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In this paper work, pattern formation in ultra thin polymer film, adsorbed on chemically patterned substrates, is reported under strong confinement. The observations indicate for the strong influence of the surface attraction over evolution of spindoal waves, leading to the flattening of the film. But, the film appears to be torn apart in strip or nano fiber like structures, because of coalescences of the monomers at the free ends of the chains. The beads at the free ends of the chain are relatively more mobile. The chain diffusion towards attractive part of the chemically patterned surfaces is clearly seen. Prewetting or crystallization like phenomena seems to appear resulting into formation of strips with coexistence of molten phase drops at the top of the ruptured film. The investigation mimics spindoal dewetting because of the fact that the rupturing occurs in case of strong attractive surface. The investigation is of technical importance as it highlights the formation of nano scale strips and fibers though in a quasi equilibrium case. [ABSTRACT FROM AUTHOR]

The paper shows the mechanism of formation of functional diffusion coatings deposited in the medium of low-melting liquid metal melts. The parameters of the mechanism depend on the nature of the interaction of the elements forming the coating with the elements of the coated steel. The paper describes the characteristic features inherent in the process of forming diffusion coatings on steels. The first feature is that the formation of coatings based on carbide-forming elements is characterized by intense diffusion of carbon from steel to the surface layers of the coating and blocking the diffusion of coating elements deep into the coated material. The second feature of the mechanism of formation of coatings based on carbide-forming elements is that the blocking effect of carbon depends on the amount of carbon in the steel, the thermal stability of the carbides of the coating elements, the temperature and duration of the process. The structure of the formed coating is characterized by the presence of an adsorbed layer, a carbide layer, a transition zone and a decarbonized zone. The paper presents a scheme for the formation of diffusion coatings based on carbide-forming elements. [ABSTRACT FROM AUTHOR]

In this paper, we consider a quite general class of advection reaction diffusion systems. As an example, a special case is discussed. [ABSTRACT FROM AUTHOR]

The paper is devoted to the investigation of the possibilities of intensification of fluid diffusion in the capillary-porous space under the influence of superimposed periodic pressure pulsations. The mathematical model of fluid motion in the capillary-porous space is considered in the paper, as well as the technique and experimental setup for determining the viscous and inertial coefficients of hydraulic resistance are described. The results of experimental and numerical studies are presented, which testify to the effectiveness of using modulated oscillations. [ABSTRACT FROM AUTHOR]

The Numerical analysis of heat treatments of TiCN coated AA7075 aluminium alloys is presented in this paper. The Convection-Diffusion-Reaction (CDR) equation with solutions in the Streamlined-Upward Petrov-Galerkin (SUPG) method for different parameters is provided for the understanding of the process. An experimental process to improve the surface properties of AA-7075 aluminium alloy was attempted through the coatings of TiCN and subsequent heat treatments. From the experimental process, optimized temperature and time was obtained which gave the maximum surface hardness and corrosion resistance. The paper gives an understanding and use of the CDR equation for application of the process. Expression to determine convection, diffusion and reaction parameters are provided which is used to obtain the overall expression of the heat treatment process. With the substitution of the optimized temperature and time, the governing equation may be obtained. Additionally, the total energy consumed during the heat treatment process is also developed to give a mathematical formulation of the energy consumed. [ABSTRACT FROM AUTHOR]

In 1990, Perona and Malik introduced diffusion model which is known as Perona and Malik (P-M) model to preserve the edge or boundaries. The edge indicator used as the variable exponent controls the diffusion mode as edge stopping between P-M diffusion and Gaussian smoothing depending on the image. The application of nonlinear second-order PDE model of P-M model is designed such that smooth areas diffused faster than the other areas and consequently may cause the presence of blocky effect. Hence, numerous modified diffusion functions have been developed to enhance image denoising results in order to overcome the loss of detail and blur in images. The objectives of this paper are to propose modified diffusion functions and compare with existing functions in order to provide alternative diffusion functions with edge and details preservation. Besides that, the modified functions were implemented on an image with different level of noise to made visual comparison with existing functions The proposed functions must be a positive function, monotonically decreasing and also convergent to zero. Results shows that the modified functions were converged rapidly as compared to the existing diffusion functions and able to remove different level of noise. In addition, the quality of image and their details are also preserved after the denoising process. [ABSTRACT FROM AUTHOR]

