system. Also, it is of particular interest that effective interaction of vortices in a thin superconducting film can be approximated by a multiscale potential. The subject matter of the present paper is a system like this. Based on a multiscale potential we have shown that this system demonstrated a large number of different phases. It is particularly important that we analyze the influence of a long-range interaction of the system properties and show that properly taking into account long-range forces results in a dramatic change in the system phase diagram.

We report a molecular dynamics study of liquid cesium at ambient pressure intended to check the possibility of liquid-liquid phase transformation at $T=590$ K. We find the presence of small kinks on thermodynamic characteristics of the system, but no phase transition.

In the present paper we consider dispersion curves of longitudinal excitations of a model core-softened liquid and SPC/E model of water. We show that both systems demonstrate anomalous behavior of the excitation frequencies: the frequencies of the excitations can decrease with temperature along isochors, while in normal liquids they should increase. This observation allows to introduce one more water anomaly - anomalous dependence of excitation frequencies on temperature.

In the present paper we discuss a so called stripe phase of two-dimensional systems which was observed in computer simulation of core-softened system and in some experiments with colloidal films. We show that the stripe phase is indeed an oblique crystal and find out its unit vectors, i.e. we give a full description of the structure of this crystalline phase.

We present the results of a computer simulation study of the melting scenario of two-dimensional soft-disk systems with potential $U(r)=\varepsilon(\sigma/r)^n$, $n=12$ and $n=1024$, both in the presence of random pinning and without it. The melting parameters have been determined from analysis of the behavior of equations of state, correlation functions of the orientational and translational order parameters, Young modulus and renormalization group equations. The transition points obtained from these criteria are in good agreement. We have shown that the systems melted in two stages - first-order hexatic phase to liquid transition and the continuous Berezinskii-Kosterlitz-Thouless type crystal-hexatic phase transition. Random pinning widened the hexatic phase, but left the melting scenario unchanged., Comment: 9 pages, 12 figures

We present computer simulations of a system of purely repulsive soft colloidal particles interacting via the Hertz potential and constrained to a two-dimensional plane. This potential describes the elastic interaction of weakly deformable bodies and can be a reliable model for qualitative description of behavior of soft macromolecules, like globular micelles and star polymers. We find a large number of ordered phases, including the dodecagonal quasicrystal, and analyze the melting scenarios of low density triangle and square phases. It is interesting that depending on the position on the phase diagram the system can melt both through the first order transition and in accordance with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario (two continuous transitions with the intermediate hexatic phase) and also in accordance with recently proposed two-stage melting with the first order hexatic-isotropic liquid transition and continuous solid-hexatic transition. We also demonstrate the possibility of the tricritical point on the melting line., Comment: 11 pages, 18 figures

A cascade of phase transitions from square to hexagonal lattice is studied in 2D system of particles interacting via core-softened potential. Due to the presence of two length-scales of repulsion, different local configurations with four, five, and six neighbors enable, leading to formation of complex crystals. The previously proposed interpolation method is generalized for calculation of pair correlations in crystals which elemental cell consists of more than one particle. A high efficiency of the method is illustrated using a snub square lattice as a representative example. Using molecular dynamics simulations, it is found that the snub square lattice is being broken under heating, generating high density quasicrystalline phase with 12-fold symmetry. Simple theoretical model is proposed to explain the physical mechanism governing this phenomenon: With density growth (from square to hexagonal phases), the concentrations of different local configurations randomly realized through plane tilling are being changed that minimizes the energy of the system. The calculated phase diagram in the intermediate region of densities justifies the existence of HD12 phase and demonstrates a cascade of the first-order transitions "square -- HD12 -- hexagonal" solid phases with the density growth. The results allow us to better understand the physical mechanisms responsive for formation of quasicrystals, and, therefore, should be of interest for broad community on material science and soft matter., Comment: 11 pages, 9 figures

We develop a gauge theory of the critical behavior of the topological excitations-driven Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the XY model with weak quenched disorder. We find that while in two-dimensions the liquid of topological defects exhibits the BKT critical behavior, the three-dimensional system shows more singular Vogel-Fulcher-Tamman criticality heralding its freezing into a spin glass. Our findings provide insights into the topological origin of spin glass formation., Comment: 7 figures

