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We describe a new type of gravitational singularities which are caustics of spatial-temporal foliations. An example of gravitational wave solution forming a singularity with caustics is given., Comment: 4 pages. Translated from Russian by author on 07.07.2024

The neural network techniques are developed for artificial sequences based on approximate models of proteins. We only encode the hydrophobicity of the amino acid side chains without attempting to model the secondary structure. We use our approach to obtain a large set of sequences with known 3-D structures for training the neural network. By employing recurrent neural networks we describe a way to augment a neural network to deal with sequences of realistic length and long-distant interactions between the sequence regions., Comment: 10 pages, 4 postscript figures

The Lagrangian and equations of the gauge model of the fifth fundamental interaction are constructed and the corresponding corrections to the Newtonian potential are obtained., Comment: 5 pages. Translated from Russian by author on 09.07.2024

The thesis is devoted to the problem of colour confinement in the non-Abelian Yang-Mills theory (gluon part of Quantum Chromodynamics). A generalisation of the 3-dimensional Fock-Schwinger gauge is proposed where the Gauss law constraint is exactly solvable. This simplifies the theory in a finite domain and incorporates the variables at the boundary into the Hamiltonian formalism. The dependence of the partition function on the boundary value of the longitudinal component of the electric field is studied and related to the mechanism of the confinement-deconfinement transition. The free energy density is calculated for $SU(2)$ and $SU(3)$ gluodynamics in the mean-field approximation for the collective variables. Analysis of its minima reveals a phase transition at a certain temperature, below which the mean collective variables have nonzero values. This can be interpreted as a confinement-deconfinement phase transition. In the confinement phase the chromo-electric flux through any element of the boundary is strictly zero. This means the singletness with respect to the group of the residual gauge transformations and hence impossibility of observing coloured objects at spatial infinity (in asymptotic states). It is demonstrated that our confinement condition satisfies the traditional confinement criteria. The Wilson loop for $SU(N)$ theory is shown to satisfy the area law. The ratio of the transition temperature to the square root of the string tension coefficient is in a qualitative agreement with the result from lattice Monte Carlo simulations. In the deconfinement phase the global symmetry $Z_{N}$ (centre of $SU(N)$) is spontaneously broken by the surface terms. The confinement phase is characterised by unbroken symmetry with all nontrivial minima having the same depth and transformable by $Z_{N}$ actions., Comment: PhD thesis, Translated from Russian. Moscow M.V. Lomonosov State University. Defended on: 27.04.1995. 77 pages, 5 figures. Supervisor: N.A. Sveshnikov

We present two coarse-grained models of different levels of detail for the description of beta-sheet tapes obtained from equilibrium self-assembly of short rationally designed oligopeptides in solution. Here we only consider the case of the homopolymer oligopeptides with the identical sidegroups attached, in which the tapes have a helicoid surface with two equivalent sides. The influence of the chirality parameter on the geometrical characteristics, namely the diameter, inter-strand distance and pitch, of the tapes have been investigated. The two models are found to produceequivalent results suggesting a considerable degree of universality in conformations of the tapes., Comment: 24 pages, 5 PS figures. Accepted to J. Chem. Phys

Discrete wavelets are applied to parametrization of the intra-chain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulation. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. Quality of the approximation has been assessed by calculation of the scaling exponents obtained from des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in a better agreement with those from the recent renormalisation group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers., Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PRE

Conformations of isolated homo- dendrimers of G=1-7 generations with D=1-6 spacers have been studied in the good and poor solvents, as well as across the coil-to-globule transition, by means of a version of the Gaussian self-consistent (GSC) method and Monte Carlo (MC) simulation in continuous space based on the same coarse-grained model. The latter includes harmonic springs between connected monomers and the pair-wise Lennard-Jones potential with a hard core repulsion. The scaling law for the dendrimer size, the degrees of bond stretching and steric congestion, as well as the radial density, static structure factor, and asphericity have been analysed. It is also confirmed that while smaller dendrimers have a dense core, larger ones develop a hollow domain at some separation from the centre., Comment: RevTeX, 14 pages, 19 PS figures, Accepted for publication in J. Chem. Phys

A version of the Gaussian self-consistent (GSC) method, which avoids the use of the Edwards' virial expansion, is presented. Instead, the mean energy is evaluated directly via a convolution of the attractive part of the pair-wise non-bonded potential with the Gaussian trial radial distribution function. The hard sphere repulsion is taken into account via a suitably generalised Carnahan-Starling term. Comparison of the mean-squared inter-monomer distances and radius of gyration, as well as of the mean energy, between the results from the GSC calculations and Monte Carlo (MC) simulation in continuous space are made across the coil-to-globule transition for isolated ring, open and star homopolymers of varied lengths and flexibility. Importantly, both techniques utilise the same polymer model so that the data points could be directly superimposed. A surprisingly good overall agreement is found between these GSC and MC results. Caveats of the Gaussian technique and ways for going beyond it are also discussed., Comment: RevTeX 13 pages, 9 PS figures. Accepted for publication in J. Chem. Phys

