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The available experimental data on metal-body quenching in subcooled water indicate the presence of extremely intense cooling at the surface temperatures exceeding attainable limiting temperature of the liquid. At present, there is not only a theoretical description but also well-founded qualitative description of the mechanism that makes it possible to remove such heat fluxes in film boiling mode. In experiments on cooling in cryo-liquids, fluorocarbon, ethanol, and isopropanol, such a regime does not occur even at extremely high subcooling. Thus, it seems expedient to perform experiments on the cooling of high-temperature samples in a binary water–isopropanol mixture. For the first time, the boundary concentration of the isopropyl alcohol in the mixture with intensive cooling that occurs upon film boiling is determined.

Let Ω be a bounded domain in \begin{document}$\mathbb{R}^2 $\end{document} with smooth boundary, we study the following Neumann boundary value problem \begin{document}$\left\{ \begin{gathered} \begin{gathered} - \Delta \upsilon + \upsilon = 0\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\text{in}}\;\;\Omega {\text{,}} \hfill \\ \frac{{\partial \upsilon }}{{\partial \nu }} = {e^\upsilon } - s{\phi _1} - h\left( x \right)\;\;\;{\text{on}}\;\partial \Omega \hfill \\ \end{gathered} \end{gathered} \right.$ \end{document} where \begin{document} $ν$ \end{document} denotes the outer unit normal vector to \begin{document} $\partial \Omega$ \end{document} , \begin{document} $h∈ C^{0,α}(\partial \Omega)$ \end{document} , \begin{document} $s>0$ \end{document} is a large parameter and \begin{document} $\phi_1$ \end{document} is a positive first Steklov eigenfunction. We construct solutions of this problem which exhibit multiple boundary concentration behavior around maximum points of \begin{document} $\phi_1$ \end{document} on the boundary as \begin{document} $s\to+∞$ \end{document} .

This work investigates a nonlocal sinh–Gordon equation with a singularly perturbed parameter in a ball. Under the Robin boundary condition, the solution asymptotically forms a quite steep boundary layer in a thin annular region, and rapidly becomes a flat curve outside this region. Focusing more particularly on the structure of the thin annular layer in this region, the pointwise asymptotic expansion involving the domain-size is evaluated more sharply, where the domain-size exactly appears in the second term of the asymptotic expansion. It should be stressed that the standard argument of matching asymptotic expansions is limited because the model has a nonlocal coefficient depending on the unknown solution. A new approach relies on integrating ideas based on a Dirichlet-to-Neumann map in an asymptotic framework. The rigorous asymptotic expansions for the thin layer structure also matches well with the numerical results. Furthermore, various boundary concentration phenomena of the thin annular layer are precisely demonstrated.

In order to improve the atmospheric environment monitoring mechanism and realize the construction of environmental maps, this paper proposes a proximity factor concentration fusion method for the problem of sub-map fusion to the construction of multiple rotorcrafts maps. The method refines the neighboring sub-maps to coincide with the boundary concentration factor and calculates the concentration factor of the overlapping area based on the factor mean algorithm to obtain a complete gas concentration map. The fusion of two sub-concentration maps is taken as an example in this paper. The two sub-concentration maps with short time difference before and after are fused into a map, and then the feasibility of the fusion method is verified by Fluent and Matlab simulation experiments, which provides the research foundation for the fusion of multiple gas concentration maps.

This paper is motivated by a gauged Schrodinger equation in dimension 2 including the so-called Chern–Simons term. The radially symmetric case leads to an elliptic problem with a nonlocal defocusing term, in competition with a local focusing nonlinearity. In this work we pose the equations in a ball under homogeneous Dirichlet boundary conditions. By using singular perturbation arguments we prove existence of solutions for large values of the radius. Those solutions are located close to the boundary and the limit profile is given.

We present a reduced-boundary-function method for longitudinal solute transport in symmetric laminar flows. Flow is confined by two flat plates separated by a distance of 2a or by a tube with a radius of a (Figure 1). The standard advection-diffusion equation is mapped onto the boundary (r = a and r = 0, where r is the distance from the centerline shown in Figure 1). The original problem of solving c(x,r,t) is reduced to solve the solutions of c at the boundary, and the problem dimensionality is reduced from 3 to 2. Final results show that the boundary concentration ca(x,t) = c(x, r = a,t) is advected at the mean velocity with a dispersion equal to the molecular diffusion. The centerline concentration c0(x,t) = c(x,r = 0,t) is also advected at the mean velocity, but with a dispersion much larger than the Taylor dispersion. The cross-sectional average concentration is in agreement with the classical Taylor dispersion by neglecting higher order contributions. This study is relevant to the upscaling of solut...