The paper presents the results of Large eddy simulation of a free swirling jet with Reynolds number Re = 104 for different swirl numbers. Rotating nozzle was chosen as the swirl configuration. The additional case that simulated the rotating tube with a honeycomb section using the dynamic mesh was chosen as the initial conditions generator. In the second part of the work with the simulation of the rotating nozzle, the mean instantaneous velocity and the passive scalar concentration were obtained. Simulations were carried out for six swirl numbers: 0, 0.15, 0.225, 0.3, 0.46, 0.63. It was observed that for the last swirl the passive scalar reverse transfer region formed on the jet axis, also what formed was the vortex breakdown phenomenon with a central recirculation zone formation. [ABSTRACT FROM AUTHOR]

In this paper, a diffusion Monte Carlo (DMC) method to determine the ground state of a particle in a double well potential is presented. The DMC method uses displacements, creations and deletions of diffusers or walkers. The effects of double well parameters on the ground state are studied. For validation of our DMC method, a harmonic oscillator potential is used and the DMC method gives accurate results. In the double well potential, the DMC results has shown that the ground state energy increases as the depth of the double well increases. [ABSTRACT FROM AUTHOR]

The mixing processes obey the laws of molecular and turbulent diffusion. It is obvious that the total duration of the kinetic combustion process (CP) is determined by a combination of thermal and chemical factors and obeys, with known limitations, the laws of chemical kinetics. Consideration of the basic laws of the diffusion processes and the establishment of ways to intensify or inhibit them makes it possible to purposefully influence the conditions of mixing gas with air. The brief information given in the paper about the features of the emission of gas flares is not intended to equip readers with methods for calculating heat transfer in the combustion chamber (CC) of gas diesel (GD), but only help to correctly understand and evaluate the factors that determine the radiation characteristics of the torch. It is shown that the intensity of turbulent diffusion is immeasurably higher than that of molecular diffusion, since the scale of turbulence is tens and hundreds of thousands of times greater than the path length of the molecule. The final mixing process in turbulent diffusion is molecular diffusion. The determining values of these processes are revealed. [ABSTRACT FROM AUTHOR]

In this research paper, we have study about the heat and mass transfer effects of rotation and porosity of the medium on unsteady convection flow of a viscous, incompressible, and electrically conducting flow past a started vertical plate under the influence of transversely applied uniform mass diffusion. The Laplace-transform technique is used to solve the governing equations in this investigation. The results are described using graphs for various factors such as the thermal Grashof number, the mass Grashof number, the Prandtl number, the permeability parameter, and the Schmidt number. The goal of this research is to look at the rotation and porosity of the medium in a flow model. The velocity in the boundary layer was found to be higher in the study. The non-dimensional equations are solved and programmed in MATLAB R2020. Finally, it can be shown that the speed increases when warm Grashof or mass value evaluations are made. The significance of the problem can be observed in the cooling of nuclear reactor electronic components. [ABSTRACT FROM AUTHOR]

We consider two species obeying nonlinear diffusion equations. Therein, the diffusion coefficient of a each species increases locally and nonlinearly with the density of the second species. This simple assumption originates demixing of the two species if the dependence on the second density becomes over critically strong. The demixing is characterized by sequences of separated regions with higher densities of one species compared to the second one. Since the model does not contain a nonlocal interaction no interface energy is created and the density profile jumps abruptly between large values at particular positions. In this manuscript, we describe numerically this stiff behavior. We propose a conservative discretization scheme in this paper, which earlier was also applied to Cahn-Hilliard and nonlinear Diffusion-Reaction equations. We modify the scheme with respect to the demixture model and find numerically stationary stable spatial distributions. Several aspects of the model and its treatment are discussed. [ABSTRACT FROM AUTHOR]