Using the Gaussian Ansatz for the monomer-monomer correlation functions we derive a set of the self-consistent equations for determination of the conformational state in the bead-and-spring copolymer model. The latter is based on the Edwards type effective free energy functional with arbitrary two-body interaction matrix. The rate of conformational changes in kinetics may be expressed via the instantaneous gradients of the variational free energy functional in the space of the averaged dynamical variables. We study the equilibrium and kinetics for some periodic and random aperiodic amphiphilic sequences in infinitely diluted solution. Typical equilibrium phase diagrams are elucidated and the conformational structure of different states is discussed. The kinetics of compaction of an amphiphilic copolymer to the globular state proceeds through formation of locally frustrated non-equilibrium structures. This leads to a rather complicated multistep kinetic process. We observe that even a small modification in the primary sequence of a copolymer may significantly change its kinetic folding properties., Comment: 16 pages, 25 PS figures

In this paper we present a method to study the folding structure of a simple model consisting of two kinds of monomers, hydrophobic and hydrophilic. This method has three main steps: an efficient simulation method to bring an open sequence of homopolymer to a folded state, the application of a painting method called (regular hull) to the folded globule and the refolding process of the obtained copolymer sequence. This study allows us to suggest a theoretical function of disorder distribution for copolymer sequences that give rise to a compacted and well micro-phase separated globule., Comment: 11 pages incl. 6 PS figures. Paper presented at the International Conference on Morphology and Kinetics of Phase Separating Complex Fluids, Messina, Italy, June 1997

In recent experiments involving PNIPAM copolymers it has been observed that stable spherical nanoparticles are being formed by association of several chains in poor aqueous solution instead of aggregation. This type of mesoscopic structures called mesoglobules has an extremely monodispersed size distribution. Previously we have studied theoretically formation of clusters consisting of several chains in dilute solutions of amphiphilic heteropolymers. We have seen that the mesoglobules often possess an essentially micellar structure. In the current work we argue that formation of mesoglobules is strongly sequence and concentration dependent. In particular, by means of lattice Monte Carlo simulation we consider structures formed by a number of tri-block sequences and their certain mutations. For sequences consisting of two hydrophilic ends with a hydrophobic middle the size distribution of the resulting particles is rather narrow, i.e. mesoglobules are being formed. However, in the case of sequences with two hydrophobic ends and a hydrophilic middle a new type of structures seems to be prevalent. These consist of small mesoglobules interconnected by hydrophilic bridges. Clearly, on increasing the concentration these networked structures would play an important role resulting in a rapid onset of a gel-like behaviour., Comment: RevTeX, 4 pages, 7 PS figures. Accepted for publication in Colloids and Surfaces A

By means of continuous space Monte Carlo simulation we study conformational structures formed by star and comb heteropolymers during kinetics of folding from the coil to the globule, as well as the corresponding equilibrium states on going from the good to the poor solution. Particular examples of combs with hydrophobic backbone and hydrophilic side-groups (and vice versa), as well as stars with flexible and semi-stiff arms are studied. It is interesting to note that star-like conformations naturally appear for a comb polymer with a strongly hydrophobic backbone. We emphasise the crucial difference in the spatial distribution of hydrophobic and hydrophilic monomers within the globular states for the above mentioned two types of combs. In case of stars, the non-equilibrium states during kinetics of the coil-to-globule transition correspond to formation of localised pearls within flexible arms, whereas semi-stiff arms prefer to join with each other remaining essentially extended. These studies present natural extension of our previous works on the equilibrium and kinetic properties of linear and ring heteropolymers based on the Gaussian self-consistent method and lattice Monte Carlo technique. However, in studying polymers with more nontrivial topology continuous space simulation has some essential advantages., Comment: RevTeX, 5 pages, 10 PS figures. Accepted for publication in Colloids and Surfaces A

We study conformations assumed by single diblock star copolymers in a poor solvent by means of the Gaussian variational theory and Monte Carlo simulation in continuous space. Cases of stars with internal and external hydrophobic blocks are analysed. While in the former case the collapsed state has an obvious micellar shape, the latter case exhibits two nontrivial conformational structures. Apart from the equilibrium state of a globular hydrophobic core with hydrophilic daisy loops, one also finds here a metastable state of outstretched hydrophilic blocks with hydrophobic subglobules at their ends. Such a state appears to be rather long-lived during the kinetics of collapse of a swollen star. The plots of monomer densities and other observables computed by both techniques are found to be in good agreement with each other., Comment: RevTeX, 13 pages, 20 PS figures. Accepted for publication in Macromol. Theory Simul

