The 2nd Sino-German Workshop on computational and applied mathematics took place in Hangzhou, China, from October 9-13, 2007. The long list of senior Chinese numerical analysts who had spent a year or more somewhere i...
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The 2nd Sino-German Workshop on computational and applied mathematics took place in Hangzhou, China, from October 9-13, 2007. The long list of senior Chinese numerical analysts who had spent a year or more somewhere in Germany as Humboldt fellows had led to the first Sino-German Workshop in Berlin held at the Humboldt-Universitat zu Berlin in 2005. The particular purpose of the second German-Chinese Workshop on computational and applied mathematics was to attract more junior Chinese scientists to the actual research activities in Germany. A summer school in Beijing on adaptive finite element methods with Carsten Carstensen and Roll Rannacher piror to the Hangzhou workshop underlined this activity to foster the collaboration of the new generations in the fields of computational and applied mathematics. This special issue reflects the present topics therein in both countries and can be summarised under five headings （i）-（v）.
A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz ...
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A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented,where the cold component models both compression and expansion states,the thermal ion component introduces the Debye approximation and melting entropy,and the thermal electron component employs the Thomas-Fermi-Kirzhnits(TFK)*** porosity of materials is considered by introducing the dynamic porosity coefficientαand the constitutive P-αrelation,connecting the thermodynamic properties between dense and porous systems,allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense *** models enable the EOS applicable and robust at wide ranges of temperature,pressure and porosity.A systematic evaluation of the new EOS is conducted with aluminum(Al)as an example.300 K isotherm,shock Hugoniot,as well as melting curves of both dense and porous Al are calculated,which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of ***,it is for the first time Hugoniot P-σcurves up to 10~6 GPa and shock melting behaviors of porous Al are derived from analytical EOS models,which predict much lower compression limit and shock melting temperatures than those of dense Al.
We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg *** the conditions of slight density and temperature...
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We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg *** the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently ***,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.
We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum vc. The width of t...
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In this paper, we study the global existence and low Mach number limit of strong solutions to the2-D full compressible Navier-Stokes equations around the Couette flow in a horizontally periodic layer with non-slip and...
In this paper, we study the global existence and low Mach number limit of strong solutions to the2-D full compressible Navier-Stokes equations around the Couette flow in a horizontally periodic layer with non-slip and isothermal boundary conditions. It is shown that the Couette flow is asymptotically stable for sufficiently small initial perturbations, provided that the Reynolds number, Mach number and temperature difference between the top and the lower walls are small. For the case where both the top and the lower walls maintain the same temperature, we further prove that such global strong solutions converge to a steady solution of the incompressible Navier-Stokes equations as the Mach number goes to zero.
We devise fast and provably accurate algorithms to transform between an N × N × N Cartesian voxel representation of a three-dimensional function and its expansion into the ball harmonics, that is, the eigenb...
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We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck(PNP)equations,which are a nonlinear coupled system widely used in semiconductors and ion *** p...
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We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck(PNP)equations,which are a nonlinear coupled system widely used in semiconductors and ion *** presenting the semi-discrete scheme,the optimal H1 norm error estimates are presented for the time-dependent PNP equations,which are based on some error estimates of a virtual element energy *** Gummel iteration is used to decouple and linearize the PNP equations and the error analysis is also given for the iteration of fully discrete virtual element *** numerical experiment on different polygonal meshes verifies the theoretical convergence results and shows the efficiency of the virtual element method.
The unique three-dimensional orthorhombic NbS(o-NbS)compound synthesized in 1969 has recently been experimentally confirmed to be a superconductor[***.B 108174517(2023)].However,there is currently no theoretical resea...
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The unique three-dimensional orthorhombic NbS(o-NbS)compound synthesized in 1969 has recently been experimentally confirmed to be a superconductor[***.B 108174517(2023)].However,there is currently no theoretical research on its superconducting *** this work,we investigate the superconducting properties of o-Nb S from first-principles *** on the Eliashberg equation,it is found that the superconductivity mainly originates from the coupling between the electrons of Nb-4d orbitals and the vibrations of Nb atoms in the low-frequency region and those of S atoms in the high-frequency region.A superconducting transition temperature(T_c)of 10.7 K is obtained,which is close to the experimental value and higher than most transition metal chalcogenides(TMCs).The calculated thermodynamic properties in the superconducting state,such as specific heat,energy gap,isotope coefficient,etc.,also indicate that o-NbS is a conventional phonon-mediated *** results are consistent with recent experimental reports and provide a good understanding of the superconducting mechanism of o-Nb ***,the TMCs of o-TaS and o-WS are also investigated;these belong to the same and neighboring groups of Nb,and we find that o-TaS and o-WS are also phonon-mediated superconductors with T_c of 8.9 K and 7.2 K,respectively.
In this paper,we present new proofs for both the sharp Lp estimate and the decoupling theorem for the Hörmander oscillatory integral *** sharp Lp estimate was previously obtained by Stein(1986)and Bourgain and Gu...
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In this paper,we present new proofs for both the sharp Lp estimate and the decoupling theorem for the Hörmander oscillatory integral *** sharp Lp estimate was previously obtained by Stein(1986)and Bourgain and Guth(2011)via the TT^(*) and multilinear methods,*** provide a unified proof based on the bilinear method for both odd and even *** strategy is inspired by Barron’s work(2022)on the restriction *** decoupling theorem for the Hörmander oscillatory integral operator can be obtained by the approach in Beltran et al.(2020),where the key observation can be roughly formulated as follows:in a physical space of sufficiently small scale,the variable setting can be essentially viewed as *** contrast,we reprove the decoupling theorem for the Hörmander oscillatory integral operator through the Pramanik-Seeger approximation approach(Pramanik and Seeger(2007)).Both proofs rely on a scale-dependent induction argument,which can be used to deal with perturbation terms in the phase function.
The Tungsten-Rhenium(W-Re) alloys,celebrated for their high melting point,strength at elevated temperatures,electrical resistivity,and radiation resistance,have been widely utilized in high-temperature components,aero...
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The Tungsten-Rhenium(W-Re) alloys,celebrated for their high melting point,strength at elevated temperatures,electrical resistivity,and radiation resistance,have been widely utilized in high-temperature components,aerospace,electronics,and nuclear *** constituents of the topologically close-packed(TCP) phases,the sigma phase(σ) and chi phase(χ) formed within W-Re alloys wield considerable influence on the mechanical properties and the stability of the *** calculations were utilized in the present work to explore the structural,thermodynamic,and electronic properties of both ordered and disordered configurations within the σ and χ phases,culminating in a systematic elucidation of the higher phase stability exhibited by the ordered *** is found that the bulk modulus of these two phases is directly proportional to the concentration of Re in the alloy,while the equilibrium volume is inversely *** thermodynamic parameters of the σ and χ phases are calculated via the mean-field potential *** similar trends observed in the isobaric heat capacity,enthalpy increment,and entropy change curves for these two phases suggest they possess comparable thermodynamic *** is noteworthy that the contribution of ionic vibrations predominantly affects the isobaric heat capacity,while the contribution of thermal electronic excitations increases linearly with *** the structure and thermodynamic properties of TCP phases in W-Re alloys at low temperatures has profound significance for optimizing material performance,microstructures features,establishing theoretical foundations,and predicting material behavior.
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