On genus expansion of knot polynomials and hidden structure of Hurwitz tau-functions

In the genus expansion of the HOMFLY polynomials their representation dependence is naturally captured by symmetric group characters. This immediately implies that the Ooguri-Vafa partition function (OVPF) is a Hurwitz tau-function. In the planar limit involving factorizable special polynomials, it is actually a trivial exponential tau-function. In fact, in the double scaling Kashaev limit (the one associated with the volume conjecture) dominant in the genus expansion are terms associated with the symmetric representations and with the integrability preserving Casimir operators, though we stop one step from converting this fact into a clear statement about the OVPF behavior in the vicinity of q=1. Instead, we explain that the genus expansion provides a hierarchical decomposition of the Hurwitz tau-function, similar to the Takasaki-Takebe expansion of the KP tau-functions. This analogy can be helpful to develop a substitute for the universal Grassmannian description in the Hurwitz tau-functions.Comment: 8 page

Dynamic problems for metamaterials: Review of existing models and ideas for further research

Metamaterials are materials especially engineered to have a peculiar physical behaviour, to be exploited for some well-specified technological application. In this context we focus on the conception of general micro-structured continua, with particular attention to piezoelectromechanical structures, having a strong coupling between macroscopic motion and some internal degrees of freedom, which may be electric or, more generally, related to some micro-motion. An interesting class of problems in this context regards the design of wave-guides aimed to control wave propagation. The description of the state of the art is followed by some hints addressed to describe some possible research developments and in particular to design optimal design techniques for bone reconstruction or systems which may block wave propagation in some frequency ranges, in both linear and non-linear fields. (C) 2014 Elsevier Ltd. All rights reserved

Cubically convergent methods for selecting the regularization parameters in linear inverse problems

AbstractWe present three cubically convergent methods for choosing the regularization parameters in linear inverse problems. The detailed algorithms are given and the convergence rates are estimated. Our basic tools are Tikhonov regularization and Morozov's discrepancy principle. We prove that, in comparison with the standard Newton method, the computational costs for our cubically convergent methods are nearly the same, but the number of iteration steps is even less. Numerical experiments for an elliptic boundary value problem illustrate the efficiency of the proposed algorithms

Nanoscale ear drum: Graphene based nanoscale sensors

The difficulty in determining the mass of a sample increases as its size diminishes. At the nanoscale, there are no direct methods for resolving the mass of single molecules or nanoparticles and so more sophisticated approaches based on electromechanical phenomena are required. More importantly, one demands that such nanoelectromechanical techniques could provide not only information about the mass of the target molecules but also about their geometrical properties. In this sense, we report a theoretical study that illustrates in detail how graphene membranes can operate as nanoelectromechanical mass-sensor devices. Wide graphene sheets were exposed to different types and amounts of molecules and molecular dynamic simulations were employed to treat these doping processes statistically. We demonstrate that the mass variation effect and information about the graphene-molecule interactions can be inferred through dynamical response functions. Our results confirm the potential use of graphene as mass detector devices with remarkable precision in estimating variations in mass at molecular scale and other physical properties of the dopants

Influence of diesel fuel viscosity on cavitating throttle flow simulations at erosive operation conditions

This work investigates the effect of liquid fuel viscosity, as specific by the European Committee for Standardization 2009 (European Norm) for all automotive fuels, on the predicted cavitating flow in micro-orifice flows. The wide range of viscosities allowed, leads to a significant variation of orifice nominal Reynolds numbers for the same pressure drop across the orifice. This in turn, is found to affect flow detachment, formation of large-scale vortices and micro-scale turbulence. A pressure-based compressible solver is used on the filtered Navier-Stokes equations using the multi-fluid approach; separate velocity fields are solved for each phase that share a common pressure. The rates of evaporation and condensation are evaluated with a simplified model based on the Rayleigh-Plesset equation; the Coherent Structure Model is adopted for the sub-grid scales modeling in the momentum conservation equation. The test case simulated is a well reported benchmark throttled flow channel geometry, referred to as ’I-channel’; this has allowed for easy optical access for which flow visualization and LIF measurements allowed for validation of the developed methodology. Despite its simplicity, the Ichannel geometry is found to reproduce the most characteristic flow features prevailing in high-speed flows realized in cavitating fuel injectors. Following, the effect of liquid viscosity on integral mass flow, velocity profiles, vapor cavities distribution and pressure peaks indicating locations prone to cavitation erosion are reported

Physical models of seismic attenuation measurements in the lab

Classical continuum mechanics with dissipation allows the description of observed creep and phase-lag attenuation effects in solids. The frequency-dependent Q or time dependent moduli, compliances, or creep functions which are often used to describe such observations may be empirical characteristics reflecting not only the properties of the materials but also the dimensions and shapes of the samples. The theoretical paradigm employed in this study is strongly different from the conventional, Q-based (often called “viscoelastic”) model. Instead of a single, but arbitrarily frequency-dependent Q attributed to a solid, a number of specific physical parameters of energy-dissipation mechanisms (such as viscosity or thermoelasticity) are considered. The model is based on first physical principles and focuses on inverting for the intrinsic (time- and frequency-independent) properties of the material. The observed frequency-dependent Q’s or time-dependent creep (“memory”) functions are generally explained by the non-linearity of solid viscosity, which can be described by selecting the Lagrangian dissipation function. This fundamental conclusion was suggested as long ago as by Knopoff (1964) but appeared to be little developed since. I only consider a specific, power-law form of this function, and show that it is consistent with the strain-rate dependence of effective viscosity used in geodynamics. Power-law nonlinearity of solid viscosity combined with thermoelastic effects allows quantitatively predicting all key observations, such as creep, stress-strain phase lags in torsional and longitudinal oscillations, and broadening of spectral amplitude peaks near resonance. Analytical and numerical modeling of longitudinal-oscillation phase-lag measurements in Plexiglas cylinders suggest the value of rheological exponent approximately 0.56. This is interpreted as a “near-dry” internal friction in solids. The physical models of internal friction also suggest methods for inverting for the in situ dissipation properties of materials. Finally, the new models suggest several ways for enhancing the theoretical knowledge about the physical properties of Earth materials

Contributions of plasma physics to chaos and nonlinear dynamics

This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016

Plasmons in metallic monolayer and bilayer transition metal dichalcogenides

We study the collective electronic excitations in metallic single- and bilayer transition metal dichalcogenides (TMDCs) using time dependent density functional theory in the random phase approximation. For very small momentum transfers (below $q\approx0.02$~\AA$^{-1}$) the plasmon dispersion follows the $\sqrt{q}$ behavior expected for free electrons in two dimensions. For larger momentum transfer the plasmon energy is significantly red shifted due to screening by interband transitions. At around $q\approx 0.1$ \AA$^{-1}$ the plasmon enters the dissipative electron-hole continuum and the plasmon dispersions flatten out at an energy around 0.6-1.1 eV, depending on the material. Using bilayer NbSe$_2$ as example, we show that the plasmon modes of a bilayer structure take the form of symmetric and anti-symmetric hybrids of the single-layer modes. The spatially anti-symmetric mode is rather weak with a linear dispersion tending to zero for $q=0$ while the energy of the symmetric mode follows the single-layer mode dispersion with a slight blue shift.Comment: 6 pages, 4 figure