In this paper, we study the properties of self-similar solutions of a cross-diffusion parabolic system. In particular, we find the Zeldovich Barenblatt type solution to the cross diffusive system. The asymptotic behavior of self-similar solutions are analyzed for both the slow and fast diffusive regimes. It is shown that coefficients of the main term of the asymptotic of solution satisfy some system of nonlinear algebraic equations.

We consider the reflection-transmission of the Gaussian wave packet through the moving wall with absorbing boundary conditions based on the time dependent one-dimensional Schrӧdinger equation. The reflection coefficient is calculated for the case when the walls are fixed, and probability density is calculated for the case when the wall is moving linearly.

In this paper we will report on a one-dimensional, non-separable quantum many-particle system. It consists of two (distinguishable) particles moving on the half-line R+ being subjected to two different kinds of two-particle interactions: singular many-particle interactions localized at the origin and a binding-potential leading to a molecular-like state. We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian for our system) and elaborate on its spectral properties. In addition, we will present possible directions for future research.

We consider the stationary (cubic) nonlinear Schrӧdinger equation (NLSE) on a simple metric graph in the form of a triangle with three infinite outgoing bonds. Exact solutions are obtained for primary star graph with the boundary vertex conditions providing the wave function weights continuity and flux conservation for the case of repulsive nonlinearity.

We treat the stationary nonlinear Schrӧdinger equation on two-dimensional branched domains, so-called fat graphs. The shrinking limit when the domain becomes one-dimensional metric graph is studied by using analytical estimate of the convergence of fat graph boundary conditions into those for metric graph. Detailed analysis of such convergence on the basis of numerical solution of stationary nonlinear Schrӧdinger equation on a fat graph is provided. The possibility for reproducing different metric graph boundary conditions studied in earlier works is shown. Practical applications of the proposed model for such problems as Bose-Einstein condensation in networks, branched optical media, DNA, conducting polymers and wave dynamics in branched capillary networks are discussed.

Cellular automaton rules are derived from a set of reaction-diffusion partial differential equations by means of ultradiscretization method. The rulesres produce dynamical properties of pulse: annihilation, soliton-like preservation and periodic generation with a pacemaker.

We study the dynamics of a Gaussian wave packet in a branched system of periodic lattices driven by an external time-dependent field. Motivated by recent numerical experiments with the manipulation of wave packet transmission in quantum star graph, we provide further discussion based on some achievements obtained from one-dimensional tight-binding models with arbitrary external time-dependent fields and on numerical calculations.

Among all the experimental observations of cuprate physics, the metal-insulator-crossover (MIC), seen in the pseudogap (PG) region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field when the superconductivity is suppressed, is most likely the most intriguing one. Since it was expected that the PG-normal state for these materials, as for conventional superconductors, is conducting. This MIC, revealed in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy, resistivity temperature upturn, insulating ground state, nematicity- and stripe-phases and Fermi pockets, unambiguously indicates on the insulating normal state, from which high-temperature superconductivity (HTS) appears. In the present work (article I), we discuss the MIC phenomena mentioned in the title of article. The second work (article II) will be devoted to discussion of other listed above MIC phenomena and also to interpretation of the recent observations in the hidden magnetic order and scanning tunneling microscopy (STM) experiments spin and charge fluctuations as the intra PG and HTS pair ones. We find that all these MIC (called in the literature as non-Fermi liquid) phenomena can be obtained within the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of single fermions into those of single bosons. We show that this MIC originates from bosons of Coulomb two liquid model and fermions, whose origin is these bosons. At an increase of doping up to critical value or temperature up to PG boundary temperature, the boson system undegoes bosonic insulator– bosonic metal– fermionic metal transitions.

In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal- insulator (fermion-boson)- crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [Abdullaev B., et al. arXiv:cond-mat/0703290], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to the PG pair intra charge and spin fluctuations. We will try to obtain an answer to the question; why ground state of YBCO is Fermi liquid oscillating and of Bi-2212 is insulating? We will also clarify the physics of the recently observed MIC results of Lalibert et al. [arXiv:1606.04491] and explain the long-discussed transition of the electric charge density from doping to doping+1 dependence at the critical doping. We predict that at the upturns this density should have the temperature dependences n T3n2 for T 0, where n2 is density for dopings close to the critical value. We understood that the upturns before and after the first critical doping have the same nature. We will find understanding of all above mentioned phenomena within PG pair physics.

Short channel effects, such as DIBL are compared for SOI-FinFETs with different silicon body geometries. The original device considered was straight without narrowing at the top and a set of devices that exhibit the mentioned narrowing, up to the extreme case where the top of the gate has no surface and so the body cross-section is essentially a triangle. We have studied five different variations from the original geometry of a 25 nm gate length SOI-FinFET device with 1.5 nm thick oxide layer. The P-type channel had a doping concentration of 1015 cm 3 and n-type S/D areas are doped at concentrations of 1020 cm 3. The silicon body of the device accordingly had a height of 30 nm and a width of 12 nm. Simulation results show the source-drain barrier decreasing with increasing the upper body thickness. The DIBL effect of the considered FinFETs depends on upper body thickness, tending to increase with thicker upper body widths. Results of a comparison of two devices with different shapes but with the same cross-sectional area shows the relationship mainly depends on the shape rather than the cross-section area of the device body.