Water is the most important liquid in the Universe. At the same time it is the most anomalous liquid. It demonstrates several dozens of anomalies, among which are density anomaly, diffusion anomaly etc. Anomalous behavior of water is a topic numerous publications. However, most of the publications investigate the anomalous behavior of water in the vicinity of critical points: the liquid-gas critical point and the second hypothetical critical point in supercooled region. Here we analyze experimental data on such properties of water as heat capacity, speed of sound, dynamic viscosity and thermal conductivity. We show that these properties demonstrate anomalous maxima and minima in a region which is far from both critical points. Therefore, we find a novel region of anomalous properties of water (anomalous triangle) which cannot be related to critical fluctuations. We also perform a molecular dynamics simulations of this region with two common water models - SPC/E and TIP4P - and show that these models fail to describe the novel anomalous region.

Despite about forty years of investigations, the nature of the melting transition in two dimensions is not completely clear. In the framework of the most popular Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) theory, 2D systems melt through two continuous Berezinskii-Kosterlitz-Thouless (BKT) transitions with intermediate hexatic phase. The conventional first-order transition is also possible. On the other hand, recently on the basis of computer simulations the new melting scenario was proposed with continuous BKT type solid-hexatic transition and first order hexatic-liquid transition. However, in the simulations the hexatic phase is extremely narrow that makes its study difficult. In the present paper, we propose to apply the random pinning to investigate the hexatic phase in more detail. The results of molecular dynamics simulations of two dimensional system having core-softened potentials with narrow repulsive step which is similar to the soft disk system are outlined. The system has a small fraction of pinned particles giving quenched disorder. Random pinning widens the hexatic phase without changing the melting scenario and gives the possibility to study the behavior of the diffusivity and order parameters in the vicinity of the melting transition and inside the hexatic phase., Comment: 7 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1608.05232

The random disorder can drastically change the melting scenario of two-dimensional systems and has to be taken into account in the interpretation of the experimental results. We present the results of the molecular dynamics simulations of the two dimensional system with the core-softened potentials with two repulsive steps in which a small fraction of the particles is pinned, inducing quenched disorder. It is shown that without the quenched disorder the system with small repulsive shoulder, which is close in the shape to the soft disks, melts in accordance with the melting scenario proposed in Refs. [30,31,33] (first-order liquid-hexatic and continuous hexatic-solid transitions). Random pinning widens the hexatic phase, but leaves the melting scenario unchanged. For the system with larger repulsive step at high densities the conventional first-order transition takes place without random pinning. However, in the presence of disorder the single first-order transition transforms into two transitions, one of them (solid-hexatic) is the continuous KTHNY-like transition, while the hexatic to isotropic liquid transition occurs as the first order transition., Comment: 10 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:1507.01802

We present the molecular simulation study of the behavior of water and sodium chloride solution confined in lizardite asbestos nanotube which is a typical example of hydrophilic confinement. The local structure, orientational and dynamic properties are studied. It is shown that the diffusion coefficient drops about two orders of magnitude comparing to the bulk case, and water in lizardite asbestos tubes experiences vitrification rather then crystallization upon cooling in accordance with the results for some other hydrophilic confinements. The behavior of sodium chloride solutions also considered and the formation of double layer is observed. It is shower that both sodium and chlorine have larger diffusion coefficients then water., Comment: 8 pages, 12 figures

Simple closed analytical expression for approximate direct correlation function (DCF) for multi--Yukawa hard--core system of particles is presented. The obtained DCF is a solution of the Ornstein--Zernike equation with multi--Yukawa closure valid in the linear approximation in the potential. This approximation includes linear corrections to the hard-- sphere DCF inside the core radius., Comment: 5 pages

It is well known that confining a liquid into a pore strongly alters the liquid behavior. Investigations of the effect of confinement are of great importance for many scientific and technological applications. Here we present a molecular dynamics study of the behavior of cyclohexane confined in carbon slit pores. The local structure and orientational ordering of cyclohexane molecules are investigated. It is shown that the system freezes with decreasing the pore width, and the freezing temperature of nanoconfined cyclohenae is higher than the bulk one., Comment: 18 pages, 7 figures

Supercritical state has been viewed as an intermediate state between gases and liquids with largely unknown physical properties. Here, we address the important ability of supercritical fluids to sustain collective excitations. We directly study propagating modes on the basis of correlation functions calculated from extensive molecular dynamics simulations, and find that the supercritical system sustains propagating solid-like transverse modes below the Frenkel line but becomes devoid of transverse modes above the line where it supports longitudinal modes only. Important thermodynamic implications of this finding are discussed. We directly detect positive sound dispersion (PSD) below the Frenkel line where transverse modes are operative, quantitatively explain its magnitude on the basis of transverse and longitudinal velocities. PSD disappears above the Frenkel line which therefore demarcates the supercritical phase diagram into two areas where PSD does and does not operate.

