Nearby cycles for log smooth families

We calculate l-adic nearby cycles in the étale cohomology for families with log smooth reduction using log étale cohomology. In particular, nearby cycles for log smooth families coincide with tame nearby cycles, as L. Illusie expected, and nearby cycles for semistable families depend only on the first infinitesimal neighborhood of the special fiber.     

Lyapunov spectra for KMS states on Cuntz-Krieger algebras

We study relations between (H,β)-KMS states on Cuntz-Krieger algebras and the dual of the Perron-Frobenius operator . Generalising the well-studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one-one correspondence between (H,β)-KMS states and eigenmeasures of for the eigenvalue 1. We then apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups G which may have parabolic elements. We show that for the Cuntz-Krieger algebra arising from G there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen-Series map associated with G. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of G. If G has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with G. The second author was supported by the DFG project “Ergodentheoretische Methoden in der hyperbolischen Geometrie”.     

Slowdown of atomic diffusion in liquid gallium–indium alloy under different nanoconfinements

NMR studies were carried out on three isotopes, ⁷¹Ga, ⁶⁹Ga, and ¹¹⁵In, in liquid gallium-indium (Ga–In) alloy embedded into porous glasses with 200 and 5 nm pore sizes at two magnetic fields, 9.4 and 17.6 T. Spin-lattice relaxation and the Knight shift were found to depend on pore size. For porous glass with 5 nm pores the relaxation rate was field-dependent which evidenced that the extreme narrowing limit was no longer valid. Magnetization recovery data were used to evaluate the correlation times of atomic mobility and the quadrupole constants under nanoconfinement.     

歼击机进气道结构强度设计方法研究

重点介绍了基于几何非线性和总体-局部(GLOBAL-LOCAL)求解策略的进气道结构强度仿真分析技术,以此技术建立先进的进气道结构强度设计方法。该方法精度高,工程实用性强。该方法对现代歼击机进气道结构设计能够大幅度提高进气道结构强度品质,降低设计成本,提高设计一次成功率。给出了应用实例。     

A novel geometry for rheological characterization of viscoelastic materials

A novel geometry for generating a viscometric flow presents advantages of both cone and plate and parallel plate geometries, regarding uniform shear field and adjustable range of measurement. Kinematics and dynamics of the generated flow have been described mathematically utilizing an orthogonal curvilinear coordinate system based on the shapes of the shearing surfaces which are similar to the surface that generates the flow. Simple equations that allow the calculation of quantities of experimental interest in the rheological characterization of liquid materials, namely, shear rate, shear stress and two normal stress differences, have also been derived.The geometry, called pseudosphere, was tested with two types of fluids (Newtonian and pseudoplastic). Results show that the geometry can be used with low viscosity liquids (Newtonian liquids) by only adjusting the gapH. The behavior of pseudoplastic fluids for both low and moderately high viscosity could also be studied with this geometry. Very reproducible results were obtained when compared with those obtained with cone and plate geometry. Regions of lower shear rate could be studied using only the pseudosphere geometry.     

Non-existence of degree bounds for weighted sums of squares representations

Given a fixed family of polynomials , we study the problem of representing polynomials in the form

(*)

f=s₀+s₁h₁++s_rh_r