Inhomogeneous pion condensed phase hosting topologically stable baryons

We discuss the inhomogeneous pion condensed phase within the framework of chiral perturbation theory. We show how the general expression of the condensate can be obtained solving three coupled differential equations, expressing how the pion fields are modulated in space. Upon using some simplifying assumptions, we determine an analytic solution in (3+1)-dimensions. The obtained inhomogeneous condensate is characterized by a non-vanishing topological charge, which can be identified with the baryonic number. In this way, we obtain an inhomogeneous system of pions hosting an arbitrary number of baryons at fixed position in space.

BPS black hole entropy and attractors in very special geometry. Cubic forms, gradient maps and their inversion

We consider Bekenstein-Hawking entropy and attractors in extremal BPS black holes of $$ \mathcal{N} $$ N = 2, D = 4 ungauged supergravity obtained as reduction of minimal, matter-coupled D = 5 supergravity. They are generally expressed in terms of solutions to an inhomogeneous system of coupled quadratic equations, named BPS system, depending on the cubic prepotential as well as on the electric-magnetic fluxes in the extremal black hole background. Focussing on homogeneous non-symmetric scalar manifolds (whose classification is known in terms of L(q, P, Ṗ) models), under certain assumptions on the Clifford matrices pertaining to the related cubic prepotential, we formulate and prove an invertibility condition for the gradient map of the corresponding cubic form (to have a birational inverse map which is given by homogeneous polynomials of degree four), and therefore for the solutions to the BPS system to be explicitly determined, in turn providing novel, explicit expressions for the BPS black hole entropy and the related attractors as solution of the BPS attractor equations. After a general treatment, we present a number of explicit examples with Ṗ = 0, such as L(q, P), 1 ⩽ q ⩽ 3 and P ⩾ 1, or L(q, 1), 4 ⩽ q ⩽ 9, and one model with Ṗ = 1, namely L(4, 1, 1). We also briefly comment on Kleinian signatures and split algebras. In particular, we provide, for the first time, the explicit form of the BPS black hole entropy and of the related BPS attractors for the infinite class of L(1, P) P ⩾ 2 non-symmetric models of $$ \mathcal{N} $$ N = 2, D = 4 supergravity.

Application of near-infrared spectroscopy technology in the complex fermentation system to achieve high-efficiency production

The fermentation process is dynamically changing, and the metabolic status can be grasped through real-time monitoring of environmental parameters. In this study, a real-time and on-line monitoring experiment platform for substrates and products detection was developed based on non-contact type near-infrared (NIR) spectroscopy technology. The prediction models for monitoring the fermentation process of lactic acid, sophorolipids (SLs) and sodium gluconate (SG) were established based on partial least-squares regression and internal cross-validation methods. Through fermentation verification, the accuracy and precision of the NIR model for the complex fermentation environments, different rheological properties (uniform system and multi-phase inhomogeneous system) and different parameter types (substrate, product and nutrients) have good applicability, and R2 was greater than 0.98, exhibiting a good linear relationship. The root mean square error of prediction shows that the model has high credibility. Through the control of appropriate glucose concentration in SG fermentation as well as glucose and oil concentrations SLs fermentation by NIR model, the titers of SG and SLs were increased to 11.8% and 26.8%, respectively. Although high cost of NIR spectrometer is a key issue for its wide application in an industrial scale. This work provides a basis for the application of NIR spectroscopy in complex fermentation systems.

Calculation of the optimal parameters of corrective elements in induction acceleration systems

