Narrow Results

Quantization needs evaluation of all of states of a quantized object rather than its stationary states with respect to its energy. In this paper, we have investigated moduli of a quantized elastica, a quantized loop with an energy functional associated with the Schwarz derivative, on a Riemann sphere ℙ. Then it is proved that its moduli space is decomposed to a set of equivalent classes determined by flows obeying the Korteweg-de Vries (KdV) hierarchy which conserve the energy. Since the flow obeying the KdV hierarchy has a natural topology, it induces topology in the moduli space . Using the topology, is classified.

Studies on a loop space in the category of topological spaces Top are well-established and its cohomological properties are well-known. As the moduli space of a quantized elastica can be regarded as a loop space in the category of differential geometry DGeom, we also proved an existence of a functor between a triangle category related to a loop space in Top and that in DGeom using the induced topology.

As Euler investigated the elliptic integrals and its moduli by observing a shape of classical elastica on , this paper devotes relations between hyperelliptic curves and a quantized elastica on ℙ as an extension of Euler's perspective of elastica.

The stochastic Anderson model in discrete or continuous space is defined for a class of non-Gaussian spacetime potentials W as solutions u to the multiplicative stochastic heat equation with diffusivity κ and inverse-temperature β. The relation with the corresponding polymer model in a random environment is given. The large time exponential behavior of u is studied via its almost sure Lyapunov exponent λ = lim_t→∞ t^-1log u(t, x), which is proved to exist, and is estimated as a function of β and κ for β²κ^-1 bounded below: positivity and nontrivial upper bounds are established, generalizing and improving existing results. In discrete space λ is of order β²/log(β²/κ) and in continuous space it is between β²(κ/β²)^H/(H+1) and β²(κ/β²)^H/(1+3H).

Long polymer chains that mainly exhibit thermoplastic properties are recognized to demonstrate excellent thermal and mechanical features at the molecular level. For the purpose of facilitating its study, we present the results of a coarse-grained Molecular Dynamics (MD) and Dissipative Particle Dynamics (DPD) simulations under the Canonical ensemble (NVT) conditions. For each simulation method, the structure, static and dynamic properties were analyzed, with particular emphasis on the influence of density and temperature on the equilibrium of the polymer. We find, after correcting the Soft Repulsive Potential (SRP) parameters used in DPD method, that both simulation methods describe the polymer physics with the same accuracy. This proves that the DPD method can simplify the polymer simulation and can reproduce with the same precision the equilibrium obtained in the MD simulation.