Pattern formation in diffusion-limited reactions

The conditions for macroscopic segregation ofA andB in a steady-stateA+B 0 reaction are studied in infinite systems. Segregation occurs in one and two dimensions and is marginal ford=3. We note the dependence of these results on the precise experimental conditions assumed in the theory. We also note the difference between these results and our earlier ones for finite systems where the critical dimension isd=2.     

Quantitative study on selective stacking of zwitterions in large-volume sample matrix by moving reaction boundary in capillary electrophoresis

The paper advanced the theoretical procedures for quantitative design on selective stacking of zwitterions in full capillary sample matrix by a cathodic-direction moving reaction boundary (MRB) in capillary electrophoresis (CE) under control of electroosmotic flow (EOF). With the procedures, we conducted the theoretical computations on the selective stacking of two test analytes of L-histidine (His) and L-tryptophan (Trp) by the MRB created with 30 mM pH 3.0 formic acid-NaOH buffer and 2-80 mM sodium formate. The results revealed the following three predictions. At first, the MRB cannot stack His and Trp plugs if less than 12.5 mM sodium formate is used to form the MRB and prepare the sample matrix. Second, the MRB can stack His and/or Trp sample plugs completely if higher than 50 mM sodium formate is chosen to form the MRB. Third, the MRB can only focus His plug completely, but stack Trp plug partially if 20-50 mM sodium formate is used; this implied the complete MRB-induced selective stacking to His rather than Trp. All the three predictions were quantitatively proved by the experiments. With great dilution of sample matrix and control of EOF, controllable, simultaneous and MRB-induced selective stacking and separation of zwitterions were achieved. The theoretical results hold evident significances to the quantitative design of selective stacking conditions and the increase of detection sensitivity of zwitterions in CE. In addition, the control of EOF by cetyltrimethylammonium bromide (CTAB) can evidently improve the stacking efficiency to both His and Trp.     

二组分混合物的最小流化特性 Ⅰ.混合/分离状态与最小流化空隙率

分析了二组分混合物的３种混合／分离状态及在完全混合时发生连续相转变的极限组成。提出一个判别非等密度体系混合／分离状态的法则与确定混合物空隙率简易可行的随意松散堆积方法。     

Segregation in zirconia: equilibrium versus non‐equilibrium segregation

The present work considers the differences between the following two phenomena: equilibrium segregation, which is a thermodynamic phenomenon where the driving force is excess interfacial energy; and non‐equilibrium segregation, which can be produced by phenomenological shocks applied to the solid surface. Fully stabilized cubic yttria‐stabilized zirconia (YSZ) is used as the exemplar for these considerations. Equilibrium segregation in YSZ results in enrichment of the surface and near‐surface layers in constituent elements, typically yttria and impurities. This segregation is an intrinsic material property and has an impact on the performance of zirconia at elevated temperatures. On the other hand, non‐equilibrium segregation leads to a complex distribution of properties (structure and concentration gradients) that are determined by the experimental procedures used rather than being a material property. However, such non‐equilibrium segregation can result in localized structural changes. The present paper also considers the effect of the gas phase on surface properties of metal oxides, including YSZ, and the surface dynamics of YSZ at temperatures below that required to reach equilibrium. Copyright © 2005 John Wiley & Sons, Ltd.     

On a double degenerate fourth-order parabolic equation

The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit.     

On Two-point Boundary Value Problems for Second-order Difference Equation

In this paper, we aim to investigate the difference equation \begin{align*} \Delta^{2}y(t-1)+|y(t)|=0, \ \ \ \ \ t\in[1,T]_{\mathbb{Z}} \end{align*} with different boundary conditions $y(0)=0$ or $\Delta y(0)=0$ and $y(T+1)=B$ or $\Delta y(T)=B$,\ where\ $T\geq 1$ is an integer and $B\in\mathbb{R}$. We will show that how the values of $T$ and $B$ influence the existence and uniqueness of the solutions to the about problem. In details, for the different problems, the $TB$-plane explicitly divided into different parts according to the number of the solutions to the above problems. These parts of $TB$-plane for the value of $T$ and $B$ guarantee the uniqueness, the existence and the nonexistence of solutions respectively.     