The formulations of a number of optimization problems for a linear induction acceleration system with respect to the adjustment parameters are considered. The dynamics of the transverse motion of electrons in the horizontal plane is investigated in the presence of given energy values for each resonator period: the particles at the initial moment of time are somewhat displaced relative to the accelerator axis (we neglect the displacements of the ends of the solenoids and the centers of the accelerating gaps relative to the accelerator axis). A connection is established between the initial and final coordinates and the components of the momentum. The presence of parasitic electric and magnetic fields arising as a result of the displacement of particles relative to the axis of the accelerator, which change the transverse components of the pulses, is taken into account. For the mathematical formulation of problems, in order to apply algorithms of practical stability, the original difference model of the induction system was converted to a linear form. By introducing into consideration the vector of parameters, the scatter of phase coordinates, and tolerances on the parameters, the problem of calculating the tolerances for given linear constraints on the scatter of phase coordinates for the corresponding inhomogeneous system is formulated. For the case of nonlinear dynamic constraints on the spread of the vector of phase coordinates, it is proposed to approximate a convex closed set by tangent hyperplanes. Numerical estimation of the range of tolerances for the parameters of correcting elements is reduced to the problems of practical stability of discrete parametric systems. In this case, the region of the initial conditions on the state vector, the tolerances on the parameters, are given structurally in the form of an ellipsoid, which makes it possible to numerically solve the original problem as an extremal one. From the standpoint of practical stability in the corresponding space of functions, the problem of assessing the range of tolerances for the parameters of correcting elements in the presence of specified restrictions on the spread of the quality criterion is considered. Attention is focused on an important class of problems of numerical modelling of a linear induction acceleration system − problems of practical stability. Numerical estimation of the region of initial displacements of the transverse coordinates of the linear induction acceleration system in the given structures in the presence of linear constraints on the vector of phase coordinates in dynamics is carried out. Key words: modeling, induction system of acceleration, solenoid, parameters, elements of correction, optimization, stability

Real-time and on-line parallel detection of key fermentation process parameters by near-infrared spectroscopy in different environments

The fermentation process is dynamically changing, and the metabolic status can be grasped through real-time monitoring of environmental parameters. In this study, a real-time and on-line monitoring experiment platform for substrates and products detection was developed based on non-contact type near-infrared (NIR) spectroscopy technology. The prediction models for monitoring the fermentation process of lactic acid, sophorolipids and sodium gluconate were established based on partial least-squares regression and internal cross-validation methods. Through fermentation verification, the accuracy and precision of the NIR model for the complex fermentation environments, different rheological properties (uniform system and multi-phase inhomogeneous system) and different parameter types (substrate, product and nutrients) have good applicability, and R2 is greater than 0.90, exhibiting a good linear relationship. The root mean square error shows that the model has high credibility. This research provides a basis for the application of NIR spectroscopy in complex fermentation systems.

ELASTIC BENDING OF A THREE-LAYER CIRCULAR PLATE WITH STEP-VARIABLE THICKNESS

The bending of a three-layer elastic circular plate with step-variable thickness is considered. To describe kinematics of asymmetrical in thickness core pack, the broken line hypotheses are accepted. In thin bearing layers, Kirchhoff’s hypotheses are valid. In a relatively thick filler incompressible in thickness, Timoshenko’s hypothesis on the straightness and incompressibility of the deformed normal is fulfilled. The formulation of the corresponding boundary value problem is presented. Equilibrium equations are obtained by the variational Lagrange method. The solution of the boundary value problem is reduced to finding three required functions in each section, deflection, shear and radial displacement of the median plane of the filler. An inhomogeneous system of ordinary linear differential equations is obtained for these functions. The boundary conditions correspond to rigid pinching of the plate contour. A parametric analysis of the obtained solution is carried out.

NON-AXISYMMETRIC DEFORMATION OF A CIRCULAR THREE-LAYER PLATE IN ITS OWN PLANE

A statement is given for the boundary value problem of non-axisymmetric deformation of an elastic threelayer circular plate in its own plane. The plate contour is pinched. Physical equations of state in the plate layers are described using the linear theory of elasticity, taking into account temperature influence on the elastic characteristics of materials. Equilibrium equations are obtained by the Lagrange variational method. Boundary conditions on the plate contour are formulated. The solution of the boundary value problem is reduced to finding the radial and tangential displacements in the layers of the plate. These displacements satisfy an inhomogeneous system of ordinary linear differential equations. To solve it, the method of decomposition into trigonometric Fourier series is applied. After substituting the series into the original system of equilibrium equations and performing the corresponding transformations, a system of ordinary linear differential equations is obtained to determine the four radial functions in each term of the series. The analytical solution is written out in the final form in the case of cosine radial and sinusoidal circumferential loads that depend linearly on the radial coordinate. The load is applied in the middle plane of the filler. Numerical approbation of the solution is carried out. The dependence of radial and tangential displacements on polar coordinates and temperature is investigated. Graphs of changes in displacements along the radius of the plate for different values of the angular coordinate are given. The weak dependence of displacements on temperature is illustrated when the plate contour is fixed.

