Evolution of weak noise and regular waves on dissipative shock fronts described by the Burgers model

The interaction of weak noise and regular signals with a shock wave having a finite width is studied in the framework of the Burgers equation model. The temporal realization of the random process located behind the front approaches it at supersonic speed. In the process of moving to the front, the intensity of noise decreases and the correlation time increases. In the central region of the shock front, noise reveals non-trivial behaviour. For large acoustic Reynolds numbers the average intensity can increase and reach a maximum value at a definite distance. The behaviour of statistical characteristics is studied using linearized Burgers equation with variable coefficients reducible to an autonomous equation. This model allows one to take into account not only the finite width of the front, but the attenuation and diverse character of initial profiles and spectra as well. Analytical solutions of this equation are derived. Interaction of regular signals of complex shape with the front is studied by numerical methods. Some illustrative examples of ongoing processes are given. Among possible applications, the controlling the spectra of signals, in particular, noise suppression by irradiating it with shocks or sawtooth waves can be mentioned.     

Total energy decay for the wave equation in exterior domains with a dissipation near infinity

We show that the energy of solutions to the initial boundary value problem for the wave equation in exterior domains with a dissipation which is localized only near infinity tends to zero as the time goes to infinity. We do not make any geometrical condition like star-shapedness on the boundary.     

Free energy and states of fractional-order hereditariness

Complex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.     

A modified Lin equation for the energy balance in isotropic turbulence

At sufficiently large Reynolds numbers, turbulence is expected to exhibit scale-invariance in an intermediate (“inertial”) range of wavenumbers, as shown by power law behavior of the energy spectrum and also by a constant rate of energy transfer through wavenumber. However, there is an apparent contradiction between the definition of the energy flux (i.e., the integral of the transfer spectrum) and the observed behavior of the transfer spectrum itself. This is because the transfer spectrum T(k) is invariably found to have a zero-crossing at a single point (at k = k_*), implying that the corresponding energy flux cannot have an extended plateau but must instead have a maximum value at k = k_*. This behavior was formulated as a paradox and resolved by the introduction of filtered/partitioned transfer spectra, which exploited the symmetries of the triadic interactions (J. Phys. A: Math. Theor., 2008). In this paper we consider the more general implications of that procedure for the spectral energy balance equation, also known as the Lin equation. It is argued that the resulting modified Lin equations (and their corresponding Navier–Stokes equations) offer a new starting point for both numerical and theoretical methods, which may lead to a better understanding of the underlying energy transfer processes in turbulence. In particular the filtered partitioned transfer spectra could provide a basis for a hybrid approach to the statistical closure problem, with the different spectra being tackled using different methods.     

生长及耗散波色-爱因斯坦凝聚中的怪波

利用达布变换法(Darboux transformation),解析的研究了生长及耗散波色-爱因斯坦凝聚(BEC)中的怪波.通过降维和无量纲化,将描述BEC的Gross-Pitaevskii (GP)方程转化成一维无量纲非线性薛定谔方程.利用达布变换,得到了一维非线性薛定谔方程的怪波解析解.根据解析结果,数值模拟了生长及耗散BEC中怪波的性质.结果表明,BEC中出现了一种典型的双洞怪波,并且BEC生长会延缓怪波的消失,而BEC的耗散会加速怪波的消失.     

Group and phase velocities in the free-surface visco-potential flow: New kind of boundary layer induced instability

Water wave propagation can be attenuated by various physical mechanisms. One of the main sources of wave energy dissipation lies in boundary layers. The present work is entirely devoted to thorough analysis of the dispersion relation of the novel visco-potential formulation. Namely, in this study we relax all assumptions of the weak dependence of the wave frequency on time. As a result, we have to deal with complex integro-differential equations that describe transient behaviour of the phase and group velocities. Using numerical computations, we show several snapshots of these important quantities at different times as functions of the wave number. Good qualitative agreement with previous study [D. Dutykh, Eur. J. Mech. B/Fluids 28 (2009) 430] is obtained. Thus, we validate in some sense approximations made anteriorly. There is an unexpected conclusion of this study. According to our computations, the bottom boundary layer creates disintegrating modes in the group velocity. In the same time, the imaginary part of the phase velocity remains negative for all times. This result can be interpreted as a new kind of instability which is induced by the bottom boundary layer effect.     

Granular dampers for the reduction of vibrations of an oscillatory saw

Instruments for surgical and dental application based on oscillatory mechanics submit unwanted vibrations to the operator’s hand. Frequently the weight of the instrument’s body is increased to dampen its vibration. Based on recent research regarding the optimization of granular damping we developed a prototype granular damper that attenuates the vibrations of an oscillatory saw twice as efficiently as a comparable solid mass.     

Dissipative or conservative cosmology with dark energy?

All evolutional paths for all admissible initial conditions of FRW cosmological models with dissipative dust fluid (described by dark matter, baryonic matter and dark energy) are analyzed using dynamical system approach. With that approach, one is able to see how generic the class of solutions leading to the desired property—acceleration—is. The theory of dynamical systems also offers a possibility of investigating all possible solutions and their stability with tools of Newtonian mechanics of a particle moving in a one-dimensional potential which is parameterized by the cosmological scale factor. We demonstrate that flat cosmology with bulk viscosity can be treated as a conservative system with a potential function of the Chaplygin gas type. We characterize the class of dark energy models that admit late time de Sitter attractor solution in terms of the potential function of corresponding conservative system. We argue that inclusion of dissipation effects makes the model more realistic because of its structural stability. We also confront viscous models with SNIa observations. The best fitted models are obtained by minimizing the χ² function which is illustrated by residuals and χ² levels in the space of model independent parameters. The general conclusion is that SNIa data supports the viscous model without the cosmological constant. The obtained values of χ² statistic are comparable for both the viscous model and ΛCDM model. The Bayesian information criteria are used to compare the models with different power-law parameterization of viscous effects. Our result of this analysis shows that SNIa data supports viscous cosmology more than the ΛCDM model if the coefficient in viscosity parameterization is fixed. The Bayes factor is also used to obtain the posterior probability of the model.     

Dissipation in Turbulent Shear Flows: A Wall Function Approach for High Reynolds Numbers

Dissipation effects that are neglected in almost all numerical codes when it comes to turbulent flows are analysed systematically. It is shown how the direct and the indirect dissipation can be implemented into the codes when asymptotic considerations about the flow behaviour close to a wall are taken into account. As an example, adiabatic pipe flow is analysed with special emphasis on the distribution of energy between the mechanical and thermal part of the total energy.     

Application of a self-sensing conductive probe for Si device imaging

For the evaluation of two-dimensional carrier profiles in semiconductor devices, we have developed a novel form of probe–sensor combined unit that uses an etched tungsten wire as a conductive probe, and commercially available quartz tuning fork as the force sensor. This unit has a self-sensing capability due to the piezoelectric effect of quartz tuning fork, thus obviating optical setup, and its conductivity is higher and more stable than that of conventional metal-coated Si cantilever. In addition, this probe–sensor combined unit is inexpensive and easy to use, when compared to the well-known optical methods of Si-based cantilever vibration detection system. Our scanning probe microscope using this probe–sensor combined unit is able to mapping the capacitive gradient signal (dC/dZ image) and internal damping of quartz tuning fork oscillation (dissipation image) while scanning the sample surface. In this letter, we show the results of visualization of the p–n junction locus of a Si metal–oxide–semiconductor field effect transistor in both dC/dZ and dissipation images.