COMBINED EXTRUSION OF GLASSES WITH A CONICAL BOTTOM. KINEMATIC AND STRESS STATES OF THE PLASTIC REGION IN CONTACT WITH THE CONICAL SURFACE OF THE MATRIX

For the extrusion of glasses with a conical bottom using the method of plastic flow by A. L. Vorontsov, the kinematic and stress states of the extruded metal in the area of the plastic deformation zone in contact with the conical surface of the matrix were determined. The results are combined with the results obtained earlier for the cylindrical region located under the forming glass wall. The resulting formulas will be used to determine the stress state in the areas of the focus located under the end of the punch. The derived formula for the maximum pressure on the matrix wall is necessary for calculating the matrix strength and making an informed decision about the need for its banding.

Correction of thermographic images based on the minimization method of Tikhonov functional

The paper considers the method of correction of thermographic images (thermograms) obtained by recording in the infrared range of radiation from the surface of the object under study using a thermal imager. A thermogram with a certain degree of reliability transmits an image of the heat-generating structure inside the body. In this paper, the mathematical correction of images on a thermogram is performed based on an analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study towards the heat sources. The continuation is carried out by solving an ill-posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. To construct a stable solution to the problem, the principle of the minimum of the Tikhonov smoothing functional we used.

CONTRIBUTION OF THERMAL-HYDRAULICS SIMULATION TO CRITICALITY ANALYSIS OF A DEBRIS BED NUMERICAL MOCK-UP

In this work, we evaluate the impact of simulating the thermal-hydraulics feedback in criticality risk assessment in a benchmark configuration corresponding to a simplified debris bed. We have recently discussed the coupling of the multi-phase thermal-hydraulics code MC3D with a reactivity evaluation scheme based on multi-point kinetics, which paves the way towards the assessment of the system behavior in terms of energy release. In this work, we analyze the system reactivity as a function of the thermal-hydraulics state of the system. For our investigation, we have considered a simplified cylindrical region and assumed that the fuel particles in the mixture consist of spheres of small diameter. The power has been adjusted to be representative of nuclear decay heat. For most of the examined configurations, the maximum reactivity lies below zero, which shows that the occurrence of a criticality event is likely to be excluded, thanks to the contribution of the decay heat of the fuel.

IXED PROBLEM FOR THREE-DIMENSIONAL HYPERBOLIC EQUATIONS WITH DEGENERATION OF TYPE AND ORDER

It is known that in space during mathematical modeling of electromagnetic fields in space, the nature of the electromagnetic process is determined by the properties of the medium. If the medium is non-conductive, then we get degenerating multidimensional hyperbolic equations. Therefore, the analysis of electromagnetic fields in complex environments (for example, if the conductivity of the medium changes) is reduced to degenerating multidimensional hyperbolic equations. It is also known that oscillations of elastic membranes in space according to the Hamilton principle can be modeled by degenerating multidimensional hyperbolic equations. Therefore, by studying mathematical modeling of the process of heat propagation in oscillating elastic membranes, we also come to degenerating multidimensional hyperbolic equations. When studying these applications, it becomes necessary to obtain a clear representation of the solutions to the investigated problems. The mixed problem for degenerating multidimensional hyperbolic equations in generalized spaces is well researched. This task is also studied in the works of S. A. Aldashev, where it is shown that its correctness significantly depends on the height of the cylindrical region under consideration. A.V. Bitsadze drew attention to the importance of studies of multidimensional hyperbolic equations with degeneration of type and order. Mixed problems for these equations have not previously been studied. In this work, the solvability of a mixed problem is shown and a clear form of a classical solution for three-dimensional hyperbolic equations with degeneration of type and order is obtained.