It is well known that some liquids can demonstrate anomalous behavior. Interestingly, this be- havior can be qualitatively reproduced with simple core-softened isotropic pair-potential systems. Although anomalous properties of liquids usually take place at low and moderate temperatures it was recently recognized that many important phenomena can appear in supercritical fuids. However, no studies of supercritical behavior of core-softened fuids is reported. This paper reports a study of dynamical crossover in supercritical core-softened systems. The crossover line is calculated from three different criteria and good agreement between them is observed. It is found that the behavior of the dynamical crossover line of core-softened systems is quite complex due to its quasi-binary nature.

In experiments the two-dimensional systems are realized mainly on solid substrates which introduce quenched disorder due to some inherent defects. The defects of substrates influence the melting scenario of the systems and have to be taken into account in the interpretation of the experimental results. We present the results of the molecular dynamics simulations of the two dimensional system with the core-softened potential in which a small fraction of the particles is pinned, inducing quenched disorder.The potentials of this type are widely used for the qualitative description of the systems with the water-like anomalies. In our previous publications it was shown that the system demonstrates an anomalous melting scenario: at low densities the system melts through two continuous transition in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory with the intermediate hexatic phase, while at high densities the conventional first order melting transition takes place. We find that the well-known disorder-induced widening of the hexatic phase occurs at low densities, while at high density part of the phase diagram random pinning transforms the first-order melting into two transitions: the continuous KTHNY-like solid-hexatic transition and first-order hexatic-isotropic liquid transition., Comment: 5 pages, 4 figures

Dynamical crossover in water is studied by means of computer simulation. The crossover temperature is calculated from the behavior of velocity autocorrelation functions. The results are compared with experimental data. It is shown that the qualitative behavior of the dynamical crossover line is similar to the melting curve behavior. Importantly, the crossover line belongs to experimentally achievable $(P,T)$ region which stimulates the experimental investigation in this field., Comment: 5 pages, 3 figures

In the framework of the density functional theory of freezing proposed in our previous works, we calculate the phase diagram of two-dimensional system of particles interacting through the repulsive shoulder potential. This potential consists of the hard core and repulsive shoulder of the larger radius. It is shown that at low densities the system melts through the continuous transition in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario, while at high densities the conventional first order transition takes place., Comment: 7 pages, 4 figures

Behavior of supercritical fluids attracts a lot of attention nowadays. It is important both from the point of view of fundamental science and technological applications. However, up to now the progress in the field is rather moderate. In this article we report a computational study of supercritical carbon dioxide which is one of the most important fluids for chemical industry. We study the response functions of $CO_2$ in supercritical regime and calculate the locations of their maxima (Widom lines). We also make preliminary calculations of the line of crossover of microscopic dynamics of particles (Frenkel line). The conclusions on the Frenkel line location can be applied to study of the atmosphere of Venus., Comment: 6 pages, 8 figures

We present the molecular dynamics study of benzene molecules confined into the single wall carbon nanotube. The local structure and orientational ordering of benzene molecules are investigated. It is found that the molecules mostly group in the middle distance from the axe of the tube to the wall. The molecules located in the vicinity of the wall demonstrate some deviation from planar shape. There is a tilted orientational ordering of the molecules which depends on the location of the molecule. It is shown that the diffusion coefficient of the benzene molecules is very small at the conditions we report here., Comment: 14 pages, 7 figures

A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the degenerate states. The final relations for the second order ground state energy and first order wave function do not contain singularities at integer values of the chemical potentials. The resulting equation for the phase boundary between superfluid and Mott states coincides with the prediction based on the conventional mean field perturbation approach., Comment: 4 pages, 1 figure

