Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III

A unified treatment of monodromy and spectrum preserving deformations is presented. In particular a general procedure is described to reduce the latter into the former consistently. The concept of the τ-function, previously introduced for the former [2], is extended to the isospectral context. It is shown that the general monodromy and spectrum preserving deformation equations can be written as Hirota's bilinear differential equations by using the τ-functions as dependent variables.     

Relaxation spectra of concentrated polystyrene solutions

The relaxation modulus G(t) and the stress decay after cessation of steady shear flow were measured on concentrated solutions of polystyrenes in diethyl phthalate. Ranges of concentration c and molecular weight M of the polymer were from 0.112 to 0.329 g/ml and from 1.23 × 10⁶ to 7.62 × 10⁶, respectively. The relaxation spectrum H(τ) as calculated from G(t) for the solution of very high M was found to be composed of two parts. One, at relatively short times, was a broad distribution (plateau zone) with height proportional to c². The second, at the long-time end, was very sensitive to concentration and gave rise to a maximum in H(τ) for very high concentrations. The behavior of H(τ) at long times was examined quantitatively by evaluating the longest relaxation time τ₁⁰ and the corresponding relaxation strength G₁⁰ from G(t) and from the stress decay function, on the assumption of a discrete distribution of relaxation times at long times. The longest relaxation time was approximately proportional to M^3.5, even at relatively low concentrations where the zero-shear viscosity was not proportional to M^3.5. The strengths of relaxation modes with the longest few relaxation times are proportional to the third power of concentration.     

A remark on coefficients of connection with two gauge fields

Recently a geometrical gravitational theory based on the coefficients of connection with two gauge fields was proposed. The objective of the present paper is to show that the geometry based on the coefficients of connection with two gauge fields can be obtained by the successive operations of conformal and projective transformations on Riemannian metric.     

Highlights of Supersymmetry, Superstrings, and M-Theory

The present lecture is a beginer's guide to supersymmetry, superstrings, and M-theory. It addresses students and scientists whose basic research topic in theoretical physics is a different one but who, nonetheless, wish to gain a glimpse into this exciting new field of theoretical physics.     

Physical properties and structure of silk. VI. Conformational changes in silk fibroin induced by immersion in water at 2 to 130°c

Silk fibroin films in the random-coil and β-form conformations were immersed in water at temperatures from 2 to 130°C, and conformational changes were followed by x-ray diffraction, infrared spectroscopy and differential scanning calorimetry. On treatment with water below 60°C, the random-coil conformation is converted to the α form and above 70°C to mixtures of the α and β conformations. The β-form content increases as the immersion temperature is raised. The β form is not affected by immersion in water in the temperature range studied.     

A novel synthesis of dl-marmelolactone and dl-rose oxide by electrochemical oxyselenenylation-deselenenylation sequence

One-step transformation of olefins $\text{1}$ into allylic alcohols and ethers $\text{3}$ has been accomplished by electrooxidative oxyselenenylation-deselenenylation sequence. The electrochemical process furnished efficient syntheses of dl-marmelolactone $\text{4}$ and dl-rose oxide $\text{5}$.     

QuantumR matrix for the generalized Toda system

We report the explicit form of the quantumR matrix in the fundamental representation for the generalized Toda system associated with non-exceptional affine Lie algebras.     

Energy density analysis of cluster size dependence of surface-molecule interactions: H2, C2H2, C2H4, and CO adsorption onto Si(100)-(2x1) surface

Adsorption of H2, C2H2, C2H4, and CO onto a Si(100)-(2x1) surface has been treated theoretically using Si(12n - 3)H(8n + 4) (n = 1-4) clusters. The energy density analysis (EDA) proposed by Nakai has been adopted to examine surface-molecule interactions for different cluster sizes. EDA results for the largest model cluster Si45H36 have shown that the adsorption-induced energy density variation in Si atoms decays with distance from the adsorption site. Analysis of this decay, which can be carried out using the EDA technique, is important because it enables verification of the reliability of the model cluster used. In the cases of H2, C2H2, C2H4, and CO adsorption onto the Si(100)-(2x1) surface, it is found that at least a Si21H20 cluster is necessary to treat the surface-molecule interaction with chemical accuracy.     

Slow dynamics and re-entrant melting in a polydisperse hard-sphere fluid

Extensive molecular dynamics simulations are performed at 6% polydispersity to investigate the phase diagram of a polydisperse hard-sphere fluid and the dynamical behavior in each phase. As the volume fraction phi is increased, the existence of a supercooled liquid is suggested above phi = 0.5524 by the mean-field analysis proposed recently. The first-order phase transition from supercooled liquid to crystal is then shown to occur around phi = 0.5630. The occurrence of re-entrant melting, a first-order phase transition from crystal to supercooled liquid, is also found around phi = 0.5715. The existence of the glass transition is thus suggested, even in the hard-sphere fluid with small polydispersity.