Diffusion equations in multicomponent environments, as parabolic evolutionary systems, have many physical and engineering applications; another their application was accentuated in 2020 due to the Covid19 infection. This short paper demonstrates the possibility of numerical analysis of direct and inverse problems of this type using some algorithms from computational heat, mass, etc. transfer, with special nonlinear terms originated in mathematical biology. One simple example sketches the benefits and hazards of such prediction for the MATLAB-based analysis of readily available Covid19 spread data from the Czech Republic. [ABSTRACT FROM AUTHOR]

This paper emphasizes the role of the stiffness ratio that characterizes differential problems modeling the diffusion of fake news. In particular, we propose the employ of the stiffness ratio in order to understand how fast is the transit of fake news in a given population, providing a numerical evidence supporting our approach, based on real data. [ABSTRACT FROM AUTHOR]

In this paper we investigate the influence of thermal oxidation during and after POCl3 diffusion. The main focus here is on the question of how far the presence of a thermally grown oxide layer has an influence on the emitter passivation. For this purpose, characterization methods such as electrochemical capacitance-voltage measurements and QSSPC are used. The novel finding of this paper is that in the case of a stack of passivation layers, the presence of the thermal oxide does not make a significant contribution to improved emitter passivation. [ABSTRACT FROM AUTHOR]

Reynolds number is the basic parameter determining the flow-field topology and its evolution in time unambiguously if only inertial, pressure and viscous effects are involved. However the Reynolds number definition is not unique and its physical meaning depends strongly on its actual definition. In the paper Reynolds number definition is given. Then, its role in typical situations in fluid dynamics is to be explained. The laminar flow, transition from laminar state to turbulence and fully turbulent flow are to be taken into account respectively. The physical meaning of Reynolds number vary accordingly. In conclusion the final statement is adopted, that the Reynolds number should be understood as a measure of convective and viscous effects in terms of length-, time- and/or velocity-scales presented in a given flow-field as a result of competing convection and diffusion effects. [ABSTRACT FROM AUTHOR]

This paper deals with the combined effect mass transfer and sorect effect for the oscillatory flow in the transverse attractive field and radiative warmth exchange to shaky stream of a directing optically dainty liquid through a channel recorded with immersed permeable medium and non-uniform dividers temperature. The thermal diffusion and mass transfer effects are added into the governing equations and the results are obtained through petribution technique. Various parameters like Grashof number, Modified Grashof number, Magnetic parameter, Radiation parameter, Peclet number, Darcy number, Heat source parameter, Chemical reaction parameter, Porous medium parameter, Schmidt number, Thermal diffusion parameter are all discussed, and results are analyzed by s graphs for velocity temperature and concentration profiles. The rate of skin friction and Nusselt number are also discussed. [ABSTRACT FROM AUTHOR]

The Ward-Tordai integral equation governs the diffusion-controlled surfactant adsorption at air/liquid interfaces. In this paper the Ward-Tordai equation is generalized in two directions. First, the adsorption is assumed to take place at a liquid/liquid interface, where the surfactant is soluble in both liquid phases. Second, the diffusion in the bulk phases is anomalous and is governed by time-fractional diffusion equations. For the computation of the change of adsorption with time two numerical techniques are proposed and compared. Numerical results are presented. [ABSTRACT FROM AUTHOR]

The diffusion equations with non-local boundary conditions arise in the mathematical modeling of many physical phenomena. In this paper, we present higher order diagonal Padé scheme for the numerical solution of two-dimensional diffusion equations subject to non-local boundary conditions. These numerical schemes based on (m, m)—Padé approximations to the matrix exponentials arising from the method of lines semi discretization approach. The numerical results for a model problem with known theoretical solutions are used to prove the accuracy of these schemes. [ABSTRACT FROM AUTHOR]

