Samarkand State University

About: Samarkand State University is a education organization based out in Samarkand, Uzbekistan. It is known for research contribution in the topics: Computer science & Essential spectrum. The organization has 633 authors who have published 693 publications receiving 4868 citations. The organization is also known as: Samarkand State University named after Alisher Navoi & Alisher Navoiy nomidagi Samarqand Davlat Universiteti.

Nonlinear susceptibilities, absorption coefficients and refractive indices of colloidal metals

Abstract: The investigations of the nonlinear optical parameters of Au, Ag, Pt and Cu colloidal solutions using the Z-scan method and third-harmonic generation (THG) are presented. The nonlinear refractive indices, nonlinear absorption coefficients and Kerr-induced nonlinear susceptibilities (χ(3)(-ω;ω,-ω,ω)) of these solutions on the wavelengths of picosecond and nanosecond Nd:YAG laser radiation (λ = 1064 nm) and its second harmonic (λ = 532 nm) have been measured. A tenfold increase of nonlinear susceptibilities on the wavelength of 532 nm in comparison with λ = 1064 nm is shown for these colloidal metals. The application of colloidal metals as optical limiters of picosecond and nanosecond radiation (λ = 1064 nm and 532 nm) was studied. The influence of aggregation of colloidal clusters on optical limiting in these media was considered. It was shown that the appearance of the long-wave wing of absorption at the final stages of aggregation led to the nonlinear absorption of picosecond pulses. The investigations of the THG of picosecond Nd:YAG laser radiation in colloidal metals (Pt and Cu) are presented. THG efficiency was found to be 7×10-7 for colloidal platinum. Nonlinear susceptibilities χ(3)(-3ω;ω,ω,ω) of colloidal platinum and copper were measured to be (1.5±0.75)×10-14 esu and (1±0.5)×10-14 esu, respectively.

Nonlinear refraction in CS 2

Abstract: The nonlinear refractive index (γ) of CS2 was measured using the Z-scan technique and laser radiation of various (femto-, pico-, and nano-second) pulse durations. We observed the growth of γ with the increase of the pulse duration (from (3±0.6)×10-15 cm2 W-1 at 110 fs to (4±2)×10-14 cm2 W-1 at 75 ns) due to the additional influence of the molecular reorientational Kerr effect in the case of longer (picosecond and nanosecond) pulses. Acoustic wave induced negative nonlinear refraction was observed using wavefront analysis. We analyzed the simultaneous influence of both electronic and molecular processes leading to the positive nonlinear refraction and acoustic processes leading to the negative nonlinear refraction in carbon disulfide. Variations of the refractive index due to the thermal effect at high pulse repetition rates were also investigated.

Schrodinger Operators on Lattices. The Efimov Effect and Discrete Spectrum Asymptotics

Abstract: The Hamiltonian of a system of three quantum mechanical particles moving on the three-dimensional lattice $$ \mathbb{Z}^3 $$ and interacting via zero-range attractive potentials is considered For the two-particle energy operator h(k), with $$ k \in \mathbb{T}^3 = (-\pi, \pi]^3 $$ the two-particle quasi-momentum, the existence of a unique positive eigenvalue below the bottom of the continuous spectrum of h(k) for k ≠ 0 is proven, provided that h(0) has a zero energy resonance The location of the essential and discrete spectra of the three-particle discrete Schrodinger operator H(K), $$ k \in \mathbb{T}^3 $$ being the three-particle quasi-momentum, is studied The existence of infinitely many eigenvalues of H(0) is proven It is found that for the number N(0, z) of eigenvalues of H(0) lying below $$ z < 0 $$ the following limit exists $$ \lim_{z \to 0-}\, {N(0, z)\over |\log|z\|} = {\mathcal U}_0 $$ with $$ {\mathcal U}_0 > 0 $$ Moreover, for all sufficiently small nonzero values of the three-particle quasi-momentum K the finiteness of the number $$ N(K, \tau_{ess}(K))$$ of eigenvalues of H(K) below the essential spectrum is established and the asymptotics for the number N(K, 0) of eigenvalues lying below zero is given

The threshold effects for the two-particle Hamiltonians on lattices

Abstract: For a wide class of two-body energy operators h(k) on the d-dimensional lattice ℤ d , d≥3, k being the two-particle quasi-momentum, we prove that if the following two assumptions (i) and (ii) are satisfied, then for all nontrivial values k, k≠0, the discrete spectrum of h(k) below its threshold is non-empty. The assumptions are: (i) the two-particle Hamiltonian h(0) corresponding to the zero value of the quasi-momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and (ii) the one-particle free Hamiltonians in the coordinate representation generate positivity preserving semi-groups.

Simulation of dictyostelium discoideum aggregation via reaction-diffusion model.

Abstract: We propose a reaction-diffusion model for simulation of the process of aggregation of Dictyostelium discoideum amoebae. The model is based on FitzHugh-Nagumo-type equations for cyclic adenosine 3\ensuremath{'}-monophosphate waves and a continuity equation for amoebae motion. We simulate the process of aggregation induced by a periodic point source and by spiral wave. We show that the aggregation pattern is formed as a result of front instabilities due to dependence of wave velocity on density of amoebae. This instability can also result in formation of wave breaks and generation of spiral waves.