Wong–Zakai approximations and limiting dynamics of stochastic Ginzburg–Landau equations

This paper deals with the Wong–Zakai approximations and random attractors for stochastic Ginzburg–Landau equations with a white noise. We first prove the existence of a pullback random attractor for the approximate equation under much weaker conditions than the original stochastic equation. In addition, when the stochastic Ginzburg–Landau equation is driven by an additive white noise, we establish the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation tends to zero.

PHYSICO-MATHEMATICAL MODEL OF VENTILATION SYSTEM FORCING OF CLEAN AIR IN LIVESTOCK PREMISES

The microclimate of livestock facilities is determined by a range of factors, including physical parameters: humidity, atmospheric pressure, light, temperature, speed and direction of air movement. Air quality plays an important role - the concentration of harmful gases and microorganisms, dust. The parameters of the microclimate affect not only the productivity of animals, but also their health. In order not to harm the health of the animal and achieve the desired performance, these parameters must be adjusted with special equipment. The purpose of research is to substantiate the design and technological parameters of the ventilation system for the injection of clean air in livestock premises to ensure uniformity of its distribution. The article presents the results of research to substantiate the design and technological parameters of the ventilation system for the injection of clean air in pig farms to ensure uniformity of its distribution. As a result of analytical studies of the parameters of the slit of the nozzle for air injection from the condition of uniform air distribution, an approximate equation for its width δ'y depending on the y-axis location for different effective diameters of the nozzle d'H. For the system of injection of clean air the condition according to which at opening of all discharge valves it is necessary to provide uniformity of distribution of air by system of injection is set. For this purpose the central air duct for air injection should have a wedge-shaped form of length L' with constant height b', with initial width a'N and final a'1. As a result of theoretical researches dependences of a lateral angle of a wedge θ the central air duct of system of injection of pure air and its width on the end a1' on distance between adjacent sections L'0, width of the central air duct on its beginning aN' and quantity of branch pipes for injection N' are established. As a result of analytical studies of pressure losses of the ventilation system of pure air injection of the pigsty, the dependences of changes in pressure losses Δp2 and power NW2 required for pumping air through it on the width of the central air duct aN, air flow through the system qk, length between system pipes L0 and their number N.

Analytical Green’s functions for continuum spectra

Green’s functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along the extra dimension z, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS5, thus solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to z → ∞. This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green’s functions (with a mass gap mg ∼ TeV and a continuum for s >$$ {m}_g^2 $$ m g 2 ) which could then be easily incorporated in the experimental codes. The theory contains Standard Model gauge bosons in the bulk with Neumann boundary conditions in the UV brane. To cope with electroweak observables the theory is also endowed with an extra custodial gauge symmetry in the bulk, with gauge bosons with Dirichlet boundary conditions in the UV brane, and without zero (massless) modes. All Green’s functions have analytical expressions and exhibit poles in the second Riemann sheet of the complex plane at s = $$ {M}_n^2 $$ M n 2 − iMnΓn, denoting a discrete (infinite) set of broad resonances with masses (Mn) and widths (Γn). For gauge bosons with Neumann or Dirichlet boundary conditions, the masses and widths of resonances satisfy the (approximate) equation s = −4$$ {m}_g^2{\mathcal{W}}_n^2 $$ m g 2 W n 2 [±(1 + i)/4], where $$ \mathcal{W} $$ W n is the n-th branch of the Lambert function.

Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay

This paper proposes an extrapolation method to solve a class of non-linear weakly singular kernel Volterra integral equations with vanishing delay. After the existence and uniqueness of the solution to the original equation are proved, we combine an improved trapezoidal quadrature formula with an interpolation technique to obtain an approximate equation, and then we enhance the error accuracy of the approximate solution using the Richardson extrapolation, on the basis of the asymptotic error expansion. Simultaneously, a posteriori error estimate for the method is derived. Some illustrative examples demonstrating the efficiency of the method are given.

Anisotropic frequency-dependent characteristics of PP- and PS-waves in partially saturated double-porosity rocks

Most frequency-dependent AVO inversions are currently based on an approximate equation derived using an isotropic medium. However, actual reservoirs usually show anisotropy, such as shale reservoirs, tight sandstone reservoirs and fractured reservoirs. We propose a joint frequency-dependent AVO (JFAVO) inversion in an anisotropic medium based on a periodic layered double-porosity medium. This JFAVO will allow us to quantitatively study the influence of fluids on the dispersion of PP- and PS-wave velocities and anisotropic parameters. First, we used a double-porosity medium to analyse the frequency-dependent characteristics of velocities and anisotropy parameters. We found that the anisotropic parameters show obvious dispersions, similar to those of velocities. Then, we derived the JFAVO inversion based on Rüger's equation to extract the dispersion of velocities and anisotropic parameters. Finally, we analysed the stability and applicability of the inversion algorithm, and used three sets of models to analyse the sensitivity of dispersion properties to fluids. The numerical analysis results show that PP-wave velocity dispersion and anisotropic parameter δ dispersion are sensitive to fluids, whereas, the velocity dispersion of the PS-wave is not. When saturation exceeds 80%, the velocity dispersion and anisotropic parameter dispersion properties are not sensitive to fluids.