Fringe patterns produced by various optical interferometric techniques encode the information of deformation, refractive index, vibration, etc. Noise as one of the key problems affects further processing of the fringe patterns and reduces the final measurement quality. Coherence enhancing diffusion (CED) is a partial differential equation based denoising model that suppresses the noise as well as preserves the flow-like structure. Windowed Fourier transform-based windowed Fourier filtering (WFF) is another useful fringe pattern denoising tool that removes noise by thresholding the windowed Fourier transform spectrum. An adaptive windowed Fourier filtering (AWFF) that denoises the fringe pattern based on pixels' local frequencies is proposed in this paper. The performance of AWFF is compared with WFF and CED by applying them to fringe patterns that contain speckle noise and different levels of frequencies. Quantitative results will be given on simulated fringe patterns. Experimental fringe pattern will also be tested to illustrate the performance of these methods. [ABSTRACT FROM AUTHOR]

Generally, researching method of technology forecasting has been depended on intuition of expert until now. So there were many defects like consuming much time and money and so on. In this paper, we forecast diffusion of technology by using Bass model that is one of the quantitative analysis methods. We applied this model at technology market. And for input data of experiment, we use patent data that is representing each technology in technology market. We expect this research will be suggest new possibility that patent data can be applied in Bass model. [ABSTRACT FROM AUTHOR]

New product forecasting is a process that determines a reasonable estimate of sales attainable under a given set of conditions. There are several new products forecasting method in practices and Bass Diffusion Model (BDM) is one of the most common new product diffusion model used in many industries to forecast new product and technology. Hence, this paper proposed a combining BDM with Grey theory to forecast sales of new vehicle in Malaysia that certainly have limited data to build a model on. The aims of this paper is to examine the accuracy of different new product forecasting models and thus identify which is the best among the basic BDM and combining BDM with Grey theory. The results show that combining BDM with Grey theory performs better than the basic BDM based on in-sample and out-sample mean absolute percentage error (MAPE). Results also reveals combining model forecast more effectively and accurately even with insufficient previous data on the new vehicle in Malaysia. [ABSTRACT FROM AUTHOR]

The paper presents a coupled isothermal model at the initial stage of a solid surface treatment with particle beams. Mechanical stresses arising due to the interaction of particles with the surface affect the redistribution of the implanted impurity. Vacancies in the metal surface and their generation under stress are also taken into account. The kinetic law is formulated on the basis of thermodynamics of irreversible processes. The authors used numerical investigation methods. As a result' they have obtained the distributions of impurity concentration and deformations for various time moments. The authors also compare the concentration and deformation profiles with and without vacancies and study the influences of some model parameters. The effect of vacancy generation on the diffusion has been established to lead to an increase in the depth of penetration, as well as in the concentration of impurities. [ABSTRACT FROM AUTHOR]

Diffusion coefficients, D, of radionuclides in porous media are usually calculated as single values. The reason is that experimental concentration profiles are fitted with theoretical models in which D is constant. This approach could be rather inadequate. For example, potentially large discrepancies may arise when predicting radionuclides penetration through encasements in radioactive waste repositories at long timescales. In this paper we present an inverse approach based on the Bolztmann-Matano method to calculate the apparent diffusion coefficient of a sorbing radionuclide in saturated porous materials that is not constant but is a function of the radionuclide concentration. We apply our results to the diffusion of 133Ba2+ and 137Cs+ in two types of granite. [ABSTRACT FROM AUTHOR]

One of the problems in constructing mathematical models of turbulence is a description of the flows near a rough surface. An experimental study of such flows is also difficult because of the impossibility of measuring “inside” the roughness. The theoretical calculation is difficult because of the lack of equations describing the flow in this zone. In this paper, a new turbulence model based on the differential equation of turbulent viscosity balance was used to describe a turbulent flow near a rough surface. The difference between the new turbulence model and the previously known consists in the choice of constants and functions that determine the generation, dissipation and diffusion of viscosity. [ABSTRACT FROM AUTHOR]

Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented. [ABSTRACT FROM AUTHOR]

This paper is focused on a project valuation with embedded portfolio of real options including their interactions. Valuation is based on the criterion of Net Present Value on the simulation basis. Portfolio includes selected types of European-type real options: option to expand, contract, abandon and temporarily shut down and restart a project. Due to the fact, that in reality most of the managerial flexibility takes the form of portfolio of real options, selected types of options are valued not only individually, but also in combination. The paper is structured as follows: first, diffusion models for forecasting of output prices and variable costs are derived. Second, project value is estimated on the assumption, that no real options are present. Next, project value is calculated with the presence of selected European-type options; these options and their impact on project value are valued first in isolation and consequently in different combinations. Moreover, intrinsic value evolution of given real options with respect to the time of exercising is analysed. In the end, results are presented graphically; selected statistics and risk measures (Value at Risk, Expected Shortfall) of the NPV’s distributions are calculated and commented. [ABSTRACT FROM AUTHOR]

It is well known that the spiral wave solution of the reaction-diffusion equations is in the form of two qualitatively different classes of waves: rigidly rotating spirals or meandering spiral waves. The main objective of this paper is to study the stability of these waves. We develop an algorithm to deal with an operator dependent linearized system and to show that these waves are stable. This algorithm could be easily implemented. We also introduce a new approach for studying the dynamics change in the reaction diffusion system that obviates the need for tracing the path of spiral tip. Unlike tracing out the spiral tip which requires the intensive numerical procedures, our approach is easily implemented. [ABSTRACT FROM AUTHOR]

The paper proposes a two-dimensional conjugated model of a composite synthesis from pure metals with inert inclusions. The effective thermophysical properties of the model depend on the properties of the mixture components, the volumetric fraction of the inclusions and initial porosity. The chemical transformations are described by a lumped reaction "reagents–reaction products". The kinetic law considers the kinetic complications induced by severe deceleration of the reaction due to impeded diffusion through the layer of the product. The numerical study shows that the composite synthesis dynamics considerably depends on the presence of inert inclusions and initial porosity of the compact affecting its thermophysical properties. [ABSTRACT FROM AUTHOR]

Microstructure evolves during different processes; and phase transformation is one of these processes. The importance of phase transformation in the microstructure formation causes that many analytical and numerical methods are applied for its modeling. The objective of present paper is further development of 2D hybrid model of diffusional phase transformations. Heat transfer and diffusion during the transformation are considering. The model is based on Lattice Boltzmann Method (LBM) and cellular automata (CA). Diffusion and heat flow are modeled by LBM, whereas the microstructure evolution by CA. The paper presents the modeling results of the growth of new phase that is determined by the differences of carbon concentration in the phases and overheating/overcooling considering the enthalpy of transformation. Examples of simulation results are presented in the form of images, graphs and distributions. [ABSTRACT FROM AUTHOR]

This paper is a comparative study of classical spatial discretization schemes applied to an experimental case. Numerical simulations are performed according to large cell Péclet numbers. This should show the limitations of some schemes such as the upwind-difference scheme (numerical diffusion) or the central-difference scheme (overshoot and undershoot) for large cell Péclet number. However, in the case of the transport of tracer gas concentration in a ventilated enclosure, we show here that these kinds of schemes are a priori sufficient. [ABSTRACT FROM AUTHOR]

In this paper we consider singularly perturbed convection diffusion type equations with integral boundary condition. A numerical method based on Shishkin mesh on finite difference scheme is presented. The numerical method suggested is of almost first order convergent. An error analysis is derived in the discrete norm. Numerical results are presented, which validate the theoretical estimates. [ABSTRACT FROM AUTHOR]

The diffusion of a solute substance in creeping sinusoidal movement of an incompressible couple stress liquid through a pervious medium in an inclined duct with wall features is studied. The effective diffusion coefficient has been computed through long wavelength supposition and Taylor's condition for heterogeneous-homogeneous reactions. The objective of this paper is to measure the impact of perviousness, couple stress, wall feature constraints and angle of proclivity through graphs. [ABSTRACT FROM AUTHOR]