The Relationship Between Wormlike Micelle Scission Free Energy and Micellar Composition: The Case of Sodium Laurylethersulphate and Cocamidopropyl Betaine

The scission energy is the difference in energy between two hemispherical caps and the cylindrical region of a wormlike micelle. This energy difference is exponentially proportional to the average micelle length, which affects several macroscopic properties such as the viscosity of viscoelastic fluids. Here we use a recently published method by Wang et al (Langmuir 2018 34 1564-1573) to directly calculate the scission energy of micelles composed of monodisperse Sodium Laurylethersulphate (SLESnEO), an anionic surfactant. We perform a systematic study varying the number of ethoxyl groups (n) and salt concentration. The scission energy increases with increasing salt concentration, indicating that the formation of longer micelles is favoured. We attribute this to the increased charge screening that reduces the repulsion between head groups. However, the scission energy decreases with increasing number of ethoxyl groups as the flexibility of the head group increases and the sodium ion becomes less tightly bound to the head group. We then extend to look at the effect of a common co-surfactant, Cocamidopropyl Betaine (CAPB) and find that its addition increases the scission energy, stabilising wormlike micelles at a lower salt concentration.

The Relationship Between Wormlike Micelle Scission Free Energy and Micellar Composition: The Case of Sodium Laurylethersulphate and Cocamidopropyl Betaine

The scission energy is the difference in energy between two hemispherical caps and the cylindrical region of a wormlike micelle. This energy difference determines the logarithm of the average micelle length, which affects several macroscopic properties such as the viscosity of viscoelastic <br>fluids. Here we use a recently published method by Wang et al (Langmuir 2018 34 1564-1573) to directly calculate the scission energy of micelles composed of monodisperse Sodium Laurylethersulphate (SLESnEO), an anionic surfactant. We perform a systematic study varying the number of ethoxyl groups (n) and salt concentration. The scission energy increases with increasing salt concentration, indicating that the formation of longer micelles is favoured. We attribute this to the increased charge screening that reduces the repulsion between head groups. However, the scission energy decreases with increasing number of ethoxyl groups as the flexibility of the head group increases and the sodium ion becomes less tightly bound to the head group. We then extend the analysis to look at the effect of a common co-surfactant, Cocamidopropyl Betaine (CAPB) and find that its addition increases the scission energy, stabilising wormlike micelles at a lower salt concentration.

On a stable approximate solution of an ill-posedboundary value problem for the metaharmonic equation

In this paper, we consider a mixed problem for a metaharmonic equation in aregion in a rectangular cylinder. On the side faces cylinder region is set to homogeneousconditions of the first kind. The cylindrical area is bounded on one side by an arbitrarysurface on which the Cauchy conditions are set, i. e. the function and its normal derivativeare set. The other boundary of the cylindrical region, which is flat, is free. This problem is illposed,and to construct its approximate solution in the case of Cauchy data known with someerror, it is necessary to use regularizing algorithms. In this paper, the problem is reducedto the Fredholm integral equation of the first kind. Based on the solution of the integralequation, an explicit representation of the exact solution of the problem is obtained. A stablesolution of the integral equation is obtained by the method of Tikhonov regularization. Theextremal of the Tikhonov functional is considered as an approximate solution. Based on thissolution, an approximate solution of the problem as a whole is constructed. The convergencetheorem of the approximate solution of the problem to the exact one is given when the errorin the Cauchy data tends to zero and when the regularization parameter is agreed with theerror in the data. The results can be used for mathematical processing of thermal imagingdata in medical diagnostics.

Моделирование распределения дисперсной фазы при течении в цилиндрической области методами вычислительной гидродинамики

The influence of the diameter of a cylindrical region filled with water on the structure of a bubble polydisperse flow is analyzed. Numerical simulation of the flow is based on a mathematical model that uses the Euler-Euler approach to the description of multiphase media, and includes the heterogeneous MUSIG model for the description of polydispersity, the k-ω-SST turbulence model, and interfacial momentum transfer. The bubble distributions in the sections near the sparger and near the free surface are obtained. The regimes of the bubble flow with full and partial filling of the region are identified and the transition criterion is determined.