Field-driven tracer diffusion through curved bottlenecks: fine structure of first passage events.

Using scaling arguments and extensive numerical simulations, we study the dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary. The tracer particle is affected by an external force pointing along the channel, and performs an unbiased diffusion in the perpendicular direction. We present a detailed analysis (a) of the distribution function of the height above the funnel's boundary at which the first crossing of a given bottleneck takes place, and (b) of the distribution function of the first passage time to such an event. Our analysis reveals several new features of the dynamical behaviour that are overlooked in the studies based on the Fick-Jacobs approach. In particular, trajectories passing through a funnel concentrate predominantly on its boundary, which makes first-crossing events very sensitive to the presence of binding sites and microscopic roughness.

Self-isolation or borders closing: What prevents the spread of the epidemic better?

Pandemic propagation of COVID-19 motivated us to discuss the impact of the human network clustering on epidemic spreading. Today, there are two clustering mechanisms which prevent of uncontrolled disease propagation in a connected network: an "internal" clustering, which mimics self-isolation (SI) in local naturally arranged communities, and an "external" clustering, which looks like a sharp frontiers closing (FC) between cities and countries, and which does not care about the natural connections of network agents. SI networks are "evolutionarily grown" under the condition of maximization of small cliques in the entire network, while FC networks are instantly created. Running the standard SIR model on clustered SI and FC networks, we demonstrate that the evolutionary grown clustered network prevents the spread of an epidemic better than the instantly clustered network with similar parameters. We find that SI networks have the scale-free property for the degree distribution P(k)∼k^{η}, with a small critical exponent -2<η<-1. We argue that the scale-free behavior emerges as a result of the randomness in the initial degree distributions.

Spectral peculiarity and criticality of a human connectome.

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms. Considering the network evolution induced by the preference of 3-cycles formation, we discovered that for macaque and human connectomes the evolution with the conservation of local clusterization is crucial, while for primitive organisms the conservation of averaged clusterization is sufficient. Investigating for the first time the level spacing distribution of the spectrum of human connectome Laplacian matrix, we explicitly demonstrate that the spectral statistics corresponds to the critical regime, which is hybrid of Wigner-Dyson and Poisson distributions. This observation provides strong support for debated statement of the brain criticality.

Finite plateau in spectral gap of polychromatic constrained random networks.

We consider critical behavior in the ensemble of polychromatic Erdos-Rényi networks and regular random graphs, where network vertices are painted in different colors. The links can be randomly removed and added to the network subject to the condition of the vertex degree conservation. In these constrained graphs we run the Metropolis procedure, which favors the connected unicolor triads of nodes. Changing the chemical potential, µ, of such triads, for some wide region of µ, we find the formation of a finite plateau in the number of intercolor links, which exactly matches the finite plateau in the network algebraic connectivity (the value of the first nonvanishing eigenvalue of the Laplacian matrix, λ_{2}). We claim that at the plateau the spontaneously broken Z_{2} symmetry is restored by the mechanism of modes collectivization in clusters of different colors. The phenomena of a finite plateau formation holds also for polychromatic networks with M≥2 colors. The behavior of polychromatic networks is analyzed via the spectral properties of their adjacency and Laplacian matrices.

Spontaneous symmetry breaking and phase coexistence in two-color networks.

We consider an equilibrium ensemble of large Erdos-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability p. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples µ. Minimizing the system energy, we see for some positive µ the formation of two predominantly unicolor clusters, linked by a string of N_{bw} black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the N_{bw}(µ) curve, which is relevant to a spinodal decomposition in first-order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby universes in two-dimensional gravity. We conjecture that the observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

Eigenvalue tunneling and decay of quenched random network.

We consider the canonical ensemble of N-vertex Erdos-Rényi (ER) random topological graphs with quenched vertex degree, and with fugacity µ for each closed triple of bonds. We claim complete defragmentation of large-N graphs into the collection of [p^{-1}] almost full subgraphs (cliques) above critical fugacity, µ_{c}, where p is the ER bond formation probability. Evolution of the spectral density, ρ(λ), of the adjacency matrix with increasing µ leads to the formation of a multizonal support for µ>µ_{c}. Eigenvalue tunneling from the central zone to the side one means formation of a new clique in the defragmentation process. The adjacency matrix of the network ground state has a block-diagonal form, where the number of vertices in blocks fluctuates around the mean value Np. The spectral density of the whole network in this regime has triangular shape. We interpret the phenomena from the viewpoint of the conventional random matrix model and speculate about possible physical applications.

Islands of stability in motif distributions of random networks.

We consider random nondirected networks subject to dynamics conserving vertex degrees and study, analytically and numerically, equilibrium three-vertex motif distributions in the presence of an external field h coupled to one of the motifs. For small h, the numerics is well described by the "chemical kinetics" for the concentrations of motifs based on the law of mass action. For larger h, a transition into some trapped motif state occurs in Erdos-Rényi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a nonzero cubic term. A localization transition should always occur if the entropy function is nonconvex. We conjecture that this phenomenon is the origin of the motifs' pattern formation in real evolutionary networks.

Chaotic Hamiltonian systems: survival probability.

