Determining the second-harmonic signal in electrochemical systems

Processes of adsorption and desorption of the butanol-1, butanol-2, hexanol, pentanol, and isoamyl alcohol molecules on a mercury electrode are studied with use made of the method of a second-harmonic signal in the region of radiowave frequencies. Two potentials are simultaneously applied to the metal/solution interface, specifically, a constant potential and a weak variable potential. The magnitude of the constant potential is close to the corresponding potential of adsorption and the variable potential has an amplitude in the limits of 2 to 20 mV and a frequency varying from a few tens of hertzs to a few tens of kilohertzs. Despite the absence of charge transport during the adsorption between the alcohol molecules and the electrode, the quadratic dependence between a signal of electromagnetic radiation of the radiowave frequencies U and the amplitude of the variable potential E _v1 applied to the metal/solution interface is discovered for all peaks in the curves of the second-harmonic signal for various concentrations of alcohols, various frequencies, and various values of the amplitude of the variable potential. Investigations for systems containing chlorides of sodium, potassium, and cesium in addition to ethylene glycol are conducted. According to an analysis of obtained experimental data, the number of peaks increases with decreasing concentration of chlorides, whereas the size of the sodium, potassium, and cesium cations makes no impact on the magnitude of the emitted signal. At the same time, diminishing the concentration of the chlorides leads to a certain amplification of the signal.     

DNS of stochastically forced laminar plane Couette flow

Background of three dimensional hydrodynamic/vortical fluctuations in a stochastically forced, laminar, incompressible, plane Couette flow is simulated by direct numerical simulations (DNS). It was found that the fluctuating field has well pronounced peculiarities: (i) The hydrodynamic fluctuations exhibits non–exponential, transient growth; (ii) Streamwise non–constant fluctuations with the characteristic length scale of the order of the channel width are predominant in the fluctuating spectrum; (iii) Existence of coherent structures in the fluctuating background; (iv) Stochastic forcing breaks the spanwise reflection symmetry (inherent to the linear and full Navier–stokes equations in a case of the Couette flow) and inputs an asymmetry on dynamical processes. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct numerical simulation of stochastically forced laminar plane couette flow: peculiarities of hydrodynamic fluctuations

The background of three-dimensional hydrodynamic (vortical) fluctuations in a stochastically forced, laminar, incompressible, plane Couette flow is simulated numerically. The fluctuating field is anisotropic and has well pronounced peculiarities: (i) the hydrodynamic fluctuations exhibit nonexponential, transient growth; (ii) fluctuations with the streamwise characteristic length scale about 2 times larger than the channel width are predominant in the fluctuating spectrum instead of streamwise constant ones; (iii) nonzero cross correlations of velocity (even streamwise-spanwise) components appear; (iv) stochastic forcing destroys the spanwise reflection symmetry (inherent to the linear and full Navier-Stokes equations in a case of the Couette flow) and causes an asymmetry of the dynamical processes.     

Physics of the amplification of vortex disturbances in shear flows

The physics of the linear mechanism of the amplification of vortex disturbances in shear flows, which is due to the nonorthogonality of the eigenfunctions of the problem in the linear dynamics, is described. To obtain the clearest and simplest picture, a parallel flow with a linear velocity shear is studied, and the vortex disturbances are represented in the form of plane waves — spatial Fourier harmonics. On this level our physical approach is consonant with the nonmodal mathematical analysis of linear processes in shear flows, which has been actively cultivated in the last few years. The physics presented explains the non-monotonic growth of vortex disturbances in time at the linear stage of evolution. Moreover, being universal, the “language” employed in this work can also be used to describe the amplification of potential (acoustic) disturbances. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 517–522 (10 April 1996)     

Surface gravity waves in deep fluid at vertical shear flows

Special features of surface gravity waves in a deep fluid flow with a constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to a nontrivial modification of the dispersive characteristics of surface gravity wave modes. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study show that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. The generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the latter wave is generated more effectively for high shear rates. From the mathematical standpoint, the wave generation is caused by non-self-adjointness of the linear operators that describe the shear flow.     

