粒子-转子模型和推转壳模型中的能谱统计分析

用粒子–转子模型和推转壳模型研究了6个粒子分别填充在单j壳和双j壳上的混沌行为.分析了单j壳和双j壳情况下能谱的最近邻能级间距分布和谱刚度随自旋及推转频率的变化,结果表明,当组态空间大小不变时,系统在双j壳(g_7/2+d_5/2)情况下比在单j壳(i_13/2)情况下更规则,而当组态空间从单j壳(i_13/2)扩大到双j壳(i_13/2+g_9/2)时,系统的混沌程度变化不大.同时比较了将6个粒子的两体相互作用分别取为δ力和对力时的系统的混沌行为     

Structural optimization design for large mirror

The system design must be started from the concept with low cost and high performance. In this point, the topological shape of the structure is very important in the view of the structural rigidities and light-weight design.In this paper, the optimization methodology is presented in the design stage of the large optical mirror. We obtain the optimal layout through the topology optimization and then design the details through the size or shape optimization for structural rigidity.     

On the rigidity of sphericalt-designs that are orbits of finite reflection groups

The concept of rigid sphericalt-designs was introduced by Bannai. He conjectured that there is a functionf(t, d) such that ifX is a sphericalt design in thed-dimensional Euclidean space so that |X|>f(t, d), theX is non-rigid. Furthermore, he asked to find examples of rigid but not tight sperical designs. In the present article we shall investigate the case whenX is an orbit of a finite reflection group and prove thatX is rigid iff tight for the groupsA _n ,B _n ,C _n ,D _n ,E ₆,E ₇,F ₄,I ₃.Research was partially supported by Hungarian National Research fund Grant No. 4267.     

Flexural rigidity of a liquid surface

The energy of a mass of liquid is evaluated asymptotically in powers of the range of the intermolecular potential divided by a typical dimension of the liquid. The leading term is the internal energy, proportional to the liquid volume. The second term is the energy of surface tension, proportional to the area of the liquid surface. The third term is proportional to an integral over this surface of the square of the mean curvature of the surface minus one-third of its Gaussian curvature. This new term has exactly the form of the bending energy of a thin elastic plate. Comparing it with the bending energy yields expressions for the flexural rigidity and the Poisson ratio of the liquid surface. This flexural rigidity of the surface leads to new terms in the equation of equilibrium of the liquid surface, in addition to the usual surface tension terms.     

Isomorphically rigid algebras

Various classes of non-associative algebras possessing the property of being rigid under abstract isomorphisms are studied. Supported by RFBR grant No. 06-01-00159a. __________ Translated from Algebra i Logika, Vol. 46, No. 4, pp. 483–502, July–August, 2007.     

Synthesis of substituted polymethylenes by radical polymerization of N,N,N′,N′-tetraalkylfumaramides and their characterization

Radical polymerization of N,N,N′,N′-tetraalkylfumaramides (TRFAm) bearing methyl, ethyl, n-propyl, isopropyl, and isobutyl groups as N-substituents (TMFAm, TEFAm, TnPFAm, TIPFAm, and TIBFAm, respectively) was investigated. In the polymerization of TEFAm initiated with 1,1′-azobiscyclohexane-1-carbonitrile (ACN) in benzene, the polymerization rate (R_p) was expressed as follows: R_p = k [ACN]^0.28 [TEFAm]^1.26, and the overall activation energy was 102.1 kJ/mol. The introduction of a bulky alkyl group into N-substituent of TRFAm decreased the R_p in the following order: TMFAm > TEFAm > TnPFAm > TIBFAm > TIPFAm ～ 0. The relative reactivities of these monomers were also investigated in radical copolymerization with styrene (St) and methyl methacrylate (MMA). In copolymerization of TRFAm (M₂) with St (M₁), monomer reactivity ratios were determined to be r₁ = 1.07 and r₂ = 0.20 for St–TMFAm, and r₁ = 1.88 and r₂ = 0.11 for St–TEFAm, from which Q₂ and e₂ values were estimated to be 0.35 and 0.44 for TMFAm, and 0.19 and 0.47 for TEFAm, respectively. The other TRFAm were also copolymerized with St, but copolymerization with MMA gave polymers containing a small amount of TRFAm units. The polymer from TRFAm consists of a less-flexible poly(N,N-dialkylaminocarbonylmethylene) structure. The solubility and thermal property of the polymers were also investigated.     

