The Donald–Flanigan Problem for Finite Reflection Groups

The Donald–Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and Weyl groups of types B _n and D _n (whose rational group algebras are computed), leaving but six finite reflection groups with solutions unknown. We determine the structure of a wreath product of a group with a sum of central separable algebras and show that if there is a solution for H over k which is a sum of central separable algebras and if S _n is the symmetric group then (i) the problem is solvable also for the wreath product H S _n = H × ··· × H (n times) S _n and (ii) given a morphism from a finite Abelian or dihedral group G to S _n it is solvable also for H G. The theorems suggested by the Donald–Flanigan conjecture and subsequently proven follow, we also show, from a geometric conjecture which although weaker for groups applies to a broader class of algebras than group algebras.     

A note on rigidity of 3-Sasakian manifolds

Making use of the relations among 3-Sasakian manifolds, hypercomplex manifolds and quaternionic Kähler orbifolds, we prove that complete 3-Sasakian manifolds are rigid.

     

One dimensional model of dye-doped nematic layer for holography

The layer of electrically conducting nematic liquid crystal doped with photosensitive dye and confined between polyimide coated electrodes can serve as a diffraction grating. In this paper, the deformations of the nematic director field induced in such a system by external voltage were studied numerically by means of one-dimensional model. The dissociation and recombination of ions were taken into account according to weak electrolyte model. The director orientation in the deformed layers and the distributions of the electric field and of the ion concentrations were calculated for blocking and for conducting electrodes. The effective extraordinary refractive index was also determined as a function of average ion concentration.     

Numerical approaches to thermally coupled perfect plasticity

The partial differential equations describing viscoelastic solids in Kelvin–Voigt rheology at small strains exhibiting also stress‐driven Prandtl‐Reuss perfect plasticity are considered and are coupled with a heat‐transfer equation through the dissipative heat produced by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the resulting thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Numerical stability is shown and computational simulations are reported to illustrate the practical performance of the method. In a quasistatic case, convergence is proved by careful successive limit passage. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

夹持方式对频率转换KDP晶体面形的影响

 针对惯性约束聚变（ICF）系统中大口径超薄KDP晶体在不同夹持和不同姿态下的面形变化,采用有限元分析软件ANSYS,建立了大口径超薄KDP晶体在不同夹持和不同姿态下的应变模型及其边界条件的确定方法,计算了四周简支正面点力、四周固支正面压条、四周简支侧面点力、四周固支侧面压条4种夹持方式在30°和垂直姿态下大口径超薄KDP晶体的面形变化,并给出了面形变化的P-V值和RMS值。在此基础上,通过对不同夹持和不同姿态下KDP晶体面形变化的分析和比较,给出了四周固支正面压条是引起晶体面形变化相对较小的夹持方式的结论。     

A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels

An elastomeric gel is a cross-linked polymer network swollen with a solvent, and certain gels can undergo large reversible volume changes as they are cycled about a critical temperature. We have developed a continuum-level theory to describe the coupled mechanical deformation, fluid permeation, and heat transfer of such thermally responsive gels. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model based on a Flory–Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical–mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. We have numerically implemented our theory in a finite element program. We show that our theory is capable of simulating swelling, squeezing of fluid by applied mechanical forces, and thermally responsive swelling/de-swelling of such materials.     

Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

A mathematical model incorporating the higher order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. The rotor system considered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (deformation) energies of the rotor system are derived and the Rayleigh–Ritz method is used to discretize these energy expressions. Hamilton’s principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed.     

Lie-Yamaguti着色代数的导子与形变

In this paper,we introduce the representation and cohomology theory of Lie-Yamaguti color algebras.Furthermore,we introduce the notions of generalized derivations of Lie-Yamaguti color algebras and present some properties.Finally,we study linear deformations of LieYamaguti color algebras,and introduce the notion of a Nijenhuis operator on a Lie-Yamaguti color algebra,which can generate a trivial deformation.     

Deformations and derived equivalences

Suppose and are block algebras of finite groups over a complete local commutative Noetherian ring whose residue field is a field of positive characteristic. We prove that a split-endomorphism two-sided tilting complex (as introduced by Rickard) for the derived categories of bounded complexes of finitely generated modules over , resp. , preserves the versal deformation rings of bounded complexes of finitely generated modules over , resp. .