Asymmetric Perturbations Research Articles

Stability of the Shape of a Viscous Drop under Buoyancy-Driven Translation in a Hele-Shaw Cell

It has been shown (N. R. Gupta, A. Nadim, H. Haj-Hariri, and A. Borhan, J. Colloid Interface Sci.218, 338 1999) that a circular drop translating in a Hele-Shaw cell under the action of gravity is linearly stable for nonzero interfacial tension. In this paper, we use the boundary integral method to examine the nonlinear evolution of the shape of initially noncircular drops translating in a Hele-Shaw cell. For prolate initial deformations, it is found that the drop reverts to a circular shape for all finite Bond numbers considered. Initially oblate drops, on the other hand, are found to become unstable and break up if the initial shape perturbation is of sufficiently large magnitude. The critical conditions for the onset of drop breakup are examined in terms of the magnitude of the initial deformation as a function of Bond number. Two branches of marginal stability are identified and the effects of viscosity ratio and asymmetric initial perturbations on the stability diagram are discussed.

A Study on Regional Stability Analysis Methodology with a One-Point Neutron Kinetics Model

A methodology for boiling water reactor (BWR) regional stability with a one-point neutron kinetics model is proposed from the higher harmonics viewpoint and is verified with the Ringhals-1 stability benchmark test data. A one-point neutron kinetics model for regional stability analysis is derived from the spatial neutron diffusion equation using the mode decomposition technique. From the derivation, the intermode coupled reactivity coefficient is defined and applied to a frequency-domain BWR stability analysis model. The analysis model traces a unit power perturbation and calculates the open-loop transfer function as the power response to the input perturbation. Combined with the aforementioned reactivity coefficient and the asymmetric shape perturbation that reflects the first azimuthal mode, the first azimuthal mode is excited exclusively without any assumption on the ex-core model. Therefore, the regional stability can be evaluated with a normal recirculation flow model, which is employed for core-wide stability analysis. The methodology is verified with the Ringhals-1 stability benchmark test data, whose stability conditions were widely distributed and suitable for verification. The results show that the proposed methodology is quite appropriate for BWR regional stability analysis.

Generalized Stability Analyses of Asymmetric Disturbances in One- and Two-Celled Vortices Maintained by Radial Inflow

The dynamics of both transient and exponentially growing disturbances in two-dimensional vortices that are maintained by the radial inflow of a fixed cylindrical deformation field are investigated. Such deformation fields are chosen so that both one-celled and two-celled vortices may be studied. The linearized evolution of asymmetric perturbations is expressed in the form of a linear dynamical system dx/dt = Ax. The shear of the mean flow results in a nonnormal dynamical operator A, allowing for the transient growth of perturbations even when all the modes of the operator are decaying. It is found that one-celled vortices are stable to asymmetric perturbations of all azimuthal wavenumbers, whereas two-celled vortices can have low-wavenumber instabilities. In all cases, generalized stability analysis of the dynamical operator identifies the perturbations that grow the fastest, both instantaneously and over a finite period of time. While the unstable modal perturbations necessarily convert mean-flow vorticity to perturbation vorticity, the perturbations with the fastest instantaneous growth rate use the deformation of the mean flow to rearrange their vorticity fields into configurations with higher kinetic energy. Also found are perturbations that use a hybrid of these two mechanisms to achieve substantial energy growth over finite time periods. Inclusion of the dynamical effects of radial inflow—vorticity advection and vorticity stretching—is found to be extremely important in assessing the potential for transient growth and instability in these vortices. In the two-celled vortex, neglecting these terms destabilizes the vortex for azimuthal wavenumbers one and two. In the one-celled vortex, neglect of the radial inflow terms results in an overestimation of transient growth for all wavenumbers, and it is also found that for high wavenumbers the maximum transient growth decreases as the strength of the radial inflow increases. The effects of these perturbations through eddy flux divergences on the mean flow are also examined. In the one-celled vortex it is found that for all wavenumbers greater than one the net effect of most perturbations, regardless of their initial configuration, is to increase the kinetic energy of the mean flow. As these perturbations are sheared over they cause upgradient eddy momentum fluxes, thereby transferring their kinetic energy to the mean flow and intensifying the vortex. However, for wavenumber one in the one-celled vortex, and all wavenumbers in the two-celled vortex, it was found that nearly all perturbations have the net effect of decreasing the kinetic energy of the mean flow. In these cases, the kinetic energy of the perturbations accumulates in nearly neutral or unstable modal structures, so that energy acquired from the mean flow is not returned to the mean flow but instead is lost through dissipation.