Робота присвячена експериментальному дослідженню залежності електричного опору, коефіцієнту теплопровідності та пористості електропровідних композиційних матеріалів (ЕКМ) системи «кераміка-вуглець» від вмісту нанорозмірних вуглецевих наповнювачів та технологічних режимів виготовлення. Проаналізовано аналітичні залежності питомого електричного опору від деформованого стану ЕКМ у рамках теорії перколяції. Результати експериментальних досліджень показали, що зменшення дисперсності частинок електропровідної фази композиту (використання нанопластинок графіту замість термічно розширеного графіту) дозволяє значно зменшити гістерезис кривих залежності електричного опору від температури при нагріванні та охолодженні. Експериментально підтверджено вплив зміни об’єму діелектричної складової ЕКМ на електричний опір при зміні температури в межах 20–620 °C., The work is devoted of the experimental study the dependence of electrical resistance, the thermal conductivity coefficient and porosity of the electro conductive composite materials (ECM) system «ceramics-carbon» on the content of nanosized carbon fillers and technological regimes of manufacture. The analytical dependences of the specific electric resistance on the deformed state of the ECM in the percolation theory has been analyzed. The results The results of experimental studies have shown that the decrease of the dispersion of the particles of the conductive phase of the composite (usage of graphite nanoplates instead of thermally extended graphite) was able to significantly reduced the hysteresis of the curves of the resistance of the electric resistance to the temperature when heated and cooled. The influence of the change in the volume of the dielectric component of the ECM on the electrical resistance at a temperature change of 20-620 °C has been experimentally confirmed., Работа посвящена экспериментальному исследованию зависимости электрического сопротивления, коэффициента теплопроводности и пористости, электропроводящих композиционных материалов (ЭКМ) системы «керамика-углерод» от содержания наноразмерных углеродных наполнителей и технологических режимов изготовления. Проанализированы аналитические зависимости удельного электрического сопротивления от деформированного состояния ЭКМ в рамках теории перколяции. Результаты экспериментальных исследований показали, что уменьшение дисперсности частиц электропроводящей фазы композита (использование нанопластинок графита вместо термически расширенного графита) позволяет значительно уменьшить гистерезис кривых зависимости электрического сопротивления от температуры при нагревании и охлаждении. Экспериментально подтверждено влияние изменения объема диэлектрической составляющей ЭКМ на электрическое сопротивление при изменении температуры в пределах 20–620 °С.

Ozone pollution over the Pearl River Delta (PRD) in October 2004 has been simulated using the regional air quality models Models-3/CMAQ and CAMx. The results from both models were evaluated and compared with the observed concentrations from 12 monitoring stations. By integrated process rate analysis, the influences of different physical and chemical processes were quantified, and the causes of the deviations between the two models were investigated. Both CMAQ and CAMx reproduced the magnitudes and variations of ozone at most stations over the PRD. The correlation coefficients (R) between the simulated results and monitoring data were 0.73 for CMAQ and 0.74 for CAMx. The normalized mean bias (NMB) for CMAQ and CAMx over the 12 sites was − 8.5% and 8.8% on average, respectively. The normalized mean error (NME) for CMAQ and CAMx was 36.7% and 37.9%, respectively. The correlation between the results of two models was very high (R = 0.92), and their simulated ozone spatial distributions exhibited common features. But the values obtained using CMAQ simulation were about 17% lower than those obtained using CAMx on average. The results of simulations using the two models were not identical in certain regions, or for different types of monitoring stations. The differences in dry deposition, reaction parameters and vertical transport near the Pearl River Estuary can account for the discrepancies in the results obtained using the two models. In the upwind areas, the discrepancy in the boundary concentration of the finest nest was the main cause of the higher values obtained using CAMx compared with those obtained using CMAQ. There is a need for CAMx to provide more choices of dry deposition algorithms. Improvement of the calculation methods for photolysis rates would also improve the ozone simulation of CMAQ.

Depending on the contents of alloying elements (Nb, up to 5.4 at.%; W, up to 7.4 at.%; Re, up to 4.1 at.%; Mo, up to 9.5 at.%; V, up to 10.1 at.%; Mn, up to 22.1 at.%; Al, 12.0 at.%; and Cr, up to 22.0 at.%) texture, structure, and physical and mechanical properties are studied in thin tapes that serve as substrates for epitaxial deposition of a high-temperature superconductor on the nickel-based binary alloys. The upper limit of alloying element content is established at which sharp cube texture of primary recrystallization is feasible to be formed. It is shown that such boundary concentration of alloying elements is associated with a certain quantitative ratio between the deformation texture components and with a certain magnitude of the concentration expansion of lattice parameter. Some mechanical and physical properties of alloys with cube texture are determined.

