Interfacial tension and Rusanov parameter for highly curved surfaces with different types of curvature

The expressions for the size dependence of interfacial tension σ(r) for surfaces with positive and negative curvature are derived. The parameter k in the formula σ = kr for highly curved interfaces is found in the analytical form and calculated. The length of the linear portion is estimated for different curvature types.     

Surface pressure characteristics of a highly loaded turbine blade at design and off-design conditions; a CFD methodology

The flow field passing through a highly loaded low pressure (LP) turbine cascade is numerically investigated at design and off-design conditions. The Field Operation And Manipulation (OpenFOAM) platform is used as the computational Fluid Dynamics (CFD) tool. In this regard, the influences of grid resolution on the results of k-ε, k-ω, and large-eddy simulation (LES) turbulence models are investigated and compared with those of experimental measurements. A numerical pressure undershoot is appeared near the end of blade pressure surface which is sensitive to grid resolution and flow turbulence modeling. The LES model is able to resolve separation on both coarse and fine grid resolutions. In addition, the off-design flow condition is modeled by negative and positive inflow incidence angles. The numerical experiments show that a separation bubble generated on blade pressure side is predicted by LES. The total pressure drop has also been calculated at incidence angles between -20° and +8°. The minimum total pressure drop is obtained by k-ω and LES at design point.     

A study of the critical properties of the Ising model on body-centered cubic lattice taking into account the interaction of next behind nearest neighbors

The replica Monte Carlo method has been used to investigate the critical behavior of a threedimensional antiferromagnetic Ising model on a body-centered cubic lattice, taking into account interactions of the adjacent behind neighbors. Investigations are carried out for the ratios of the values of exchange interactions behind the nearest and next nearest neighbors k = J ₂/J ₁ in the range of k ∈ [0.0, 1.0] with the step Δk = 0.1. In the framework of the theory of finite-dimensional scaling the static critical indices of heat capacity α, susceptibility γ, of the order parameter β, correlation radius ν, and also the Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is kept in the interval of k ∈ [0.0, 0.6]. It is established that a nonuniversal critical behavior is observed in the range k ∈ [0.8, 1.0].     

Structural features and the microscopic dynamics of the three-component Zr<Subscript>47</Subscript>Cu<Subscript>46</Subscript>Al<Subscript>7</Subscript> system: Equilibrium melt,supercooled melt,and amorphous alloy

The structural and dynamic properties of the three-component Zr₄₇Cu₄₆Al₇ system are subjected to a molecular dynamics simulation in the temperature range T = 250–3000 K at a pressure p = 1.0 bar. The temperature dependences of the Wendt–Abraham parameter and the translation order parameter are used to determine the glass transition temperature in the Zr₄₇Cu₄₆Al₇ system, which is found to be T_c ≈ 750 K. It is found that the bulk amorphous Zr₄₇Cu₄₆Al₇ alloy contains localized regions with an ordered atomic structures. Cluster analysis of configuration simulation data reveals the existence of quasi-icosahedral clusters in amorphous metallic Zr–Cu–Al alloys. The spectral densities of time radial distribution functions of the longitudinal (C?_L(k, ω)) and transverse (C?_T(k, ω)) fluxes are calculated in a wide wavenumber range in order to study the mechanisms of formation of atomic collective excitations in the Zr₄₇Cu₄₆Al₇ system. It was found that a linear combination of three Gaussian functions is sufficient to reproduce the (C?_L(k, ω)) spectra, whereas at least four Gaussian contributions are necessary to exactly describe the (C?_T(k, ω)) spectra of the supercooled melt and the amorphous metallic alloy. It is shown that the collective atomic excitations in the equilibrium melt at T = 3000 K and in the amorphous metallic alloy at T = 250 K are characterized by two dispersion acoustic-like branches related with longitudinal and transverse polarizations.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

Rayleigh instability in liquid-crystal jets

Capillary instability of isothermal incompressible liquid-crystal (LC) jets is considered within the linear hydrodynamics of uniaxial nematic LCs. Free boundary conditions with strong tangential anchoring of director n at the surface are formulated in terms of the mean surface curvature ? and the Gaussian surface curvature G. The static version of the capillary instability is shown to depend on the elasticity modulus Κ, the surface tension σ₀, and the radius r₀ of the LC jet, expressed in terms of the characteristic parameter κ = Κ/σ₀r₀. The problem of the capillary instability in LC jets is solved exactly, and a dispersion relation that reflects the effect of elasticity is derived. It is shown that increase in the elasticity modulus results in decrease in both the cut-off wavenumber k and the disturbance growth rate s. This implies an enhanced stability of LC jets in comparison to ordinary liquids. In the specific case where the hydrodynamic and orientational LC modes can be decoupled, the dispersion equation is given in a closed form.     