We consider the dynamical system described by the area-preserving standard mapping. It is known for this system that P(t), the normalized number of recurrences staying in some given domain of the phase space at time t (so-called "survival probability") has the power-law asymptotics, P(t) approximately t{-nu}. We present new semiphenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective "ultrametric diffusion" on the boundary of a treelike space with hierarchically organized transition rates. In the framework of our approach we have estimated the exponent nu as nu=ln 2/ln(1+r{g}) approximately 1.44, where rg=([square root] 5-1)/2 is the critical rotation number.

High-resolution absorption measurements by use of two-tone frequency-modulation spectroscopy with diode lasers.

The capability of two-tone frequency-modulation spectroscopy (TTFMS) in deriving spectral line-shape information was investigated. Two oxygen A-band transitions at 760 nm were selected, and the Voigt profile and two different collisionally narrowed line profiles were employed in their analysis. By means of a least-squares fitting procedure, we obtained accurate information regarding transition strengths and pressure-induced broadening, shift, and narrowing coefficients. Both TTFMS and direct absorption line shapes were modeled with deviations as small as 0.3% over a wide pressure range by use of the collisionally narrowed line profiles. Line parameters measured with TTFMS showed excellent agreement with the parameters measured with direct absorption. The experimental technique used constant-current fast-wavelength scanning, which improved measurement accuracy.

Mirror symmetry breaking at the molecular level.

Reasoning from two basic principles of molecular physics, P invariance of electromagnetic interaction and the second law of thermodynamics, one would conclude that mirror symmetry retained in the world of chiral molecules. This inference is fully consistent with what is observed in inorganic nature. However, in the bioorganic world, the reverse is true. Mirror symmetry there is definitely broken. Is it possible to account for this phenomenon without going beyond conventional concepts of the kinetics of enantioselective processes? This study is an attempt to survey all existing hypotheses containing this phenomenon.

Two-tone frequency-modulation spectroscopy for quantitative measurements of gaseous species: theoretical, numerical, and experimental investigation of line shapes.

The capability of retrieving spectral information from line shapes recorded by two-tone frequency-modulation spectroscopy (TTFMS) is investigated. A TTFMS theory accounting for dispersion and nonlinear distortion of diode laser frequency modulation response is presented. The adequacy of the theory for a detailed modeling of line shapes recorded with high resolution is examined. An extensive error analysis of line parameters (i.e., width, intensity, and line center) retrieved by a nonlinear least-squares fitting procedure is made. Plots of residual errors with characteristic signatures that are due to incorrectly assigned modulation parameters and choice of line profile are presented. In least-squares fits to experimental oxygen data with a Voigt profile influence from collisional(Dicke) narrowing is clearly exhibited, and when we used a collisionally narrowed line profile deviations of the model were reduced to less than 0.2%. We demonstrate that accurate quantitative measurements by TTFMS over a wide range of concentrations, temperatures, and pressures are possible.

[The clinical trial of a prototype of the new LAR-2 serially produced laser optometer]. / Klinicheskaia aprobatsiia obraztsa novogo seriinogo lazernogo optometra LAR-2.

Based on results of clinical trials of a new commercial laser optometer LAR-2, the authors suggest methodologic recommendations for ametropia diagnosis making use of this apparatus. The new device can adequately solve the major refraction problems: express diagnosis of ametropia, specification of the optimal vision correction in selection of eyeglasses, assessment of dynamic refraction. LAR-2 was found useful in the treatment of vision fatigue and amblyopia. A conclusion is made about diagnostic and clinical fitness of LAR-2 laser optometer; some minor shortcomings of the device are to be eliminated.

Handedness, origin of life and evolution.

Biological polymers have a preferred chirality ond can replicate themselves. Physical arguments provide insight into which of these unique and apparently related properties evolved first, and by what mechanism.

Homochirality and stereospecific activity: evolutionary aspects.

The problem discussed in this paper is the connection between the unique property of biopolymers (proteins, DNA and RNA), i.e. homochirality, and their main functional property, i.e. self-replication. Our approach is based on an analysis of the conditions for the origination of the mechanism of self-replication of chiral polymers. It is demonstrated that self-replication could originate only on the basis of homochiral structures, possessing stereospecific (enzymatic) activity. It is also shown that complete breaking of the mirror symmetry of the organic medium is required both at the stage of polymeric takeover and at the stage of formation of structures possessing stereospecific activity. This requirement is satisfied only in the framework of the mechanism of spontaneous symmetry breaking i.e. the mechanism of non-equilibrium phase transition from the racemic state of the organic medium to the chirally pure one. The results obtained suggest that homochirality is a necessary condition for the origination of biological specificity and plays a fundamental role in the formation of structures capable of self-replication.

Chiral purity of nucleotides as a necessary condition of complementarity.

This work discusses the question about the role of chiral purity (homochirality) of nucleotides in the formation of complementary replicas. A qualitative answer to this question can be obtained from molecular models constructed to simulate the chiral defect in the polynucleotidic chain. It shows the necessity of homochirality of nucleotides for the complementarity preservation. The necessity of the strong mirror-symmetry breaking in the abiogenic formation of the self-replicating oligonucleotide structures is discussed in the context of prebiological evolution.