Dopant distribution and energy transfer processes in crystals

This paper discusses the effects of the mutual asymmetric crystal field perturbations produced by near active and sensitizer ions in co-doped crystals. It is shown that modification of the spectral and dynamic properties of the perturbed ions justifies the division of the active and sensitizer ions systems in homogeneous subsystems and the particularities of energy transfer processes in these subsystems are presented. The discussion is illustrated for active rare earth ions in garnet crystals sensitized by Cr 3+ (in octahedral sites), Fe 3+ (in tetrahedral sites) or Yb 3+ (in dodecahedral sites). It is thus shown that the emission in sensitized laser crystals manifests different spectral and temporal properties from crystals with simple activation.

EXACT BOUNDARY CONDITION PERTURBATION FOR EIGENSOLUTIONS OF THE WAVE EQUATION

A perturbation method is presented to analytically calculate eigensolutions of the two dimensional wave equation when asymmetric perturbations are present in the boundary conditions. The unique feature of the method is that the sequence of boundary value problems governing the eigensolution perturbations are solved exactly through fifth order perturbation. Two classes of asymmetry are considered: irregular domain shapes that cannot be treated by analytical means, and variation of the boundary condition along the boundary. The unperturbed eigensolutions are those for an annular domain with axisymmetric boundary conditions. Irregularly shaped domains are studied in detail to demonstrate the method and the accuracy of the results, which are compared with exact values for the elliptical and rectangular domain cases. The results show excellent agreement with these known solutions for large shape distortions, an achievement resulting from the extension to higher order perturbation. Fourier representation of the boundary asymmetries allows analysis of arbitrary distributions of asymmetry. Additionally, the exact perturbation solution retains the explicit parameter dependence of continuous system analysis, generates simple expressions for the perturbed eigensolutions, addresses all distinct and degenerate axisymmetric system eigensolutions, and requires minimal computation and programming.

Singularities on Free Surfaces of Fluid Flows

Isolated singularities on free surfaces of two‐dimensional and axially symmetric three‐dimensional steady potential flows with gravity are considered. A systematic study is presented, where known solutions are recovered and new ones found. In two dimensions, the singularities found include those described by the Stokes solution with a 120° angle, Craya's flow with a cusp on the free surface, Gurevich's flow with a free surface meeting a rigid plane at 120° angle, and Dagan and Tulin's flow with a horizontal free surface meeting a rigid wall at an angle less than 120°. In three dimensions, the singularities found include those in Garabedian's axially symmetric flow about a conical surface with an approximately 130° angle, flows with axially symmetric cusps, and flows with a horizontal free surface and conical stream surfaces. The Stokes, Gurevich, and Garabedian flows are exact solutions. These are used to generate local solutions, including perturbations of the Stokes solution by Grant and Longuet‐Higgins and Fox, perturbations of Gurevich's flow by Vanden‐Broeck and Tuck, asymmetric perturbations of Stokes flow and nonaxisymmetric perturbations of Garabedian's flow. A generalization of the Stokes solution to three fluids meeting at a point is also found.

Numerical simulation of flow between rotating cylinders

A hybrid method combining pseudo-spectral and spectral element methods is used to simulate the three dimensional incompressible flow between rotating cylinders with moderate h R value and asymmetric perturbations. Results at different Reynolds numbers show that when instability sets in, the flow undergoes different states, indicating the existence of mode competition when a band of wave numbers becomes unstable.

Interaction of a slender vortex with a rigid sphere: Dynamics and far-field sound

Interactions between a slender vortex filament and a stationary rigid sphere are analyzed using a vortex element scheme which tracks the motion of the filament centerline. The filament velocity is expressed as the sum of a self-induced velocity and potential velocity due to the presence of the sphere. The self-induced velocity is estimated numerically using a line Biot–Savart integral which is carefully desingularized so as to reflect the correct asymptotic behavior of the core vorticity distribution under the influence of stretching and viscous diffusion. Meanwhile, the potential velocity is evaluated from a recently derived formula, which expresses it as a line integral along the image of the filament centerline in the sphere with regular weight functions. From the far-field behavior of an unsteady vortical flow outside a stationary sphere, formulas for the acoustic far field are obtained. It is shown that the interaction between the slender vortex filament and the sphere generates dipoles and quadrupoles in addition to the quadrupoles generated by the filament alone in space. The strengths and orientations of the dipoles and quadrupoles are completely determined by the time evolution of the weighted first and second moments of vorticity. The formulas are applied to compute the far-field sound generated by the passage of a slender vortex ring over the sphere. Both coaxial and noncoaxial passage events are analyzed in the computations, as well as the effects of initial core size and asymmetric perturbations.