Fluctuation background due to incompressible disturbances in laminar shear flows

The incompressible fluctuation background in laminar shear flows with a smooth velocity profile is investigated. Concrete calculations are performed for parallel Couette flow using nonmodal analysis of the linear dynamics of the disturbances. Nonmodal analysis makes it possible to grasp phenomena that could not be grasped in the early investigations, and thereby makes it possible to represent the fluctuation background in a completely new light: In incompressible shear flows the spatial spectral energy density of the fluctuation background is anisotropic, and furthermore in certain regions of wave-number space it is higher than that of the thermal noise. It is also shown that in the stationary state of the nonequilibrium system studied there exists a new, indirect channel for thermalization of the energy of the mean flow—energy is constantly transferred from the mean flow into the spatial Fourier harmonics of vortex pertubations and ultimately into heat. Possible manifestations of the fluctuation background described in this paper are listed. Zh. éksp. Teor. Fiz. 112, 1664–1674 (November 1997)     

A turbulence model in unbounded smooth shear flows: The weak turbulence approach

We discuss a new concept of the subcritical transition to turbulence in unbounded smooth (noninflectional) spectrally stable shear flows. This concept (the so-called bypass transition) follows from considering the nonnormality of the linear dynamics of vortex disturbances in shear flows and is most easily interpreted by tracing the evolution of spatial Fourier harmonics (SFHs) of the disturbances. The key features of the concept are as follows: the transition of the flow by only finite-amplitude vortex disturbances despite the fact that the phenomenon is energetically supported by a linear process (the transient growth of SFHs); the anisotropy of processes in the k space; the onset of chaos due to the dynamical (not stochastic) process—nonlinear processes that close the transition feedback loop by the angular redistribution of SFHs in the k space. The evolution of two-dimensional small-scale vortex disturbances in a parallel flow with a uniform shear is analyzed within the weak turbulence approach. This numerical test analysis is carried out to prove the most problematic statement of the concept, the existence of a positive feedback caused by the nonlinear process. Numerical calculations also show the existence of a threshold: if the amplitude of the initial disturbance exceeds the threshold value, the self-maintenance of disturbances becomes realistic. The latter is a characteristic feature of the flow transition to the turbulent state and its maintenance.     

A parallel multi-configuration self-consistent field algorithm

A scalable multi-configuration self-consistent field (MCSCF) algorithm is described. The method for optimizing the orbital and configurational parameters is based upon the two-step Newton–Raphson approach with an augmented orbital Hessian matrix. A single copy of the two-electron integrals in the molecular orbital basis is distributed over the memory of all processors. Storage of the augmented Hessian is avoided by re-computing its elements as needed. A replicated data approach is used to parallelize the configuration interaction step. Scalability to 1024 processors is demonstrated.     

Linear Dynamics of Perturbations in Flows with Constant Horizontal Shear

The dynamics of perturbations in shallow water and incompressible stratified fluid flows with constant horizontal shear are described using the nonmodal analysis. It is shown that the shear flow perturbations can be divided into two classes on the basis of the potential vorticity: rapidly oscillating wave perturbations with zero potential vorticity and slow vortex perturbations with nonzero potential vorticity. In the cases of weak and strong shear the main features of the dynamics of wave and vortex perturbations are studied analytically (using the WKBG method) and numerically. It is shown that for large times the wave perturbation energy increases linearly, i.e., the shear flow is algebraically unstable due to the growth of rapid wave perturbations. This instability can be of importance in processes of turbulence development and surface and internal wave generation.     

Discrete coherent amplification of oscillations by nonresonant forcing

A new mechanism of generation of oscillations in a linear forced oscillatory system is found. Natural oscillations may be generated at a "sharp" pulse (rapid variation) of the natural frequency. In this process oscillations are generated by nonresonant forcing, e.g., by the action of a constant, nonperiodic or periodic force (with driving frequency much less than the natural one). Repetitive pulses of the natural frequency result in emergence of oscillations that interfere and may give a powerful resultant output. These phenomena relate to a basis of the theory of open linear oscillatory systems.