Short channel effects such as DIBL are compared for trigate SOI Junctionless MOSFET with extended and non-extended lateral part of the gate. A trigate SOI JLMOSFET with gate length L_gate, a silicon body width W_tin and thickness of 10 nm are simulated. In order to calculate the DIBL, the transfer characteristics of JLMOSFETs was simulated at a donor concentration of 5⋅10¹⁹ cm^-3 in the silicon body. The equivalent oxide thicknesses of the HfO₂ gate insulator used in simulation was 0.55 nm. Simulation result showed the DIBL for the trigate JLMOSFET depended on the length of the lateral part of the gate Lext. DIBL is high for devices with gates having extended lateral parts. This is a result of parasitic source (drain)-gate capacitance coupling which is higher for longer L_ext.

The possibility of using digital holographic interferogram obtained via laser radiation at different wavelengths and different pulse lengths in different times for the reconstruction of dynamic phase changes was explored. The opportunities for applying the digital holographic interferometry method to the study of resonant mode shapes in resonant acoustic spectroscopy are shown. The results of experimental measurements and analytical calculations are submitted.

We introduce Khujakulov and Nakamura’s scheme for the exact fast-forwarding of standard quantum dynamics for a charged particle. The idea allows the acceleration of both amplitude and phase of the wave function throughout the fast-forwarding time range. Firstly we shall apply the proposed method to 1-D free wave packet dynamics and obtain the electromagnetic field to ensure its rapid propagation and diffusion. Then we proceed to study 1-D quantum tunneling phenomenon, namely a rapid penetration of wave function through a delta-function type barrier. We elucidate the distribution of the tunneling current density to show the remarkable enhancement of the tunneling rate (tunneling power) due the fast-forwarding. We introduce two types of time-magnification factors and confirm the stability of fast-forward against the variation of such factors.

Interface engineering plays important role in the fabrication of tandem and perovskite-based solar cells. Recent experiments show that the interface effects are caused by the coupling of the electron bands and the pairing of surface contact geometry. In particular, it has been experimentally revealed that the transition from a planar to a rough interface improves many photoelectric parameters of the device. This means that the value of the fractal dimension of the interface may be key factor in device performance. It is possible to formulate two problems: firstly, the understanding on simple models why the electrical properties are improved with fractal interfaces, and, secondly, to discuss one of the most promising approaches in modern electronics, namely technology of radiation applications in the creation of rough interfaces.

We study a scheme for the acceleration of adiabatic quantum dynamics. Masuda-Nakamura’s theory of acceleration uses a strategy of combining two opposite ideas: infinitely-large time-magnification factor (α) and infinitely-small growth rate (∈) for the adiabatic parameter. We apply the proposed method to a system with a parameter-dependent asymmetric double-well potential which has no scale invariance, and obtain the elctromagnetic field required to accelerate the system. The ground state wave function, initially localized in one well, quickly moves to another well. We investigate two kinds of ground-state wave functions: with and without space-dependent phase ŋ. For the system with non-zero ŋ, we show the fast-forward of the adiabatic change for current density distribution more clearly characterizes the well-to-well transport and is deformed as the finite renormalized time-multiplication factor (v=∈α) is varied.

The entropic sampling Monte Carlo method within Wang-Landau algorithm is applied to investigate properties of a lattice model of strongly charged flexible 3-arm star-shaped polyelectrolyte. The density of states is calculated, from which the canonical properties of the system in a wide temperature range are obtained by simple integration. The effects of the arm length and the short-range monomer-monomer potential on the thermal and structural properties of star polyions are studied. We calculate such characteristics as mean square radius of gyration and its components, the radius vector of the center of mass, components of the tensor of inertia and parameters characterizing the shape of the polyion. In this work, we focus on how these characteristics are influenced by the change of the reduced temperature which, within the considered model, is a parameter combining the effect of real temperature, linear charge density and solvent dielectric permittivity. The coil-globule transition is observed in most of the considered cases, and for the polyions with the longest length of arms (24), the transition from a liquid globule to a solid-like state is observed. Comparison of polyelectrolyte models with neutral ones is given.

An adiabatic cycle involving the-function potential is shown to excite Bose particles confined in a one-dimensional box. We consider a cycle, during which a wall described by a potential is applied and its strength and position are slowly varied. When the system is initially prepared in the equilibrium ground state, the adiabatic cycle brings all bosons into the first excited one-particle state, leaving the system in a nonequilibrium state. The absorbed energy during the cycle is proportional to the number of bosons.

Using density functional theory, the structures and properties of carbon diamond-like phases, all of whose atoms occupy equivalent crystallo graphic positions, were studied. Structures of these phases were obtained by linking or superposing ofcarbon clusters. It was found that thirteen such phases can exist. The calculated structural characteristics and properties (density, cohesive energy, bandgap, bulk modulus, hardness, and x-ray diffraction pattern) of the diamond-like phases under study differ significantly from respective parameters of cubic diamond.

The digital two-dimensional Fourier decomposition of surface scanning electron microscopy (SEM) micrographs is used to detect the regular morphological structures on a polymer composite surface. Analyzing the SEM images of fluorinated and sulfonated low density polyethylene (LDPE), we identify and specify both regular and irregular submicron surface structures. The possibility of similar information processing techniques generalization for the morphological simulating of modified polymers bulk structures is discussed.