In the present paper, using a molecular dynamics simulation, we study a nature of melting of a two-dimensional ($2D$) system of classical particles interacting through a purely repulsive isotropic core-softened potential which is used for the qualitative description of the anomalous behavior of water and some other liquids. We show that the melting scenario drastically depends on the potential softness and changes with increasing the width of the smooth repulsive shoulder. While at small width of the repulsive shoulder the melting transition exhibits what appears to be weakly first-order behavior, at larger values of the width a reentrant-melting transition occurs upon compression for not too high pressures, and in the low density part of the $2D$ phase diagram melting is a continuous two-stage transition, with an intermediate hexatic phase in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario. On the other hand, at high density part of the phase diagram one first-order transition takes place. These results may be useful for the qualitative understanding the behavior of water confined between two hydrophobic plates., Comment: 10 pages, 9 figures. arXiv admin note: text overlap with arXiv:1311.7534

Some fluids are known to behave anomalously. The so-called structural anomaly which means that the fluid becomes less structures under isothermal compression is among the most frequently discussed ones. Several methods for quantifying the degree of structural order are described in the literature and are used for calculating the regions of structural anomalies. It is implied that all of the structural order determinations yield qualitatively identical results. However, no explicit comparison was made. This paper presents such a comparison for the first time. the results of some definitions are shown to contradict the intuitive notion of a fluid. On the basis of this comparison we show that the structural anomaly can be most reliably determined from the behavior of the excess entropy., Comment: 7 pages, 5 figures

Recent advance in understanding the supercritical state posits the existence of a new line above the critical point separating two physically distinct states of matter: rigid liquid and non-rigid gas-like fluid. The location of this line, the Frenkel line, remains unknown for important real systems. Here, we map the Frenkel line on the phase diagram of supercritical iron using molecular dynamics simulations. On the basis of our data, we propose a general recipe to locate the Frenkel line for any system, the recipe that importantly does not involve system-specific detailed calculations and relies on the knowledge of the melting line only. We further discuss the relationship between the Frenkel line and the metal-insulator transition in supercritical liquid metals. Our results enable predicting the state of supercritical iron in several conditions of interest. In particular, we predict that liquid iron in the Jupiter core is in the "rigid liquid" state and is highly conducting. We finally analyse the evolution of iron conductivity in the core of smaller planets such as Earth and Venus as well as exoplanets: as planets cool off, the supercritical core undergoes the transition to the rigid-liquid conducting state at the Frenkel line., Comment: 5 pages, 5 figures

In the present paper we propose the van der Waals-like model, which allows a purely analytical study of fluid properties including the equation of state, phase behavior and supercritical fluctuations. We take a square-well system as an example and calculate its liquid - gas transition line and supercritical fluctuations. Employing this model allows us to calculate not only the thermodynamic response functions (isothermal compressibility $\beta_T$, isobaric heat capacity $C_P$, density fluctuations $\zeta_T$, and thermal expansion coefficient $\alpha_T$), but also the correlation length in the fluid $\xi$. It is shown that the bunch of extrema widens rapidly upon departure from the critical point. It seems that the Widom line defined in this way cannot be considered as a real boundary that divides the supercritical region into the gaslike and liquidlike regions. As it has been shown recently, the new dynamic line on the phase diagram in the supercritical region, namely the Frenkel line, can be used for this purpose., Comment: 6 pages, 4 figures

The system with the square shoulder (SS) potential is considered in the frame of Mode Coupling Theory (MCT) approach. An approximation for the structure factor is used that emphasizes the quasibinary character of the system. The qualitative phase diagram is constructed that includes continuous and discontinuous glass-glass transitions. The phase diagram is governed by two swallow tails connected with two $A_4$ singularities., Comment: 8 pages, 5 figures

We consider the phase behavior of two-dimensional ($2D$)system of particles with an isotropic core-softened potential introduced in our previous publications. As one can expect from the qualitative consideration for the three dimensional case, the system demonstrates a reentrant-melting transition at low densities along with waterlike anomalies in the fluid phase near the melting maximum. In contrast with the three dimensional case, in two dimensions melting is a continuous two-stage transition in the low density part of the phase diagram with an intermediate hexatic phase corresponding to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario. At the same time, at high densities the system melts through one first-order transition. We also show, that the order of the region of anomalous diffusion and the regions of density and structural anomalies are inverted in comparison with the $3D$ case and have silicalike sequence., Comment: 6 pages, 6 figures