Thermodynamics of interfaces extended to nanoscales by introducing integral and differential surface tensions

As a system shrinks down in size, more and more molecules are found in its surface region, so surface contribution becomes a large or even a dominant part of its thermodynamic potentials. Surface tension is a venerable scientific concept; Gibbs defined it as the excess of grand potential of an inhomogeneous system with respect to its bulk value per interface area [J. W. Gibbs, “The Collected Works” in Thermodynamics (1928), Vol. 1]. The mechanical definition expresses it in terms of pressure tensor. So far, it has been believed the two definitions always give the same result. We show that the equivalence can break down for fluids confined in narrow pores. New concepts of integral and differential surface tensions, along with integral and differential adsorptions, need to be introduced for extending Gibbs thermodynamics of interfaces. We derived two generalized Gibbs adsorption equations. These concepts are indispensable for an adequate description of nanoscale systems. We also find a relation between integral surface tension and Derjaguin’s disjoining pressure. This lays down the basis for measuring integral and differential surface tensions from disjoining pressure by using an atomic force microscope.

Mathematical modeling of the process of ferrum removal in a biological reactor by bacteria Gallionella and Leptothrix

This paper proposes a mathematical model for computer prediction of the process of biological deironing of groundwater in a bioreactor, taking into account the presence of two types of iron bacteria Leptothrix and Gallionella in groundwater while maintaining a constant filtration rate. An algorithm for a numerical-analytical method for solving the corresponding nonlinear boundary value problem for an inhomogeneous system of differential equations in partial derivatives of the first order has been developed. The developed model allows to use computer experiments to predict the change in time on the depth of contact loading of cleaning efficiency, distribution of bacterial biomass values ​​in both filtered water and in filter loading, mass of stationary and mobile matrix structures. Also, the proposed model allows to predict the duration of effective operation of the biological reactor of iron deironing between its washing.

Precipitation and Growth Simulation of γ′ Phase in Single Crystal Superalloy DD6 with Multiphase-Field Method and Explicit Nucleation Algorithm

The microstructure evolution of Ni-based superalloys during heat treatment is of great significance for obtaining better service performance. However, heat treatment experimentation is costly and time-consuming, and sometimes fails to reveal physical mechanisms well. In the present study, a multiphase-field model coupled with an explicit nucleation algorithm was established to simulate the precipitation and growth of γ′ phase in DD6 superalloy, which can be applied to a multicomponent elastic-inhomogeneous system. The PanNickel© database was used to calculate thermodynamic and kinetic data in multicomponent superalloys. First, the coupling method of multiphase-field model and explicit nucleation algorithm was introduced. The coupled model was used to simulate the precipitation of γ′ phase under isothermal and non-isothermal conditions. It was found that a unimodal microstructure was formed under isothermal conditions and there was a “soft impingement” phenomenon, while a bimodal distribution composed of cuboidal γ′ precipitates and fine secondary γ′ precipitates was formed during a cooling process of 25–125 °C/min. The effect of cooling rate was studied. Then, the chemical and elastic driving forces were analyzed. It was found that Al and Ta contributed most to the chemical driving force, while Re and W gathered at the γ/γ′ interface and inhibited the growth of γ′ phase. γ′ precipitates had a cuboidal shape under the influence of elastic driving force. Finally, the growth and coarsening process of γ′ phase was studied and compared with the well-known Lifshitz−Slyosov−Wagner (LSW) theory. The growth of γ′ phase can be divided into rapid growth, coarsening and quasi-static coarsening stages according to the simulation results, among which the coarsening stage is basically consistent with the LSW theory. The current model can be used to simulate the precipitation and growth of single crystal superalloys where multicomponent and elastic effects are considered.