Quasi-periodic stability of normally resonant tori

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts.     

Utilization of inverse approach in the design of materials over nano‐ to macro‐scale

In the light of recent developments in computer technology, a promising and efficient way to design a material with a desired property would be to solve the inverse problem: use a physical property to predict structure. Here, we discuss the basic idea and mathematical foundation of the inverse approach, and proposed strategies for its utilization in the design of materials over nano‐ to macro‐scales. At the nano‐scale, analyzed strategies include scanning of a high‐dimensional space of chemical compounds for those compounds that have a targeted property, and identification of correlations in large databases of materials. However, unlike utilization of inverse approach at nano‐scale where full structural information ‐ atoms and their positions‐ is linked to targeted properties, at the meso‐ and macro‐scale, only partial structural information, manifested via structural motifs or representative volume elements, is available. We discuss the role of partial structural information in the inverse approach to the design of materials at those scales. Risks and limitations of the inverse approach are analyzed and dependence of the approach on factors such as structure parametrization, approximations in theoretical models, and feedback from structural characterization, is addressed.

     

Exploring Microstructures and Interphase Properties of Surface- Grafted Diblock Copolymers in a Homopolymer Melt by Self-Consistent Field Theory Simulations

Polymeric self-consistent field theory is used to investigate microstructures and interphase properties of diblock copolymers grafted onto solid surfaces in a homopolymer melt. The calculations show that the grafted diblock copolymers can self-assemble into hemispherical microstructures at low grafting densities of the diblock copolymers. The morphology transforms into hemicylinder-like and sandwich-like lamellar microstructures with an increase in the chain-grafting density. The effective thickness of the grafted block layer and the interphase width between the homopolymer melt and the grafted copolymers strongly depend on the physicochemical parameters of the system, such as the composition of the grafted copolymer, the chemical incompatibility between the different components, the length ratio of grafted copolymer to homopolymer, and the grafting density of the diblock copolymers. In addition, the above computational results of microphase-separated structures and interphase properties are qualitatively compared with our previous experimental observations. The comparison indicates that our theoretical results not only reproduce the general feature of the experimental observations, but also elucidate the internal structural information and complement the findings in the region of high grafting densities of diblock copolymers.     

Fields,particles and universality in two dimensions

We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical case, considering systems both on the whole plane and in presence of boundaries. The topics we discuss include magnetism, percolation, phase separation, interfaces, wetting.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

Quantum-corrected finite entropy of noncommutative acoustic black holes

In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1$2+1$-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.     

Generally covariant vs. gauge structure for conformal field theories

We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group.     

On the symmetry of three identical interacting particles in a one-dimensional box

We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group D_3d$D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh–Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.