With exponential type, a class of alternating group finite difference scheme based on the saul’yev asymmetric schemes is derived for solving convection-diffusion equation in this paper. The scheme has the obvious property of Parallelism. The result of stability analysis shows that the scheme is unconditionally stable. In the end of the paper, numerical experiment is given, which illustrates the scheme presented is of high accuracy. [ABSTRACT FROM AUTHOR]

This paper addresses the lifetime prediction of polydicyclopentadiene submitted to thermal oxidation, using a multiscale approach. The chemical changes monitored by FTIR revealed the depletion in double bonds and the appearance of carbonyls. Such molecular changes result in the drop of mechanical properties. A kinetic model was implemented to predict the degradation rate depending on external conditions (temperature, oxygen concentration). This model can be completed to take into account the effect of antioxidants (delaying the thermal degradation) and the oxygen diffusion effects (heterogenous degradation) so as to get closer of real cases. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model of phase composition evolution in TiNi + Si and TiNi + Ta systems under pulsed electron beam action. In the second system, the coating contains a small amount of residual oxygen. In both systems, the kinetics, diffusion and chemical reactions were analyzed in two-dimensional problem formulation with distinguishing a trijunction of grains. Depending on the correlation of domains of the bulk of the grain and domain of the boundary effect, different regimes of titanium nickelide surface were distinguished. [ABSTRACT FROM AUTHOR]

In the real world, forecasts would always be based on historical data with the assumption that the behaviour be the same for the future. But how do we forecast when there is no such data available? New product or new technologies normally has limited amount of data available. Knowing that forecasting is valuable for decision making, this paper presents forecasting of new product or new technologies using aggregate diffusion models and modified Bass Model. A newly launched Proton car and its penetration was chosen to demonstrate the possibility of forecasting sales demand where there is limited or no data available . The model was developed to forecast diffusion of new vehicle or an innovation in the Malaysian society. It is to represent the level of spread on the new vehicle among a given set of the society in terms of a simple mathematical function that elapsed since the introduction of the new product. This model will forecast the car sales volume. A procedure of the proposed diffusion model was designed and the parameters were estimated. Results obtained by applying the proposed diffusion model and numerical calculation shows that the model is robust and effective for forecasting demand of the new vehicle. The results reveal that newly developed modified Bass diffusion of demand function has significantly contributed for forecasting the diffusion of new Proton car or new product. [ABSTRACT FROM AUTHOR]

The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic Jump-Diffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton Jump-Diffusion (MJD) model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the effectiveness of the Quarter-Sweep Alternating Group Explicit (QSAGE) iterative method by solving linear system generated from the discretization of one-dimensional fuzzy diffusion problems. In addition, the formulation and implementation of the proposed method are also presented. The results obtained are then compared with Full-Sweep Gauss-Seidel (FSGS), Full-Sweep AGE (FSAGE) and Half-Sweep AGE (HSAGE) to illustrate their feasibility. [ABSTRACT FROM AUTHOR]

This paper reports the optical properties of the optical planar waveguides in a soda lime glass fabricated by ion exchange. Planar waveguide fabrication was carried out by immersing the soda lime glass in molten 100% AgNO3 bath for different duration (ranging from 15 minutes to 735 minutes) and at temperature of 280°C. The results show that the surface refractive index values of the ion exchanged glasses are independent of both the ion exchange duration and temperature. The number of modes and the effective diffusion depth, however, increase with increasing the duration of ion exchange process. [ABSTRACT FROM AUTHOR]

