Interaction of acoustic waves and piezoelectric structures

In the paper, we investigate the basic transmission problems arising in the model of fluid‐solid acoustic interaction when a piezo‐ceramic elastic body ( Ω ⁺ ) is embedded in an unbounded fluid domain ( Ω ^? ). The corresponding physical process is described by boundary‐transmission problems for second order partial differential equations. In particular, in the bounded domain Ω ⁺ , we have 4 × 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain Ω ^? , we have a scalar Helmholtz equation describing acoustic wave propagation. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations, the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces. Copyright © 2014 John Wiley & Sons, Ltd.     

Temperature‐concentration oscillations as a result of nanoheterophase structure of concentrated aqueous solutions of salts

Detailed precision investigation of aqueous solutions of NaBr·2H₂O, KBr, RbNO₃, and K₂SO₄ salts showed oscillations of crystal‐solution phase equilibria in the temperature range of 15–45 °C. The maximum deviations from the smooth correlation between the saturation temperature and the salt concentration (up to 4% of concentration and up to 10 °C) were found to correspond to simplest salt‐water ratios. Recently, similar trends were observed for NaNO₃, KNO₃ and K₂CrO₄ solutions. Oscillation amplitudes for saturation temperature in the investigated series decreased in the following orders: Na⁺→K⁺, Rb⁺, NH₄⁺ (nitrate systems), CrO₄^2–→SO₄^2– and Br^–→NO₃^– (potassium systems), and NO₃^–→Br^– (sodium systems). Increase in total content of impurities (2‐4‐fold) in solution results in 1.5‐2‐fold elevation of the oscillation amplitudes. A concept of nanoheterophase solution was suggested to account for the observed temperature‐concentration oscillations. The concept is based on the original experimental data on interrelated variation of different properties of aqueous salt solutions depending on their concentrations. Characteristic features of the phase diagrams are discussed and influence of the oscillations on crystal growth is elucidated. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Landau–Zener–Stückelberg interferometry

A transition between energy levels at an avoided crossing is known as a Landau–Zener transition. When a two-level system (TLS) is subject to periodic driving with sufficiently large amplitude, a sequence of transitions occurs. The phase accumulated between transitions (commonly known as the Stückelberg phase) may result in constructive or destructive interference. Accordingly, the physical observables of the system exhibit periodic dependence on the various system parameters. This phenomenon is often referred to as Landau–Zener–Stückelberg (LZS) interferometry. Phenomena related to LZS interferometry occur in a variety of physical systems. In particular, recent experiments on LZS interferometry in superconducting TLSs (qubits) have demonstrated the potential for using this kind of interferometry as an effective tool for obtaining the parameters characterizing the TLS as well as its interaction with the control fields and with the environment. Furthermore, strong driving could allow for fast and reliable control of the quantum system. Here we review recent experimental results on LZS interferometry, and we present related theory.     

Numerical simulation of bubble dynamics in a Phan-Thien–Tanner liquid: Non-linear shape and size oscillatory response under periodic pressure

We study non-linear bubble oscillations driven by an acoustic pressure with the bubble being immersed in a viscoelastic, Phan-Thien–Tanner liquid. Solution is provided numerically through a method which is based on a finite element discretization of the Navier–Stokes flow equations. The proposed computational approach does not rely on the solution of the simplified Rayleigh–Plesset equation, is not limited in studying only spherically symmetric bubbles and provides coupled solutions for the velocity, stress fields and bubble interface. We present solutions for non-spherical bubbles, with asphericity being addressed by means of Legendre polynomials or associated Legendre functions. A parametric investigation of the bubble dynamical oscillatory response as a function of the fluid rheological properties shows that the amplitude of bubble oscillations drastically increases as liquid elasticity (quantified by the Deborah number) increases or as liquid viscosity decreases (quantified by the Reynolds number). Extensive numerical calculations demonstrate that increasing elasticity and/or viscosity of the surrounding liquid tend to stabilize the shape anisotropy of an initially non-spherical bubble. Results are shown for pressure amplitudes 0.2–2 MPa and Deborah, Reynolds numbers in the intervals of 1–8 and 0.094–1.256, respectively.     

Physical understanding of complex multiscale biochemical models via algorithmic simplification: Glycolysis in Saccharomyces cerevisiae

Large-scale models of cellular reaction networks are usually highly complex and characterized by a wide spectrum of time scales, making a direct interpretation and understanding of the relevant mechanisms almost impossible. We address this issue by demonstrating the benefits provided by model reduction techniques. We employ the Computational Singular Perturbation (CSP) algorithm to analyze the glycolytic pathway of intact yeast cells in the oscillatory regime. As a primary object of research for many decades, glycolytic oscillations represent a paradigmatic candidate for studying biochemical function and mechanisms. Using a previously published full-scale model of glycolysis, we show that, due to fast dissipative time scales, the solution is asymptotically attracted on a low dimensional manifold. Without any further input from the investigator, CSP clarifies several long-standing questions in the analysis of glycolytic oscillations, such as the origin of the oscillations in the upper part of glycolysis, the importance of energy and redox status, as well as the fact that neither the oscillations nor cell-cell synchronization can be understood in terms of glycolysis as a simple linear chain of sequentially coupled reactions.     