Bifurcation points of rotating magnetized Newtonian polytropes with an index close to unity

The existence of bifurcation points of Newtonian rotating polytropes in the interval of polytropic index 0.9989 < n ≤ 1.0795, in which asymmetric with respect to the axis of rotation solutions describing the density distribution are branched, is proved for the first time. It is shown that, in this interval of values of n, the parameter of the rotation rate at critical points ? _k takes values 0.0442 > ? _k ≥ 0.     

Kramers–Kronig Relations in Representation of Modulation Polarimetry by an Example of the Transmission Spectra of GaAs Crystal

The increments of the real and imaginary components of the complex refractive index ΔN = Δn–iΔk of a lightly doped GaAs crystal with a donor concentration of ~10¹⁶ cm^–3 have been measured using modulation polarimetry. It is shown that, within this representation, the birefringence and dichroism spectra (Δn(ω) and Δk(ω), respectively) obtained in the transparency window of a sample subjected to probe strain are derivatives of the corresponding functions: Δn(ω) ≈ dn/dω and Δk(ω) ≈ dk/dω. The experimental characteristics and primary dependences n(ω) and k(ω) derived from them by graphical integration are in agreement with the results of other researchers and measurements carried out by independent methods. The results obtained are compared (taking into account the integral (Kramers–Kronig) relations) with the resonance parameters: amplitude and phase in the Drude–Lorenz model. Agreement between the experimental characteristics and theoretical model predictions can be obtained by choosing an appropriate value of resonance damping parameter.     

Investigation of the Balitsky-Fadin-Kuraev-Lipatov dynamics of gluon distributions in the inelastic production of <Emphasis Type="Italic">J/ψ</Emphasis> mesons at the HERA collider

The inelastic photo-and electroproduction of J/ψ mesons at the HERA collider are considered within the semihard (k _T -factorization) QCD approach and the color-singlet model. The total, differential, and double-differential cross sections for the inelastic production of J/ψ mesons are investigated versus the Pomeron intercept Δ, which is the basic parameter of low-x physics; also studied here is the spin alignment parameter α versus the square of the transverse momentum, p _ψT ² , and the variable z. The theoretical results obtained in the present study are compared with the latest experimental data of the H1 and ZEUS Collaborations. It is shown that experimental investigations of the polarization properties of J/ψ mesons at the HERA collider for Q²<1 GeV² may provide an additional test of the Balitsky-Fadin-Kuraev-Lipatov dynamics of gluon distributions.     

Hall-Petch analysis for temperature and strain rate dependent deformation of polycrystalline lead

A dislocation pile-up analysis of the Hall-Petch constant k _ε for the tensile deformation of polycrystalline lead over a wide range of temperature T and at two strain rates has been made. The predicted and experimental Hall-Petch dependencies k _ε ² = f (T) are in good agreement. Lower than predicted k _ε values at very low temperatures are attributed to the high curvature of grain boundaries which experience high localized plasticity and consequent shear banding.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Zero-sound branches in asymmetric nuclear matter

A polarization operator constructed in the random phase approximation is used to obtain zero-sound excitations in isospin asymmetric nuclear matter (ANM). Two families of the complex solutions ω_sτ(k),τ= p,n are presented. The imaginary part of the solutions corresponds to the damping of the collective mode due to its overlapping with the particle-hole modes and the subsequent emission of a proton (ω_sp(k)) or a neutron (ω_sn(k)). The dependence of the solutions on the asymmetry parameter is studied.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.     

