Some new results on the two-dimensional kinetic Ising model in the phase coexistence region

We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL with open boundary conditions, in the absence of an external field and at large inverse temperature . We prove that the gap in the spectrum of the generator restricted to the invariant subspace of functions which are even under global spin flip is much larger than the true gap. As a consequence we are able to show that there exists a new time scalet _even, much smaller than the global relaxation timet _rel, such that, with large probability, any initial configuration first relaxes to one of the two phases in a time scale of ordert _even and only after a time scale of the order oft _rel does it reach the final equilibrium by jumping, via a large deviation, to the opposite phase. It also follows that, with large probability, the time spent by the system during the first jump from one phase to the opposite one is much shorter than the relaxation time.     

On the layering transition of an SOS surface interacting with a wall. I. Equilibrium results

We consider the model of a 2D surface above a fixed wall and attracted toward it by means of a positive magnetic fieldh in the solid-on-solid (SOS) approximation when the inverse temperature is very large and the external fieldh is exponentially small in . We improve considerably previous results by Dinaburg and Mazel on the competition between the external field and the entropic repulsion with the wall, leading, in this case, to the phenomenon of layering phase transitions. In particular, we show, using the Pirogov-Sinai scheme as given by Zahradník, that there exists a unique critical valueh _k ^* () in the interval (1/4e ^–4k , 4e ^–4k ) such that, for allh(h _k+1 ^* ,h _k ^* ) and large enough, there exists a unique infinite-volume Gibbs state. The typical configurations are small perturbation of the ground state represented by a surface at heightk+1 above the wall. Moreover, for the same choice of the thermodynamic parameters, the influence of the boundary conditions of the Gibbs measure in a finite cube decays exponentially fast with the distance from the boundary. Whenh=h _k ^* () we prove instead the convergence of the cluster expansion for bothk andk+1 boundary conditions. This fact signals the presence of a phase transition. In the second paper of this series we will consider a Glauber dynamics for the above model and we will study the rate of approach to equilibrium in a large finite cube with arbitrary boundary conditions as a function of the external fieldh. Using the results proven in this paper, we will show that there is a dramatic slowing down in the approach to equilibrium when the magnetic field takes one of the critical values and the boundary conditions are free (absent).     

溴仿在冲击压缩下的光辐射及化学反应

 利用多通道光学高温计测量了溴仿在37 GPa到85 GPa压力范围内的温度,并观察了溴仿/单晶氯化钠界面的热驰豫过程。结果发现,当冲击波压力升高到46 GPa时,溴仿的光辐射强度随时间的变化呈现出“双阶梯”或“双台阶”形状的剖面结构,且台阶之间的时间间隔随冲击压力的增高而减小。当压力达到85 GPa时,上述“双台阶”结构消失,呈现为普通的单台阶剖面结构。冲击波温度测量表明,当压力低于50 GPa时,实测温度与Gokulya报道的数据一致;当压力增至76 GPa以上时,冲击波温度出现突跃性增加。结合对溴仿/氯化钠界面上的热驰豫过程的分析,文中提出,溴仿在上述冲击压力区间内发生了一次带有时间驰豫（或化学诱导期）的化学放热反应。     

Structure and properties of TentaGel resin beads: Implications for combinatorial library chemistry

Summary In view of the widespread use of TentaGel resin beads for the synthesis of combinatorial libraries, the properties of TentaGel resin have been examined using a combination of confocal laser microscopy and NMR spectroscopy. Evidence is presented that trypsin, a 23.5-kDa enzyme, can penetrate to the core of 90-m TentaGel beads, and that the matrix of such beads permits molecular motion at a similar rate to that in solution. The beads act as a separate gel phase rather than as a porous solid. These conclusions have important implications for the bioassay of on-bead combinatorial chemical libraries.     

Studies of the enthalpy relaxation and the “multiple melting” behavior of semicrystalline poly(arylene ether ether ketone) (PEEk)

We report the results of an investigation by differential scanning calorimetry (DSC) of two mobility controlled processes in the amorphous phas e of semicrystalline PEEK — enthalpy relaxation below the glass transition (T _g) and secondary crystallization aboveT _g. Both result in the observation of an endothermic peak just above the annealing temperature in the DSC scan of the polymer — the enthalpy recovery peak and the low temperature melting peak, respectively. There is a striking similarity in the time and temperature dependence of the endothermic peak for these two processes. These results are reminiscent of those obtained from small strain creep studies of physical aging of semicrystalline PEEK below and aboveT _g.We gratefully acknowledge support of this work by the National Science Foundation, Science and Technology Center for High Performance Polymeric Adhesives and Composites under DMR grant 91-2004 and by an NSF Young Investigator Award (DMR 93-57512).     

A probabilistic analysis of the multiknapsack value function

The optimal solution value of the multiknapsack problem as a function of the knapsack capacities is studied under the assumption that the profit and weight coefficients are generated by an appropriate random mechanism. A strong asymptotic characterization is obtained, that yiclds a closed form expression for certain special cases.This research was partially supported by NSF Grant ECS-83-16224, and MPI Project Matematica computazionale.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Exact solution for rotational relaxation times for problems governed by axially symmetric Fokker-Planck equations

Exact integral expressions valid for any potential barrier height for mean first passage times (and so the exit time and the reaction rate) for relaxation processes governed by the rotational Fokker-Planck equation with an axially symmetric potential are derived in a manner exactly analogous to that used to derive an integral expression for the correlation time by Coffey and Crothers (W.T. Coffey and D.S.F. Crothers, Phys. Rev. E. 54 (1996) 4768). This is accomplished by constructing the adjoint Fokker-Planck operator (Kolmogorov backward operator) and so forming the partial differential equation for the mean first passage time, which for axial symmetry may be directly integrated by quadratures. The results constitute a generalization of the work of Klein, (G. Klein, Proc. R. Soc. London, Ser. A 211 (1952) 431) originally given for the free rotational Brownian movement, to the rotational Brownian movement in an axially symmetric potential.     

Dielectric relaxation study of atactic poly(epichlorohydrin)/poly(3-hydroxybutyrate) blends

Binary blends of atactic poly(epichlorohydrin) (aPECH) and poly(3-hydroxybutyrate) (PHB) were investigated as a function of blend composition and crystallization conditions by dielectric relaxation spectroscopy. The quenched samples were found to be miscible in the whole composition range by detecting only one glass transition relaxation, for each composition, which could be closely described by the Gorden-Taylor equation. The cold-crystallized blends displayed two glass transition relaxations at all blend ratios indicating the coexisting of two amorphous populations: a pure aPECH phase dispersed mainly in the interfibrillar zones and a mixed amorphous phase held between crystal lamellae. The interlamellar trapping of aPECH was small and decreases with increasing the overall PHB content in the blend. At high crystallization temperatures the aPECH molecules was found to reside mainly in the interfibrillar regions due to its high mobility relative to the crystal growth rate of PHB. Our results suggest that because the intersegmental interaction in aPECH/PHB blends is weak, the mobility of the amorphous component at a given crystallization temperature decides diluent segregation.     

环氧交联网T_g转变的tanδ-T曲线解析

本文系统地研完了预聚物分子量、固化剂配比和固化条件对环氧交联网T_g松弛内耗峰松弛时间分布的影响。本实验和理论研究结果首次证明了环氧交联网T_g松弛过程具有单一松弛时间描述的线性标准固体的特征,与预聚体分子量、固化剂配比和固化条件无关。此结果可用环氧交联网的两相结构特征加以解释。