Complex dynamics of mass-closed coupled autocatalytic systems in response to minute asymmetric perturbations

The role of kinetic coupling in catering to a remote-control mechanism for the onset and regulation of self-organization phenomena in a multicompartmental biochemical system has been examined. Using two cyclic autocatalytic reaction networks operating in two chambers separated by a membrane and coupled through a common cofactor, it has been demonstrated that (i) in response to asymmetric perturbations, the coupled reaction networks exhibit a variety of temporal self-organization phenomena such as bistability, multiple periodicity, hard excitation and coexistence of aperiodic oscillation with limit cycle even in mass-closed conditions; (ii) without disturbing a network directly, its dynamic behaviour can be regulated by perturbing some other network kinetically coupled to it and (iii) the dynamics of two coupled networks can be made to flip-flop between oscillatory and steady-states simply by modulating the time of application of external perturbations. The extreme sensitivity of this model to minute asymmetric fluctuations in the environment can predict how the impact of local changes in physico-chemical conditions can be transmitted from one compartment to another through coupled biochemical pathways in a living cell.

Modulation of synaptosomal plasma membrane-bound enzyme activity through the perturbation of plasma membrane lipid structure by bupivacaine.

We investigated modulations of lipid dynamics and lipid-protein interactions of rat brain synaptosomal plasma membrane (SPM) as one of the possible mechanisms by which the local anesthetic bupivacaine (BPV) has an adverse effect on nerve cell function, with SPM-bound enzyme activity used as a functional probe. The kinetics of BPV impact on the activity of the endoenzymes Ca2+/Mg2+-stimulated ATPase and Na+/K+-stimulated ATPase and the active concentrations of the drug were relevant to those that produce biphasic systemic toxicity. Arrhenius plots of these enzymes showed a transition temperature of 26.6 +/- 1.8 degrees C and 24.5 +/- 1.2 degrees C (mean +/- SD), respectively, in control SPM, which shifted to 17.1 +/- 0.95 degrees C (P < 0.01) and 18.2 +/- 0.85 degrees C (P < 0.05) in SPM treated with 10(-5) M BPV. The Hill coefficients for the allosteric inhibition of Ca2+/Mg2+-stimulated ATPase by Na+ and Na+/K+-stimulated ATPase by fluoride decreased from 1.73 +/- 0.20 and 1.95 +/- 0.25, respectively, in controls to 0.92 +/- 0.09 (P < 0.001) and 1.09 +/- 0.11 (P < 0.001) in the presence of 10(-5) M BPV. The fluidity perturbation in the microenvironment of the ectoenzyme acetylcholinesterase was observed only at 5 x 10(-3) M BPV, as confirmed by the disparity in transition temperature between the controls (22.3 +/- 1.2 degrees C) and the BPV-treated SPM (17.5 +/- 0.8 degrees C, P < 0.01) and that in the Hill coefficient in the two groups: 2.15 +/- 0.24 and 0.97 +/- 0.12 (P < 0.001), respectively. We propose that under physiological conditions, the neutral and protonated forms of local anesthetics can affect nerve cell function through the asymmetric perturbation of the membrane lipid structure, accompanied by synaptosomal plasma membrane-bound enzyme dysfunction.

Modulation of Synaptosomal Plasma Membrane-Bound Enzyme Activity Through the Perturbation of Plasma Membrane Lipid Structure by Bupivacaine

We investigated modulations of lipid dynamics and lipid-protein interactions of rat brain synaptosomal plasma membrane (SPM) as one of the possible mechanisms by which the local anesthetic bupivacaine (BPV) has an adverse effect on nerve cell function, with SPM-bound enzyme activity used as a functional probe. The kinetics of BPV impact on the activity of the endoenzymes Ca2+/Mg2+-stimulated ATPase and Na+/K+-stimulated ATPase and the active concentrations of the drug were relevant to those that produce biphasic systemic toxicity. Arrhenius plots of these enzymes showed a transition temperature of 26.6 +/- 1.8[degree sign]C and 24.5 +/- 1.2[degree sign]C (mean +/- SD), respectively, in control SPM, which shifted to 17.1 +/- 0.95[degree sign]C (P < 0.01) and 18.2 +/- 0.85[degree sign]C (P < 0.05) in SPM treated with 10-5 M BPV. The Hill coefficients for the allosteric inhibition of Ca2+/Mg2+-stimulated ATPase by Na+ and Na+/K+-stimulated ATPase by fluoride decreased from 1.73 +/- 0.20 and 1.95 +/- 0.25, respectively, in controls to 0.92 +/- 0.09 (P < 0.001) and 1.09 +/- 0.11 (P < 0.001) in the presence of 10-5 M BPV. The fluidity perturbation in the microenvironment of the ectoenzyme acetylcholinesterase was observed only at 5 x 10-3 M BPV, as confirmed by the disparity in transition temperature between the controls (22.3 +/- 1.2[degree sign]C) and the BPV-treated SPM (17.5 +/- 0.8[degree sign]C, P < 0.01) and that in the Hill coefficient in the two groups: 2.15 +/- 0.24 and 0.97 +/- 0.12 (P < 0.001), respectively. Implications: We propose that under physiological conditions, the neutral and protonated forms of local anesthetics can affect nerve cell function through the asymmetric perturbation of the membrane lipid structure, accompanied by synaptosomal plasma membrane-bound enzyme dysfunction. (Anesth Analg 1997;85:1337-43)

