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61.
Solvable vertex models in statistical mechanics give rise to soliton cellular automata at q=0 in a ferromagnetic regime. By means of the crystal base theory we study a class of such automata associated with non-exceptional quantum affine algebras U′ $_q$ ( $\widehat {\mathfrak{g}}$ $_n$ ). Let B $_l$ be the crystal of the U′ $_q$ ( $\widehat {\mathfrak{g}}$ $_n$ )-module corresponding to the l-fold symmetric fusion of the vector representation. For any crystal of the form B = $B_{l_1 }$ ? ...? $B_{l_N }$ , we prove that the combinatorial R matrix B $_M$ ?B $\widetilde \to$ B?B $_M$ is factorized into a product of Weyl group operators in a certain domain if M is sufficiently large. It implies the factorization of certain transfer matrix at q=0, hence the time evolution in the associated cellular automata. The result generalizes the ball-moving algorithm in the box-ball systems. 相似文献
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The asymptotic behavior of viscosity solutions to the Cauchy–Dirichlet problem for the degenerate parabolic equation u
t
= Δ∞
u in Ω × (0,∞), where Δ∞ stands for the so-called infinity-Laplacian, is studied in three cases: (i) and the initial data has a compact support; (ii) Ω is bounded and the boundary condition is zero; (iii) Ω is bounded and the boundary condition is non-zero. Our method of proof is based on the comparison principle and barrier function
arguments. Explicit representations of separable type and self-similar type of solutions are also established. Moreover, in
case (iii), we propose another type of barrier function deeply related to a solution of .
Goro Akagi was supported by the Shibaura Institute of Technology grant for Project Research (no. 2006-211459, 2007-211455),
and the grant-in-aid for young scientists (B) (no. 19740073), Ministry of Education, Culture, Sports, Science and Technology.
Petri Juutinen was supported by the Academy of Finland project 108374. Ryuji Kajikiya was supported by the grant-in-aid for
scientific research (C) (no. 16540179), Ministry of Education, Culture, Sports, Science and Technology. 相似文献
66.
This paper is concerned with the uniqueness, existence, partial smoothing effect, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in Damage Mechanics due to the strong irreversibility of crack propagation or damage evolution. The existence of solutions is proved in an -framework by employing a backward Euler scheme and by introducing a new method of a priori estimates based on a reduction of discretized equations to variational inequalities of obstacle type and by developing a regularity theory for such obstacle problems. The novel discretization argument will be also applied to prove the comparison principle as well as to investigate the long-time behavior of solutions. 相似文献
67.
Liu Jijun Machida Manabu Nakamura Gen Nishimura Goro Sun Chunlong 《中国科学 数学(英文版)》2022,65(6):1179-1198
Science China Mathematics - To quantify fluorescence imaging of biological tissues, we need to solve an inverse problem for the coupled radiative transfer equations which describe the excitation... 相似文献
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Non-acoustical and acoustical properties of reticulated and partially reticulated polyurethane foams
A series of measurements on four polyurethane foam samples with pore membranes and a polyurethane foam sample without pore membranes have been made. Tortuosity has been deduced using the ultrasonic slope method. It has been found that the deduced value of tortuosity depends on the measurement temperature and for two of the polyurethane foam samples with many pore membranes physically meaningful values of tortuosity cannot be obtained at a temperature of around 25 °C. However more realistic values of tortuosity have been obtained by from measurements at or around the glass transition temperature of polyurethane foam (i.e. at ?20 °C) when using the ultrasonic slope method.Flow resistivity, Young’s moduli and loss factors have been measured also.Vibration of the pore membranes has been observed to influence the effective density and characteristic impedance derived from the surface impedance measured in an impedance tube. This paper discusses relationships between membrane vibration and the slow and fast compressional waves. The relative merits of predictions based on rigid-porous models and the Biot–Johnson–Champoux–Allard model are discussed also. 相似文献
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