PURE MODE P AND S WAVE PHASE VELOCITY EQUATIONS IN ELASTIC ORTHORHOMBIC MEDIA

In an elastic model with orthorhombic symmetry, there are nine independent stiffness coefficients that control the propagation of all intrinsically coupled wave modes. For practical applications in P-wave modeling and inversion, it is important to derive the approximate solutions that support propagation of P waves only and depends on fewer independent parameters. Due to the increasing interest in shear-wave propagation in anisotropic media, we also derive an approximate equation that supports propagation of S waves only. However, the reduction in number of independent parameters for the S wave equation is not possible. We derive pure P and S wave equations in an elastic orthorhombic model and show that the accuracy is sufficient for practical applications.

Comparison of Measurement and Electromagnetic Overall Transfer Matrix Simulation Results of MgF 2 -Nb 2 O 5 Distributed Bragg Reflectors with Different Layers

In this study, glasses were used as substrates and an e-beam was used the method to deposit MgF2 and Nb2O5 single-layer films, and the optical properties, including extinction coefficients (k values) and refractive indices (n values), were measured by using the light wavelength as variable. The equation d = λ/(4n) was used to calculate the thickness (d) of 1/4 wavelength (λ) for each layer of the MgF2-Nb2O5 bilayer films in distributed Bragg reflectors (DBRs) with a designed reflective wavelength at blue light (~450nm). Each MgF2-Nb2O5 bilayer film was called a period, and the glass substrates were used to deposit the films with two, four, and six periods for fabricating the DBRs. The field emission scanning electron microscope equipped with a focused ion beam was used to measure the thickness of each MgF2-Nb2O5 layer in the DBRs with different periods. The measured maximum reflective ratios were compared with Sheppard’s approximate equation, which calculates only the maximum reflective ratio at a specific wavelength. An overall transfer matrix was investigated to calculate the reflective spectra by incorporating the variable n values and thicknesses of the MgF2-Nb2O5 films in each layer. We show that the measured results of the fabricated DBRs matched the results simulated using Sheppard’s approximate equation and the overall transfer matrix.

The I-Love-Q Relations for Superfluid Neutron Stars

The I-Love-Q relations are approximate equation-of-state independent relations that connect the moment of inertia, the spin-induced quadrupole moment, and the tidal deformability of neutron stars. In this paper, we study the I-Love-Q relations for superfluid neutron stars for a general relativistic two-fluid model: one fluid being the neutron superfluid and the other a conglomerate of all charged components. We study to what extent the two-fluid dynamics might affect the robustness of the I-Love-Q relations by using a simple two-component polytropic model and a relativistic mean field model with entrainment for the equation-of-state. Our results depend crucially on the spin ratio Ωn/Ωp between the angular velocities of the neutron superfluid and the normal component. We find that the I-Love-Q relations can still be satisfied to high accuracy for superfluid neutron stars as long as the two fluids are nearly co-rotating Ωn/Ωp≈1. However, the deviations from the I-Love-Q relations increase as the spin ratio deviates from unity. In particular, the deviation of the Q-Love relation can be as large as O(10%) if Ωn/Ωp differ from unity by a few tens of percent. As Ωn/Ωp≈1 is expected for realistic neutron stars, our results suggest that the two-fluid dynamics should not affect the accuracy of any gravitational waveform models for neutron star binaries that employ the relation to connect the spin-induced quadrupole moment and the tidal deformability.

Step-drawdown tests in exploitation wells for thermal and mineral water – Case study from Slovenia

A comparative analysis of step-drawdown tests was performed in order to estimate the well performance in Slovenian thermal and mineral water wells. Tests were performed in 30 wells, each having its own maximum production rate determined in the concession decrees. The main focus of well performance analysis, using graphical analysis of the Jacob approximate equation, was to estimate the adequacy of the wells production rate as well as to identify possible changes in the technical status of the wells over years. 5 of total 30 wells were not included in the analysis due to technical issues during test performance. Well performance analysis includes the calculation of nonlinear well losses related to turbulent flow and linear head loss (aquifer and well) assumed to be related to laminar flow. Results indicate that the ratios between nonlinear well losses and linear head (well and aquifer) losses, in this paper referred as laminar losses, are from 6.9 % to 97.4 %. Laminar losses parameter suggests, all investigated wells were classified with either good (11 wells), medium (7 wells) or poor (7 wells) performance. The addressed analysis represents a very important basis for further thermal and mineral water extraction, e.g. optimizing the maximum allowed production rate as granted in concession decrees and diagnose potential changes in the technical status of each well