The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems

The Cox-Merz empirical relationship between the linear (oscillatory) and nonlinear (steady-state) viscosities has been shown to be valid for many polymeric systems. Here, we present an equivalent expression to relate the linear (G) and nonlinear (N ₁) elastic properties of viscoelastic systems. Like the Cox-Merz relationship, it uses a combination of elastic and viscous parameters. The modified form of the storage modulus is then equivalent to the Cox-Merz complex viscosity. It can be used to correlate with (half) the normal force at numerically equal circular frequency and shear rate, respectively.This new expression and the Cox-Merz rule are tested for a range of polymeric and colloidal systems. It is found that both expression work for the polymeric systems considered, but fail for the colloidal systems. In the latter, the steady state values of viscosity and elasticity are consistently low, and replacing them by the complex viscosity and our new elastic expression only makes matters worse.For polymer systems, we suggest this is a general but not universal observation, since we are aware of exceptions to the rule that polymeric systems obey the Cox-Merz rule for viscosity and our rule for elasticity. For colloidal systems we find that neither rule is obeyed for any of our systems.     

Nitroxide spin probe study of probe size,hydrogen bonding and polymer matrix rigidity effects on poly(acrylic acid)/poly(ethylene oxide) complexes

An electron spin resonance (ESR) spin probe study was performed on 1 : 1 by weight poly(acrylic acid) (PAA)/poly(ethylene oxide) (PEO) complex over the 100–450 K temperature range with a series of tetramethylpiperidyloxy‐based spin probes. Measurements of the parameters T_5mT, Ta and Td demonstrated the effects of probe size and the strength of hydrogen bonding. The probes in the series Tempone, Tempo, Tempol and Tamine (respectively 4‐oxo‐, unsubstituted, 4‐hydroxy‐ and 4‐amino‐2,2,6,6,‐tetramethylpiperidine ‐1‐oxyl) displayed noticeable increases in the hydrogen‐bonding effect, as indicated by Ta and Td. These increases correlated with increasing hydrogen bond acceptor strength. On the other hand, as the probe size became larger, T_5mT gradually increased due to the free volume decrease. These effects were analyzed using the established theoretical relationship of T_5mT to probe volume expressed by f. Meanwhile, in order to investigate the effect of polymer matrix rigidity, a similar study was performed with a nitroxide spin probe, 2,2,6,6‐tetramethyl‐1‐piperidine‐1‐oxyl (Tempo), on PAA/PEO complexes of different weight compositions. The quantitative fast motion fraction in the composite ESR spectrum was calculated. The influence of changes in the composition of PAA on the molecular mobility was characterized by changes of the spectral parameters and τ_c. The molecular mobility was shown to diminish with increasing content of PAA in PAA/PEO blends duo to the restriction of the polymer matrix rigidity increase. Copyright © 2003 John Wiley & Sons, Ltd.     

Integrating Rigidity Analysis into the Exploration of Protein Conformational Pathways Using RRT* and MC

To understand how proteins function on a cellular level, it is of paramount importance to understand their structures and dynamics, including the conformational changes they undergo to carry out their function. For the aforementioned reasons, the study of large conformational changes in proteins has been an interest to researchers for years. However, since some proteins experience rapid and transient conformational changes, it is hard to experimentally capture the intermediate structures. Additionally, computational brute force methods are computationally intractable, which makes it impossible to find these pathways which require a search in a high-dimensional, complex space. In our previous work, we implemented a hybrid algorithm that combines Monte-Carlo (MC) sampling and RRT*, a version of the Rapidly Exploring Random Trees (RRT) robotics-based method, to make the conformational exploration more accurate and efficient, and produce smooth conformational pathways. In this work, we integrated the rigidity analysis of proteins into our algorithm to guide the search to explore flexible regions. We demonstrate that rigidity analysis dramatically reduces the run time and accelerates convergence.     

Increased Rigidity in Complexes Formed from Negatively Charged Lariat Ethers and Alkali Metal Cations

Abstract

C-13 NMR longitudinal relaxation times have been measured for lariat ether complexes in which a negative charge is present in the ligand but the system is diamagnetic. A -CH₂COO^? group connected to the nitrogen of aza-15-crown-5 results in drastically increased T₁'s in the presence of Li⁺ compared to the values for the free carboxylic acid and for the acid in the presence of LiClO₄. Longer relaxation times upon complexation show the ‘cryptand-like’ behavior of the complexes, resulting from overall molecular reorientation rates due to compression. These conclusions are supported by molecular mechanics calculations described herein.