Interfacial segregation in Ag-Au,Au-Pd,and Cu-Ni alloys: I. (100) surfaces

Atomistic simulations of segregation to (100) free surface in Ag–Au, Au–Pd, and Cu–Ni alloy systems have been performed for a wide range of temperatures and compositions within the solid solution region of these alloy phase diagrams. In addition to the surface segregation profiles, surface free energies, enthalpies, and entropies were determined. These simulations were performed within the framework of the free energy simulation method, in which an approximate free energy functional is minimized with respect to atomic coordinates and atomic site occupation. The effects of the relaxation with respect to either the atomic positions or the atomic concentrations are discussed. For all alloy bulk compositions (0.05 C 0.95) and temperatures (400 T(K) 1,100) examined, Ag, Au, and Cu segregates to the surface in the Ag–Au, Au–Pd, and Cu–Ni alloy systems, respectively. The present results are compared with several theories for segregation. The resultant segregation profiles in Au–Pd and Ag–Au alloys are shown to be in good agreement with an empirical segregation theory, while in Cu–Ni alloys the disagreement in Ni-rich alloys is substantial. The width of the segregation profile is limited to approximately three to four atomic planes. The surface thermodynamic properties depend sensitively on the magnitude of the surface segregation, and some of them are shown to vary linearly with the magnitude of the surface segregation.     

Grain boundary segregation diagrams of α-iron

Based on thermodynamic analysis of interfacial segregation, the segregation enthalpy H ^o of a solute I in a given matrix was found to depend linearly on two mutually independent terms reflecting the type of interface and the solid solubility limit X _infI ^sup* at temperature T and can be written as In this equation, the structural dependence of interfacial segregation is contained in H ^*() which corresponds to the extrapolated segregation enthalpy of a solute with unlimited solubility in the matrix. The product [Tln(X _infI ^sup* )] is essentially constant with temperature, and can therefore be obtained from data for maximum solid solubility, [Tln(X _infI ^sup* )]_max. The parameter v>0 represents the relationship between the activity a _infI ^sup* of a solute at the bulk solid solubility limit in a given matrix and X _infI ^sup* , a _infI ^sup* =(X _infI ^sup* ) ^v , and is characteristic for the matrix. Using recent experimental data for silicon, phosphorus, and carbon segregation at well-characterized grain boundaries in oriented bicrystals of -iron, the averaged value was determined. Values of H ^*() range from -8 kJ/mol (general grain boundaries) up to +8 kJ/mol (special grain boundaries). These values are discussed and used for a more precise and generalized construction of grain boundary segregation diagrams of -iron.     

Bond-length fluctuations in transition-metal oxoperovskites

Bond-length fluctuations in transition-metal oxoperovskites may give rise to two-phase fluctuations in what appears to be a single phase to a diffraction experiment. Orbital disorder at Jahn-Teller ions results in bond-length fluctuations that give 3D-ferromagnetic, vibronic Mn(III)-O-Mn(III) superexchange interactions and allow disproportionation into Mn(IV) and Mn(II) in LaMnO₃; where orbitally ordered and disordered phases coexist, an external magnetic field stabilizes the orbitally disordered, ferromagnetic phase relative to the orbitally ordered, antiferromagnetic phase. Spin-lattice interactions in the paramagnetic phase of charge-transfer compounds give bond-length fluctuations arising from the semicovalent component of the superexchange interactions. At the crossover from localized to itinerant electronic behavior, the coexistence of two-phase fluctuations has been demonstrated in both the single-valent RNiO₃ family (R=rare-earth, A=alkaline-earth) and the mixed-valent R_0.5A_0.5MnO₃ perovskites. “Bad-metal” behavior is found to be associated with bond-length fluctuations.     

Binary alloys as a model for the multicultural society

The model of regular solutions, that may be applied to binary alloys (e.g. Au?Pt, Si?Ge) has been compared to binary societies: blacks—non-blacks in the US, catholics—non-catholics, foreigners—German citizen. The excellent agreement of phase diagrams and intermarriage data encourages a calculation of the multicultural society by functions of thermodynamics: Solubility corresponds to integration, miscibility gap to segregation, free enthalpy to happiness and temperature to tolerance of a society. Only a high level of tolerance will integrate ghettos and lead to a peaceful multicultural society.