We study the existence of steady states to the Keller–Segel system with linear chemotactical sensitivity function on a smooth bounded domain in \(\mathbb {R}^N,\)\(N\ge 3,\) having rotational symmetry. We find three different types of chemoattractant concentration which concentrate along suitable \((N-2)\)-dimensional minimal submanifolds of the boundary. The corresponding density of the cellular slime molds exhibit in the limit one or more Dirac measures supported on those boundary submanifolds.

We consider the boundary value problem { − Δ u + u = λ e u , in Ω ∂ ν u = 0 on ∂ Ω where Ω is a bounded smooth domain in R 2 , λ > 0 and ν is the inner normal derivative at ∂Ω. This problem is equivalent to the stationary Keller–Segel system from chemotaxis. We establish the existence of a solution u λ which exhibits a sharp boundary layer along the entire boundary ∂Ω as λ → 0 . These solutions have large mass in the sense that ∫ Ω λ e u λ ∼ | log ⁡ λ | .

The ductile-to-brittle transition temperature (DBTT) and hardness of an interstitial free steel solid-solution-strengthened by phosphorus are experimentally evaluated under different conditions. The results demonstrate a linear relationship between DBTT and hardness under constant phosphorus grain boundary concentration and grain size. The DBTT increases with increasing hardness, showing a hardening embrittlement effect. With reference to a previous study concerning the effect of phosphorus boundary segregation on the ductile-to-brittle transition for the same steel, which shows a non-hardening embrittlement effect, it is seen that the two embrittlement effects are independent of each other and that the combined embrittlement effect under an average grain size of ~ 70 μm can be expressed as DBTT (°C) = 0.24HV + 1.60CP − 34.8, where HV is the Vickers hardness value and CP is the phosphorus boundary concentration in at.%.

The embedded atom method (EAM) has been used to calculate boundary concentration distributions of Ni, Al, and B, and B probabilities in the "interstitial" and the "substitutional" sites, at the Ni3Al-x at.% B (100% Ni/100% Ni) [001]/Sigma5(210)/36.87degrees grain boundary at the equilibrium. It has been proposed by us that the bulk effects of B on the grain boundary include the main effect, that is, the B atoms induce Ni atoms to substitute into Al sites, and the sub-effect, that is, the B atoms substitute into Ni sites. In this work, it is found that at as x increases from 0.1 to 1.0, the B probability in the "interstitial" sites decreases from 97.3% to 38.8%, while that in the "substitutional" sites increases from 2.7% to 61.2%. It is also found that owing to combination of the main effect and the sub-effect, corresponding to B enrichment increasing, the Ni enrichment and the Al depletion become more and more obvious when x increases from 0.1 to 0.5. Then, corresponding to B enrichment decreasing, the Ni enrichment and the Al depletion also become more and more obvious when x decreases from 0.9 to 0.5. Thus, between low (x = 0.1) and high (x = 0.9) B bulk concentrations, there is a B bulk concentration (x = 0.5), at which the Ni enrichment and the Al depletion become the most obvious, and Ni is approximately saturated. (C) 2002 Elsevier Science B.V All rights reserved.

We introduce some mathematical problems which are closely related to the concentration and boundary layer phenomena in superconductivity and liquid crystals, in particular the problems on surface superconducting states and surface smectic states. The recent progresses on these problems are described, and some open questions are presented.

Several grain sizes were obtained by heat treatment at different temperatures for interstitial-free (IF) and 2.25Cr-1Mo steels. Samples of the steels with different grain sizes were aged at 600 and 680 °C for IF steel and 520 and 560 °C for 2.25Cr-1Mo steel for sufficient time to achieve their equilibrium grain boundary segregation. The grain boundary concentrations of phosphorus were examined using Auger electron spectroscopy. At the same aging temperature, the boundary segregation of phosphorus increased with increasing grain size. The effect of grain size on equilibrium grain boundary segregation thermodynamics was analyzed based on the information of both grain size and phosphorus boundary concentration. The segregation enthalpy increased with increasing grain size and simultaneously the segregation entropy became less negative. Moreover, the segregation entropy (∆S) and enthalpy (∆H) of phosphorus in both IF and 2.25Cr-1Mo steels exhibited a unified linear relationship, being expressed as ∆S = 0.85∆H − 38.06, although it segregated to different types of grain boundaries (ferrite grain boundaries in IF steel and prior austenite grain boundaries in 2.25Cr-1Mo steel). With the aid of the acquired thermodynamic parameters and grain boundary segregation theories, the equilibrium segregation concentrations at different aging temperatures were modeled under different grain sizes for both steels.