Classification of two-shell nanotubes with commensurate structures of shells

A classification of two-shell carbon nanotubes with commensurate structures of shells is proposed. The classification is based on the concept of equivalence classes as a set of shells with chiral indices of the (kf, kg) type, where f and g are the chiral indices of the equivalence class and k is the index of the shell diameter. All two-shell nanotubes with commensurate shells that are characterized by the chiral indices (k₁f₁, k₁g₁) and (k₂f₂, k₂g₂), where k₁ and k₂ are integral numbers, make up a family of nanotubes of different radii but with equal geometric parameters (such as the intershell distance, the unit cell length of the nanotube, and the difference between the chiral angles of the shells). The geometric parameters of nanotubes are calculated for a number of families, the distribution of different types of two-shell nanotubes with commensurate shells over the outer-shell radii is determined, and the threshold forces required to induce relative motion of nanotube shells are evaluated. The possible use of two-shell nanotubes with commensurate shells in nanostructures is discussed.     

On a Ströbel-Inspired <Emphasis Type="Italic">k</Emphasis>(<Emphasis Type="Italic">t</Emphasis>) FLRW Ansatz in a Class of Metric <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Models

Assuming a D≥4 dimensional FLRW (Friedmann–Lemaître–Robertson–Walker) inspired ansatz with spatial curvature being a non-trivial function of time k(t) in a class of metric and Jordan frame F(R) gravity models, non-existence theorems for several types of sources are derived in a simple manner (using specific form of the modified gravity Einstein tensor components).     

Waves in a superlattice with anisotropic inhomogeneities

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on inhomogeneities with anisotropic correlation properties are studied for the first time. The period of the superlattice is modulated by the random function described by the anisotropic correlation function K_?(r) that has different correlation radii, k _∥ ^?1 and k _⊥ ^?1 , along the axis of the superlattice z and in the plane xy, respectively. The anisotropy of the correlation is characterized by the parameter λ=1?k_⊥/k_∥ that can change from λ=0 to λ=1 when the correlation wave number k⊥ changes from k_⊥=k_∥ (isotropic 3D inhomogeneities) to k_⊥=0 (1D inhomogeneities). The correlation function of the superlattice K(r) is developed. Its decreasing part goes to the asymptote L that divides the correlation volume into two parts, characterized by finite and infinite correlation radii. The dependences of the width of the gap in the spectrum at the boundary of the Brillouin zone δν and the damping of waves ξ on the value of λ are studied. It is shown that decreasing L leads to the decrease of δν, and increase of ξ, with the increase of λ.     

Formation of an energy cascade in a system of vortices on the surface of water

The formation of an energy cascade in a system of vortices generated by perpendicular standing waves with a frequency of 6 Hz on the water surface has been experimentally studied. It has been found that peaks appear on the energy distribution over wave vectors E(k) after switching on pumping. These peaks are transformed with time because of the energy redistribution over scales. The stationary distribution E(k) established 300 s after switching on pumping can be described by a power-law function of the wave vector E(k) ～ k^1.75. It has been shown that waves with frequencies of about 18, 15, 12, 9, and 3 Hz appear on the surface of water owing to the nonlinear interaction at the excitation of a 6-Hz wave. It is assumed that the energy cascade of the turbulent motion in the wave vector range of 0.3–5 cm^?1 is formed by the nonlinear interaction between vortices generated by all waves propagating on the surface and direct energy fluxes toward high wave vectors dominate.     

Optimization of the Electromagnetic (EM) Perturbative Effects Produced by High-Frequency Gravitational Waves

For the relic gravitational waves in high frequency band, we survey the electromagnetic resonance effect generated from the high frequency gravitational waves, which can be described in the transverse perturbative photon fluxes. Under the fixed tensor-scalar ratio r = 0.2, spectral index n _t = 0 and running index α _t = 0.01, we discuss several properties and quantity changes of the transverse perturbative photon fluxes, which can be improved significantly through setting the longitudinal magnetic component of background EM field in the standard gaussian form, and wave impedance analysis on the transverse direction. Through the theoretical calculation, the transverse perturbative photon fluxes can reach up to 10³ s ^?1 with some optimal parameters such as waist of EM field W ₀ = 0.05m, initial stochastic phase of gravitational waves δ = (0.21 + n)π(n = 0,1,2...). Furthermore the interference of the background transverse photon fluxes can be removed completely through establishing a suitable wave impedance function.