We investigate the aggregation number and size distributions for inter-molecular clusters of amphiphilic diblock and triblock copolymers in poor solvent at very low concentrations. Diblocks and triblocks with hydrophilic ends are shown to possess narrow distributions corresponding to formation of monodispersed mesoglobules. Diblocks with hydrophobic ends are found to produce inter-cluster multimers due to bridging by the hydrophilic middle blocks, resulting in polydisperse distributions. Implications of these observations for preparation of monodispersed nanoparticles and, potentially, understanding of the quaternary structure of proteins are discussed., Comment: 4 pages, 4 PS figures. Accepted for publication in EPL

We study the role of topological restrictions for the conformational structure of a nonphantom homopolymer chain in a lattice Monte Carlo model. In the athermal regime we find that the standard Metropolis algorithm violates the detailed balance condition if both local monomer and global reptational moves are included. However, if about 1 reptation is performed per N local moves the balance is recovered and we obtain the Flory exponent value close to nu=0.588, where N is the degree of polymerisation. We also find that the structure of the collapsed globule is different at equilibrium from that after the late stage of folding kinetics. Namely, due to reptations the end, and even more so, the penultimate monomer groups tend to be buried inside the globule core with other monomers thus being more exposed to the surface., Comment: 13 pages, RevTeX, 3 ps figures. Accepted for publication in Progr. Colloid Polym. Sci

We study the formation of clusters consisting of several chains in dilute solutions of amphiphilic heteropolymers. By means of the Gaussian variational theory we show that in a region of the phase diagram within the conventional two-phase coexistence region mesoglobules of equal size possess the lowest free energy. Monte Carlo simulation confirms that the mesoglobules are stabilised due to micro-phase separation, which introduces a preferred length scale. The very existence of such mesoscopic structures is related to a delicate balance of the energetic and entropic terms under the connectivity constraints. The issue of size monodispersity and fluctuations for mesoglobules is investigated., Comment: 30 pages, RevTeX, 14 ps figures. Accepted for publication in J. Chem. Phys

In this paper we complete the study of the phase diagram and conformational states of a stiff homopolymer. It is known that folding of a sufficiently stiff chain results in formation of a torus. We find that the phase diagram obtained from the Gaussian variational treatment actually contains not one, but several distinct toroidal states distinguished by the winding number. Such states are separated by first order transition curves terminating in critical points at low values of the stiffness. These findings are further supported by off-lattice Monte Carlo simulation. Moreover, the simulation shows that the kinetics of folding of a stiff chain passes through various metastable states corresponding to hairpin conformations with abrupt U-turns., Comment: 9 pages, 16 PS figures. Journal of Chemical Physics, in press

We propose an efficient numerical algorithm for solving integral equations of the theory of liquids in the Reference Interaction Site Model (RISM) approximation for infinitely dilute solution of macromolecules with a large number of atoms. The algorithm is based on applying the nonstationary iterative methods for solving systems of linear algebraic equations. We calculate the solvent-solute atom-atom correlation functions for a fragment of the B-DNA duplex d(GGGGG).d(CCCCC) in infinitely dilute aqueous solution. The obtained results are compared with available experimental data and results from computer simulations., Comment: 9 pages, RevTeX, 9 pages of ps figures, accepted for publications in JCP

We analyse dependence of the partition function on the boundary condition for the longitudinal component of the electric field strength in gauge field theories. In a physical gauge the Gauss law constraint may be resolved explicitly expressing this component via an integral of the physical transversal variables. In particular, we study quantum electrodynamics with an external charge and SU(2) gluodynamics. We find that only a charge distribution slowly decreasing at spatial infinity can produce a nontrivial dependence in the Abelian theory. However, in gluodynamics for temperatures below some critical value the partition function acquires a delta-function like dependence on the boundary condition, which leads to colour confinement., Comment: 14 pages, RevTeX, submitted to Phys. Rev. D

In this paper we extend the Gaussian self-consistent method to permit study of the equilibrium and kinetics of conformational transitions for heteropolymers with any given primary sequence. The kinetic equations earlier derived by us are transformed to a form containing only the mean squared distances between pairs of monomers. These equations are further expressed in terms of instantaneous gradients of the variational free energy. The method allowed us to study exhaustively the stability and conformational structure of some periodic and random aperiodic sequences. A typical phase diagram of a fairly long amphiphilic heteropolymer chain is found to contain phases of the extended coil, the homogeneous globule, the micro-phase separated globule, and a large number of frustrated states, which result in conformational phases of the random coil and the frozen globule. We have also found that for a certain class of sequences the frustrated phases are suppressed. The kinetics of folding from the extended coil to the globule proceeds through non-equilibrium states possessing locally compacted, but partially misfolded and frustrated, structure. This results in a rather complicated multistep kinetic process typical of glassy systems., Comment: 15 pages, RevTeX, 20 ps figures, accepted for publication in Phys. Rev. E