Moisture in materials may affect its technical parameters greatly and plays significant role with close connection to durability and lifespan of building components. Moisture balance analysis and hygrothermal assessment of building components is needed to be provided during the building design stage. Recent trends in architecture integrate lightweight components with application of various foil vapor barriers to control moisture balance. While vapor barrier resistance is often decreased due to perforations in real-world application, the reliable evaluation of moisture transfer in building component is essential in thermal engineering application as well as in building science. This paper presents up to date overview of research focused on vapor diffusion through perforated materials that were conducted already in the past. While perforation of vapor barriers significantly reduces vapor resistance and air tightness corresponded to moisture balance of building element, the effect of vapor tightness decreasing is illustrated in case study based on particular wood frame wall. In this relation, a common engineering practice is compared with the complex numerical approach of heat and moisture transport on a model case with different vapor barrier permeability to identify the overall hygrothermal efficient parameters. Presented results show the importance of real vapor resistance of barriers aiming to point out the knowledge gap in the field of building civil engineering. [ABSTRACT FROM AUTHOR]

In this paper we present a novel splitting approach to solve scale-dependent Schrödinger equations, which are applied in quantum mechanical models. The energy potential is based on highly oscillating functions and we obtain a multiscale problem. We apply a multiscale solver, which is based on an operator splitting method and decouples the diffusion and reaction part of the Schödinger equation. We apply a large time step for the implicit time-discretization of the diffusion part and small time steps for the explicit time-discretization of the reaction part. With an extrapolation step, we can reduce the computational time in the highly-oscillating time-scale. We present the numerical analysis of the extrapolated operator splitting method. First numerical experiments indicate the benefit of the extrapolated splitting approaches. [ABSTRACT FROM AUTHOR]

The paper studies the effect of laser beam position in the laser welding of AISI 321 steel sheets and the Grade2 titanium alloy with a copper insert. Two position versions are considered: (1) the laser beam is positioned directly on the copper insert; (2) the laser beam is shifted into the steel. It has been found that the structure and chemical contents of the weld materials are different. When the laser beam is located on the copper plate, the steel and titanium alloy layers melt together with the copper plate, with convective mixing in the weld pool. It is demonstrated that the (Fe, Сr)2Ti and Cu4Ti intermetallics forming in the weld harden the weld material and ensure the strength of the joint at the level 325–420 MPa. When the laser beam is shifted into the steel the weld material consists from two solid solutions—one is copper-based and the other is iron-based; intermetallic compounds are not detected. The strength of such a joint proves to be low— 2.2 MPa, with the fracture occurring by the cleavage mechanism along the titanium alloy in the zone containing about 30 wt. % of copper. [ABSTRACT FROM AUTHOR]

In this paper the impurity distribution is computed in an axis-symmetric (2D) domain, which represents the meniscus and a part of the capillary channel. The model takes into account the pulling rate, thermal convection, molecular diffusion and thermo diffusion. Numerical illustration is given for Al doped cylindrical Si tube wall and the contribution of each effect is evaluated. The main novelties consist in the fact that the axis-symmetric (2D) domain is obtained by a prior computation using the Young-Laplace capillary surface equation and the heat transport equation as well in the inclusion of the thermo diffusion effect in the impurity distribution equation, respectively. [ABSTRACT FROM AUTHOR]

It is well-known that the addition of a small amount of diffusion of some material property (stress, rate of strain, structure factor, etc.) can regularise a constitutive equation which permits shear-banding. Typically, in the absence of diffusion, these models are ill-posed and permit steady banded states of a sort not observed in experiment, with many sharp-edged, closely-spaced bands. In an earlier paper [1] we looked at the two-dimensional linear stability properties of banded planar shear flow for two possible diffusive modifications to the Johnson-Segalman model. We were able to show that, for perturbations whose wavelength is not as short as the diffusion lengthscale, the diffusive stability calculation is a regular perturbation to the equivalent calculation for a non-diffusive fluid with a material interface between shear-bands. In this paper we show another, similar result using the same kind of analysis: this time for a phase-separating binary blend. We believe that in general, for the purposes of the linear stability properties, the effects of weak diffusion can be neglected and the stability or otherwise of any diffuse interface can be assessed using the simpler diffusionless model. The extensive literature on coextrusion instabilities is therefore relevant to the mechanisms for breakdown and fluctuation of banded systems, phase-separating systems and, indeed, any physical system containing interface-like regions in the presence of weak diffusion. [ABSTRACT FROM AUTHOR]