Singular Hopf bifurcations and mixed-mode oscillations in a two-cell inhibitory neural network

Recent studies of a firing rate model for neural competition as observed in binocular rivalry and central pattern generators [R. Curtu, A. Shpiro, N. Rubin, J. Rinzel, Mechanisms for frequency control in neuronal competition models, SIAM J. Appl. Dyn. Syst. 7 (2) (2008) 609-649] showed that the variation of the stimulus strength parameter can lead to rich and interesting dynamics. Several types of behavior were identified such as: fusion, equivalent to a steady state of identical activity levels for both neural units; oscillations due to either an escape or a release mechanism; and a winner-take-all state of bistability. The model consists of two neural populations interacting through reciprocal inhibition, each endowed with a slow negative-feedback process in the form of spike frequency adaptation. In this paper we report the occurrence of another complex oscillatory pattern, the mixed-mode oscillations (MMOs). They exist in the model at the transition between the relaxation oscillator dynamical regime and the winner-take-all regime. The system distinguishes itself from other neuronal models where MMOs were found by the following interesting feature: there is no autocatalysis involved (as in the examples of voltage-gated persistent inward currents and/or intrapopulation recurrent excitation) and therefore the two cells in the network are not intrinsic oscillators; the oscillations are instead a combined result of the mutual inhibition and the adaptation. We prove that the MMOs are due to a singular Hopf bifurcation point situated in close distance to the transition point to the winner-take-all case. We also show that in the vicinity of the singular Hopf other types of bifurcations exist and we construct numerically the corresponding diagrams.     

Smoothing arithmetic error terms: the case of the Euler φ function

In many cases known methods of detecting oscillations of arithmetic error terms involve certain smoothing pro‐cedures. Usually an application of the smoothing operator does not change significantly the order of magnitude of the error under consideration. This is so for instance in the case of the classical error terms known in the prime number theory. The main purpose of this paper is to show that the situation for primes is not general. Considering the error term in the asymptotic formula for the Euler totient function we show that just one application of an integral smoothing operator changes situation dramatically: the order of magnitude of drops from x to √x (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Selectivity and efficiency of different reversed-phase and mixed-mode sorbents to preconcentrate and isolate aroma molecules

A comparison of the ability of different sorbent systems, including mixed-mode resins and reversed-phase sorbents, to extract and isolate volatile molecules from hydroalcoholic medium has been carried out by means of the determination of liquid–solid distribution coefficients. Eighteen volatile compounds covering a wide range of physicochemical properties (acids, bases and neutrals) and chemical functionalities, and thirteen different sorbents have been tested. LiChrolut EN and Isolute ENV (both polymeric with high surface area) showed the highest retention capability for nearly all analytes at all pHs tested. Exceptions were 2,3,5-trimethylpyrazine, most efficiently extracted with Strata XC at acidic pH, and indole best retained with Oasis MCX and Strata XC at any pH. Although nearly all basic compounds were most selectively extracted with cationic mixed-mode resins at acid pHs and 3-mercaptohexyl acetate and m-cresol show maxima α at pH 10 with Oasis MAX, the α values obtained have been relatively low, which suggests that retention is not particularly driven by ionic forces. The study has also shown that selectivity depends on the pH, the exact kind of mixed-mode sorbent and on the polarity of the analyte. High selectivity towards ionogenic compounds can be obtained by combining retention in mixed mode, a rinsing with a non-polar solvent and further elution with a solvent containing a neutralizing agent. However, not all the ionogenic molecules seem to be retained in ionic mode in the conditions tested and the complete elution of some analytes can be difficult, which suggests that analyte-specific isolation procedures should be analyzed case by case.     

High performance liquid chromatography separation of structurally related enkephalins on quaternary ammonium-embedded stationary phase in isocratic mode

Separation of twelve enkephalins was investigated on a quaternary ammonium-embedded stationary phase (Stability BS-C23). Variation of buffer pH of the mobile phase highlighted the complex relationship between repulsive/attractive electrostatic interactions and the reversed-phase partitioning mechanism. The effect of three different anions employed as additives (phosphate, chloride and perchlorate) was examined at various concentrations and two pH values (acidic and neutral). At pH 2.5, an increase in the anion eluent concentration resulted in a higher retention factors of positively charged enkephalins. This effect was more pronounced when perchlorate ions were added to the mobile phase rather than phosphate and chloride ions, due to chaotropic and ion-pairing effects. In contrast, at pH 7.5, retention factors of negatively charged enkephalins decreased when these salts were added, due to an anion-exchange mechanism. Perchlorate caused a sharper decrease than chloride and phosphate anions did. The results presented here provide insight into the possible adjustment of retention and separation of peptides on a mixed-mode stationary phase (BS-C23) by a careful control of the buffer pH, the nature and concentration of anions, added to the buffer, and organic modifier content.     

Weak anion-exchange hypercrosslinked sorbent in on-line solid-phase extraction–liquid chromatography coupling to achieve automated determination with an effective clean-up

A mixed-mode polymeric sorbent was on-line coupled to liquid chromatography (LC) for the first time and applied to the selective solid-phase extract a group of pharmaceuticals in complex environmental water samples. The mixed-mode polymeric sorbent is a high-specific surface area hypercrosslinked polymer resin (HXLPP) in the form of monodisperse microspheres further modified with 1,2-ethylenediamine (EDA) moieties. These properties allow its application as a weak anion-exchange (WAX) sorbent in the on-line solid-phase extraction (SPE) coupling. The on-line SPE-LC method developed using the HXLPP-WAX sorbent was successfully applied to percolate a large volume of ultrapure (500 ml), river (250 ml) and effluent sewage (100 ml) water samples. In all the cases, the HXLPP-WAX resin provided near total recoveries of the most acidic compounds studied and clean chromatograms. This is because the ion-exchange interactions enable a washing step to be added to the SPE protocol that removes the compounds with weak acidic, neutral and basic properties from the sample matrix.