Geometry: The leading parameter for the Poisson’s ratio of bending-dominated cellular solids

Control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials, in particular those with negative Poisson’s ratio. This article sheds light on the old question of the relationship between geometric microstructure and mechanical response, by comparison of the deformation properties of bar-and-joint-frameworks with those of their realisation as a cellular solid made from linear-elastic material. For ordered planar tessellation models, we find a classification in terms of the number of degrees of freedom of the framework model: first, in cases where the geometry uniquely prescribes a single deformation mode of the framework model, the mechanical deformation and Poisson’s ratio of the linearly-elastic cellular solid closely follow those of the unique deformation mode; the result is a bending-dominated deformation with negligible dependence of the effective Poisson’s ratio on the underlying material’s Poisson’s ratio and small values of the effective Young’s modulus. Second, in the case of rigid structures or when geometric degeneracy prevents the bending-dominated deformation mode, the effective Poisson’s ratio is material-dependent and the Young’s modulus View the MathML sourceE˜cs large. All analysed structures of this type have positive values of the Poisson’s ratio and large values of View the MathML sourceE˜cs. Third, in the case, where the framework has multiple deformation modes, geometry alone does not suffice to determine the mechanical deformation. These results clarify the relationship between mechanical properties of a linear-elastic cellular solid and its corresponding bar-and-joint framework abstraction. They also raise the question if, in essence, auxetic behaviour is restricted to the geometry-guided class of bending-dominated structures corresponding to unique mechanisms, with inherently low values of the Young’s modulus

Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number

Conservation Laws in Higher-Order Nonlinear Optical Effects

Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schr\"{o}dinger equation. The first few currents and charges are also presented explicitly. Due to the higher-order effects, conservation laws of the nonlinear Schr\"{o}dinger equation are violated in general. The differences between the types of the conserved currents for the Hirota and the Sasa-Satsuma equations imply that the higher-order terms determine the inherent types of conserved quantities for each integrable cases of the higher-order nonlinear Schr\"{o}dinger equation

Homodyne detection for atmosphere channels

We give a systematic theoretical description of homodyne detection in the case where both the signal and the local oscillator pass through the turbulent atmosphere. Imperfect knowledge of the local-oscillator amplitude is effectively included in a noisy density operator, leading to postprocessing noise. Alternatively, we propose a technique with monitored transmission coefficient of the atmosphere, which is free of postprocessing noise.Comment: 9 pages, 5 figure

Multisoliton solutions and integrability aspects of coupled nonlinear Schrodinger equations

Using Painleve singularity structure analysis, we show that coupled higher-order nonlinear Schrodinger (CHNLS) equations admit Painleve property. Using the results of Painleve analysis, we succeed in Hirota bilinearizing the CHNLS equations, one soliton and two soliton solutions are explictly obtained. Lax pairs are explictly constructed.Comment: Eight pages and six figures. Physical Review E (to be appear

Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector

Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the leading-order asymptotics as $t$ tends to plus and minus infinity of the solution to the Cauchy initial-value problem for the modified non-linear Schrodinger equation: also obtained are analogous results for two gauge-equivalent NLEEs; in particular, the derivative non-linear Schrodinger equation.Comment: 29 pages, 5 figures, LaTeX, revised version of the original submission, to be published in Inverse Problem

Experimental feasibility of measuring the gravitational redshift of light using dispersion in optical fibers

This paper describes a new class of experiments that use dispersion in optical fibers to convert the gravitational frequency shift of light into a measurable phase shift or time delay. Two conceptual models are explored. In the first model, long counter-propagating pulses are used in a vertical fiber optic Sagnac interferometer. The second model uses optical solitons in vertically separated fiber optic storage rings. We discuss the feasibility of using such an instrument to make a high precision measurement of the gravitational frequency shift of light.Comment: 11 pages, 12 figure

Would a Flat Tax Stimulate Entrepreneurship in Germany?: A Behavioural Microsimulation Analysis Allowing for Risk

In debates about possible tax reforms, the impact on entrepreneurship is a primary concern. This paper estimates the ex-ante effects of the German tax reform 2000 and of two hypothetical flat tax scenarios on entries into and exits out of self-employment in Germany. For the estimation I apply a microsimulation model based on the tax-benefit model STSM and on structural microeconometric transition models. These structural models include an estimated parameter of risk aversion. The simulation results indicate that flatter tax systems discourage people from choosing self-employment, which is explained by the reduction of entrepreneurs ’ income risk through progressive taxation

Optical fiber relative humidity sensor based on a FBG with a di-ureasil coating

In this work we proposed a relative humidity (RH) sensor based on a Bragg grating written in an optical fiber, associated with a coating of organo-silica hybrid material prepared by the sol-gel method. The organo-silica-based coating has a strong adhesion to the optical fiber and its expansion is reversibly affected by the change in the RH values (15.0–95.0%) of the surrounding environment, allowing an increased sensitivity (22.2 pm/%RH) and durability due to the presence of a siliceous-based inorganic component. The developed sensor was tested in a real structure health monitoring essay, in which the RH inside two concrete blocks with different porosity values was measured over 1 year. The results demonstrated the potential of the proposed optical sensor in the monitoring of civil engineering structures