The paper studies a distribution of migrants coming to Europe within present refugee crisis. It employs the method of simulation, precisely, the phenomenological theory of diffusion and gravity model employed in urban geography. After 2011 the movement of migrants was affected by building fences, negotiations of readmission agreements, instability in Libya, etc. Therefore we employ statistical data from the previous period. The diffusion of people was studied as one-dimensional transport at the solid surface without activation energy. Solutions of 2nd Fick's law applied in semiconductor technology were adapted to show that in the future, especially due to climate change, the immigration to Europe may follow diffusion from a constant (infinite) source and it may overflow the continent. The diffusion coefficient characterizing the movement of people [km²/day] is been introduced. Simplified gravity model approach was used to find which factors, like gross domestic product, population of the country and their variations and combinations attract the migrants. A better quantification of migration phenomena in the future would need more reliable statistical data in much higher quantity. [ABSTRACT FROM AUTHOR]

Anomalous diffusion can be roughly characterized by the property that the diffusive particles do not follow the Gaussian statistics. When the mean squared displacement of the particles behaves in time like a power function, time- and/or space-fractional derivatives were shown to be useful in modeling of such diffusion processes. In this paper, a special class of anomalous diffusion processes, the so called neutral-fractional diffusion, is considered. The starting point is a stochastic formulation of the model in terms of the continuous time random walk processes. The neutralfractional diffusion equation in form of a partial differential equation with the fractional derivatives of the same order both in time and in space is then derived from the master equation for a special choice of the probability density functions. An explicit form of the fundamental solution of the Cauchy problem for the neutral-fractional diffusion equation is presented. Its properties are studied and illustrated by plots. [ABSTRACT FROM AUTHOR]

The plasma nitriding process produces a hard near-surface thin layer of the nitrided material. The thickness of the diffused layer, produced in the course of this process, is between 0.001 and 0.6 mm. The paper presents a diffusion model of plasma nitriding that allows one to predict the material hardness distribution within the near-surface layer as a function of time for a modified nitrogen diffusion coefficient. The temperature dependence of the diffusion coefficient are considered in the paper. Hence, the model involves the reaction rates of nitrides formation. The one-dimensional transient diffusion model is then applied to a thin nitride layer. The solution thus obtained is compared with experimental data for a decrease of hardness as a function of depth and time, until the core hardness is reached. [ABSTRACT FROM AUTHOR]

Ion Implantation performed at very low substrate temperatures has a very different damage generation and accumulation behavior compared to that for implants at room temperature (RT). Millisecond anneals have a very different activation and damage elimination signature compared to conventional soak or spike anneals. This paper investigates the combination of cold implants and flash millisecond anneals and explores any advantages of such combination. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze the convection and diffusion of a solute in a porous medium, under the influence of non-smooth chemical reactions taking place on the pore surfaces. Our model consists of a system of two coupled convection-diffusion equations, one in the fluid part and another one on the boundaries of the grains of the porous medium. The coupling is made through a nonlinear reaction term, modeling the mass exchange between the bulk and, respectively, the surface concentration. [ABSTRACT FROM AUTHOR]

The University of Maryland (UMD) Biology Education and Physics Education Research Groups are investigating students' views on the role of physics in introductory biology courses. This paper presents data from an introductory course that addresses the fundamental principles of organismal biology and that incorporates several topics directly related to physics, including thermodynamics, diffusion, and fluid flow. We examine how the instructors use mathematics and physics in this introductory biology course and look at two students' responses to this use. Our preliminary observations are intended to start a discussion about the epistemological issues resulting from the integration of the science disciplines and to motivate the need for further research. [ABSTRACT FROM AUTHOR]