Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references added

NN potentials from inverse scattering in the J-matrix approach

An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and neutron-proton in the $^3S_1-^3D_1$ channel elastic scattering. In the latter case the deuteron wave function of a realistic $np$ potential was used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo

Localization in simple multiparticle catalytic absorption model

We consider the phase transition in the system of n simultaneously developing random walks on the halfline x>=0. All walks are independent on each others in all points except the origin x=0, where the point well is located. The well depth depends on the number of particles simultaneously staying at x=0. We consider the limit n>>1 and show that if the depth growth faster than 3/2 n ln(n) with n, then all random walks become localized simultaneously at the origin. In conclusion we discuss the connection of that problem with the phase transition in the copolymer chain with quenched random sequence of monomers considered in the frameworks of replica approach.Comment: 17 pages in LaTeX, 5 PostScript figures; submitted to J.Phys.(A): Math. Ge

Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories

In this paper we study the kinetics of diffusion-limited, pseudo-first-order A + B -> B reactions in situations in which the particles' intrinsic reactivities vary randomly in time. That is, we suppose that the particles are bearing "gates" which interchange randomly and independently of each other between two states - an active state, when the reaction may take place, and a blocked state, when the reaction is completly inhibited. We consider four different models, such that the A particle can be either mobile or immobile, gated or ungated, as well as ungated or gated B particles can be fixed at random positions or move randomly. All models are formulated on a $d$-dimensional regular lattice and we suppose that the mobile species perform independent, homogeneous, discrete-time lattice random walks. The model involving a single, immobile, ungated target A and a concentration of mobile, gated B particles is solved exactly. For the remaining three models we determine exactly, in form of rigorous lower and upper bounds, the large-N asymptotical behavior of the A particle survival probability. We also realize that for all four models studied here such a probalibity can be interpreted as the moment generating function of some functionals of random walk trajectories, such as, e.g., the number of self-intersections, the number of sites visited exactly a given number of times, "residence time" on a random array of lattice sites and etc. Our results thus apply to the asymptotical behavior of the corresponding generating functions which has not been known as yet.Comment: Latex, 45 pages, 5 ps-figures, submitted to PR

Study of the graphene oxide nanoparticles effect on luminol-dependent chemiluminescence of human leukocytes

Graphene and its derivatives are increasingly used in biomedical research. Therefore, the mechanisms and consequences of the interaction of graphene nanoparticles with living objects are intensively studied. The immune system is involved in protecting the body and regulating its functions, so the question of the effect of graphene and its derivatives on immune cells is crucial. The specific response of monocytes, macrophages, and neutrophils to a stimulus is to increase the production of reactive oxygen species (ROS). Published data on graphene oxide (GO) and polyethylene glycol-modified graphene oxide (GO-PEG) effects on peripheral blood leukocytes are scarce and contradictory. It is due to variations in objects and conditions of study, along with the difference in particle concentrations. Thus, it was essential to evaluate the GO and GO-PEG effect on ROS production by human leukocytes. Our study aimed at the effect of particles of unmodified and PEG-modified graphene oxide (GO and GO-PEG) on the ROS production by peripheral blood leukocytes in not-stimulated and stimulated luminoldependent chemiluminescence (LCL) tests. ROS production was stimulated by opsonized zymosan (OZ). A hydrogen peroxide-luminol system was used for assessing the independent effect of GO nanoparticles on the quenching of ROS luminescence. Pristine GO (Ossila, Great Britain) nanoparticles were PEG-modified (GO-PEG). The average size of the GO flakes was 1-5 µm, the GO-PEG-flakes 569±14 nm, and the amount of PEG covering was ~ 20%. Nanoparticles were used at concentrations of 5; 2.5; 1.25 µg/ml. It has been established that GO-PEG nanoparticles in concentrations of 2.5 and 5 µg/ml suppressed ROS production in the spontaneous LCL test. At the same time, the GO effects showed a visible but a not significant tendency to inhibition of LCL. Similar results were obtained in the stimulated LCL test. However, when analyzing the process kinetics, both GO-PEG and GO decreased the ROS production, but mainly in the first minutes of the test. When analyzing the quenching effect of the LCL reaction in a cell-free system, there was no significant effect of GO and GO-PEG nanoparticles. Thus, the general vector of the obtained effects was associated with the suppression of ROS production. GO-PEG ROS-decreasing effects were more pronounced in comparison with unmodified GO. In general, we have confirmed the antioxidant effects of GO and GO-PEG using the LCL method. We can assume that in addition to the actual antioxidant effect of graphene nanoparticles, ROS production decreases due to the rapid GO uptake and blocking of several intracellular signals that induce an oxidative burst

GRAPHENE OXIDE NANOPARTICLES IN THE REGULATION OF THE OXIDATIVE ACTIVITY OF HUMAN MONOCYTES

Graphene-based materials have an opportunity for use in biomedicine, thanks to their properties. Nevertheless, due to its cytotoxic effects, the use of graphene-based drugs is problematic. However, the surface modification of graphene oxide (GO) nanoparticles with a polyethyleneglycol (PEG) is one way to reduce the harmful effects of graphene on cells. Applying nanoparticles implies their interaction with the immune system, which protects the body. Monocytes are innate immunity cells and the first line of defenсe of the human organism from microorganisms and other alien objects. One of the monocytes’ reactions to a stimulus of any nature is to produce reactive oxygen species (ROS). Published data shows an incomplete picture of modified graphene oxide nanoparticles’ effects on ROS formation by human monocytes. Thus, it was essential to evaluate the pegylated graphene oxide (GO-PEG and GO-8armedPEG) effect on ROS production by human monocytes, assessed by the luminol-dependent chemiluminescence (LCL). The objects of the study were CD14+-cells isolated from mononuclear cells of healthy donors. ROS production was stimulated by opsonized zymosan (OZ), spontaneous LCL was used as a control. PEG-modified (GO-PEG and GO-8armedPEG) GO nanoparticles with sizes of 100-200 nm (“small”) and 1-5 μm (“big”) with PEG covering ~ 20% were used at concentrations of 5 and 25 μg/ml. The study showed that small size nanoparticles at a low concentration of 5 μg/ml and big nanoparticles coated with 8-armed PEG at both concentrations have a significant suppressive effect on spontaneous ROS production. In the stimulated LCL reaction variant, it was found that small nanoparticles (25 μg/ml) also have a suppressive effect on ROS production, such as big-sized particles coated with linear PEG at the same concentration. Thus, we have established for the first time that graphene oxide nanoparticles functionalized with PEG are capable of inhibiting the ROS production by human monocytes, and therefore, we can speak of the antioxidant activity of GO-PEG

Algorithm of work of gateway for mobile radio network

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