General relationships characterizing the arrangement of singular points with a zero index with respect to the boundary concentration space are reported.

Contaminant transformation rates are routinely estimated from monitoring well data using a regression method based on a steady-state analytical model. This approach assumes one-dimensional solute transport in the presence of a continuous boundary concentration and a uniform first-order degradation coefficient. It must be recognized that this type of analysis is easily subject to misinterpretation, particularly when few monitoring points are used. This is because the dispersive nature of solute transport can produce concentration profiles which closely resemble those associated with a degrading contaminant even in the absence of any transformation processes. Monte Carlo analyses using simulated plumes suggest that this method may lead to significant overestimates of apparent transformation rates.

Rapid thermal annealing was used for short-time diffusion experiments of gold in dislocation-free floating-zone silicon of {100} orientation at 1050 °C and 1119 °C. Concentration-depth profiles measured by the spreading-resistance technique are well described within the framework of the kick-out mechanism involving generation of silicon self-interstitials. More specifically, the gold-incorporation rate appears to be controlled by the outdiffusion of excess self-interstitials towards the surfaces. As a special feature, the measurements reveal a continuous increase of the gold boundary concentration which approaches the pertaining solubility limit only after prolonged annealing. This can be interpreted in terms of a limited effectiveness of gold-alloyed {100} silicon surfaces as sinks for self-interstitials. The validity of this interpretation is supported by computer modeling of the experimental data yielding finite values for the self-interstitial surface-annihilation velocity.

Minority carrier currents of technical interest are predominantly diffusion currents and are controlled by the boundary concentration of minority carriers that can be influenced by the bias across an adjacent space-charge region. These currents are in competition with recombination currents at device surfaces or interfaces.

If two solvents in which any number of substances are dissolved are brought into contact with one another, then the concentrations slowly balance out by diffusion so that in the equilibrium state each kind of molecule has a constant division ratio between the individual solvents independently of the presence of other categories of molecules and of whether the category of molecules under consideration chemically reacts with the others or not. Riesenfeld and Zermelo 1909 presents solutions to the then unanswered question as to how great the concentrations are that occur at the dividing surface and how they change during the process of diffusion.

Regional atmospheric models simulate their pertinent processes over a limited portion of the global atmosphere. This portion of the atmosphere can be a large fraction, as in the case of continental-scale modeling, or a small fraction, as in the case of urban-scale modeling. Regional modeling of any air pollutant requires that the meteorological and chemical conditions at the boundaries of the model domain be taken into account, especially if the pollutants are long-lived. It was once a common practice for the boundary concentrations of mercury and its reactants to be specified using time-constant values based on limited historical observation. These values were often invariant in the horizontal and vertical dimensions too. This relatively simple procedure for establishing boundary concentrations could be justified based on the previous notion that mer-cury was a rather inert and long-lasting air pollutant. However, with the subsequent discovery of rapid physical and chemical transformations of atmospheric mercury and significant concentra-tions of oxidized mercury far removed from known emission sources, the presumption of mer-cury as an inert substance has generally disappeared. The effect of intercontinental transport is now treated with greater concern in regional atmospheric mercury modeling. Global mercury models are now commonly used to define boundary values for regional mercury modeling. How-ever, the global and regional models must use consistent information for emissions, surface physiology and meteorology to achieve consistent simulation results and associated source-receptor relationships. There is certainly a need for international InstitutionalAuthorNameoration on field research and numerical model development to supply the tools needed for confident assessment of source-receptor relationships for mercury on both global and regional scales.

The problem of point defects diffusing anisotropically towards spheroidal sinks is solved using an analytical treatment. Depending on the ratios between the sink semi-axes (a0, b0) and the diffusivity main components (D⟂, Dz), two different situations are solved separately: the prolate and the oblate cases. For each case two boundary conditions are considered: a) periodic sink distribution and b) a constant boundary concentration condition. The results of this study allow to derive qualitative conclusions with respect to the influence of the diffusion anisotropy, the boundary conditions, and the cavity shape on the point defect concentration profiles around spheroidal sinks. In a coming paper these results are applied to study the diffusion of irradiation produced point defects towards cavities and to calculate defect bias and cavity sink strength. Mit einem analytischen Verfahren wird das Problem der Punktdefekte, die anisotrop zu spharoiden Senken diffundieren, gelost. In Abhangigkeit vom Verhaltnis zwischen den Senken-Halbachsen (a0, b0) und den Hauptkomponenten (D⟂, Dz) des Diffusionsvermogens, werden zwei unterschiedliche Situationen getrennt gelost: der gestreckte und der abgeplattete Fall. Fur jeden Fall werden zwei Grenzbedingungen betrachtet: a) eine periodische Senkenverteilung und b) eine konstante Konzentration der Grenzen. Die Ergebnisse dieser Untersuchung erlauben qualitative Schlusse bezuglich des Einflusses der Diffusionsanisotropie, der Grenzbedingungen und der Hohlraumform auf die Profile der Punktdefektkonzentration um spharoide Senken. In einer weiteren Arbeit werden diese Ergebnisse benutzt, um die Diffusion von strahlungsinduzierten Punktdefekten zu Hohlraumen zu untersuchen und Defektvorspannung und Hohlraumsenkenstarke zu berechnen.

The determination of grain-boundary diffusion coefficients of tracers in polycrystals has been carried out so far by a graphical method derived by Le Claire. It is based on an approximate solution of the exact solution of Suzuoka The product D GBδ is calculated from the slope of log c against y 6/5 (where c is the tracer concentration and y the penetration depth) for a known volume diffusion coefficient Dv. It is limited to intermediate times (time stage B) and to great penetration depths y. In cases where these conditions cannot be fulfilled the exact solution of Suzuoka has to be applied for evaluation of the profiles. This cannot be done in an easy way owing to the complex form of the Suzuoka solution. Therefore for these cases this work offers numerical evaluation of the diffusion profiles based on the exact Suzuoka solution. It allows determination of D GBδ and also of Dv for a known grain size.

Although in many studies of fast impurity diffusion interstitial-substitutional exchange involving vacancies is suggested, until recently only for Cu in Ge convincing experimental evidence for this so-called dissociative mechanism has been found. A main reason for this is the availability of (almost) dislocation-free Ge crystals, so that the Cu diffusion can be studied under conditions free of inner vacancy sources. In metals an appreciable density of dislocations is usually unavoidable. This difficulty can be overcome by analyzing the diffusion behaviour in a narrow region below the surface as will be shown for the two-stage penetration profiles observed after Co diffusion in Nb.

Perturbation methods are employed to analyze the horizontal absorption of moisture in unsaturated soils. The present study applies to absorption under the general diffusivity function, subject to constant boundary concentration. The concept of the wetting front moving with a finite velocity plays a fundamental role in this set of papers. The solution emerges as a series of terms that can be explicitly calculated in terms of the integrals involving diffusivity functions. The examples of exponential and constant diffusivity functions, as well as the case of Yolo light clay, are computed to one or two terms to exhibit the advantages over, and the good agreement with, other published data of Parlange, Philip, etc. The method possesses great potential, and in a subsequent paper the study of vertical infiltration will be presented by utilizing the perturbation mechanism.

The diffusion of sodium chloride, nitrite, and nitrate into beef, pork, and pork fat was studied by the porous disc technique. Total salt uptake and boundary concentration analyses were performed on beef. Various salt combinations and concentrations and various muscles were studied. Chloride diffusion was normal by all three methods of analysis, but skew boundaries and decreased uptake of nitrite were observed in the boundary measurements; diffusion rates of nitrite were constant in the porous disc method. Nitrite diffused slower than chloride in meat, but the rate of nitrate diffusion was sometimes greater than that of chloride. Comparison of the results of the steady state diffusion with the total uptake and boundary concentration showed the diffusion of nitrite to be governed by both physical and chemical factors.

An ecosystem model is used to calculate and summarize carbon budgets within the Ems Estuary, The Netherlands. The similarity between model calculations and field data is established using a validation procedure. Model results show that the seaward boundary concentration for suspended matter is important in determining whether an estuary is an importer or exporter of carbon. Lowered boundary concentrations of suspended matter enhance pelagic primary production, but reduce sedimentation and hence the carbon flux from pelagic to benthic systems.

The diffusion problems with moving boundary are formulated into a general integral form. Fundamental Green's function is used to derive a transcendental equation that gives readily the interface advancement, the concentration profile, and the boundary concentration of a growing sphere. Examples dealing with the diffusion-controlled spherical growth in finite and infinite regions are calculated and compared to the results available in the literature. Potential applications of this technique are briefly discussed.