New perturbation theory for the nonstationary anharmonic oscillator

The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wave function the variational-iterational method is proposed, that make it possible to correct both the amplitude and the phase of wave function. As an application the first order correction are proposed both for wave function and S-matrix elements for asymmetric perturbation potential of type $V(x,\tau)=\alpha (\tau)x^3+\beta (\tau)x^4.$ The transition amplitude ''ground state - ground state'' $W_{00}(\lambda ;\rho)$ is analyzed in detail depending on perturbation parameter $\lambda $ (including strong coupling region $% \lambda $ $\sim 1$) and one-dimensional refraction coefficient $\rho $.

Application of Bragg-confined semiconductor structures for higher-energy resonant intersubband second-harmonic generation

The existence of bound electron states above the barrier in Bragg-confined structures is proposed as a means of extending the range of photon energies suitable for resonant intersubband second-harmonic generation beyond what is available in conventional quantum-well structures. Within the envelope-function approximation the expressions are first derived for energies and wave functions of bound states in Bragg structures with an asymmetric perturbation layer. A systematic procedure, based on supersymmetric quantum mechanics, is then described for the design of optimized structures to get the maximum nonlinear susceptibility. An example of a calculation for the case of pump photon energy \ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}240 meV is also presented and the design aspects of such structures are considered.

The nonlinear Schrödinger equation: Asymmetric perturbations, traveling waves and chaotic structures

Abstract It is well known that for certain parameter regimes the periodic focusing Non-linear Schrodinger (NLS) equation exhibits a chaotic response when the system is perturbed. When even symmetry is imposed the mechanism for chaotic behavior is due to the symmetric subspace being separated by homoclinic manifolds into disjoint invariant regions. For the even case the transition to chaotic behavior has been correlated with the crossings of critical level sets of the constants of motion (homoclinic crossings). Using inverse spectral theory, it is shown here that in the symmetric case the homoclinic manifolds do not separate the full NLS phase space. Consequently the mechanism of homoclinic chaos due to homoclinic crossings is lost. Near integrable dynamics, when no symmetry constraints are imposed, are examined and an example of a temporal irregular solution that exhibits random flipping between left and right traveling waves is provided.

Modelling the role of cell-cell adhesion in the growth and development of carcinomas

In this paper, a mathematical model is presented to describe the evolution of an avascular solid tumour in response to an externally-supplied nutrient. The growth of the tumour depends on the balance between expansive forces caused by cell proliferation and cell-cell adhesion forces which exist to maintain the tumour's compactness. Cell-cell adhesion is incorporated into the model using the Gibbs-Thomson relation which relates the change in nutrient concentration across the tumour boundary to the local curvature, this energy being used to preserve the cell-cell adhesion forces. Our analysis focuses on the existence and uniqueness of steady, radially-symmetric solutions to the model, and also their stability to time-dependent and asymmetric perturbations. In particular, our analysis suggests that if the energy needed to preserve the bonds of adhesion is large then the radially-symmetric configuration is stable with respect to all asymmetric perturbations, and the tumour maintains a radially-symmetric structure—this corresponds to the growth of a benign tumour. As the energy needed to maintain the tumour's compactness diminishes so the number of modes to which the underlying radially-symmetric solution is unstable increases—this corresponds to the invasive growth of a carcinoma. The strength of the cell-cell bonds of adhesion may at some stage provide clinicians with a useful index of the invasive potential of a tumour.

Splitting instability: the unstable double wells

In this paper we perform the semiclassical analysis of a pair of resonances in the case of a quasi-symmetrical unstable double well. We consider two kinds of asymmetric perturbations: one supported in the infinite external well, the other one of the Stark kind. We prove that the first perturbation is able to localize each state inside one of the internal wells so that we have linear Stark effect and vanishing of the splitting at the crossing point of the two resonances. This phenomenon is critical in the ratio between the internal and external barrier lengths, and the critical value of the ratio is close to two. Possible applications to the molecular structure and to the vanishing of the inversion frequency are briefly discussed.

An exact solution of the stochastic Liouville equation: The two-level system coupled to an asymmetric dichotomous field

Applying the technique of Brissaud and Firsh an exact expression can be derived for the averaged density matrix of the two-level system interacting with an asymmetric dichotomous field. Expressions for the level populations valid at any Kubo number are presented for the energetically degenerated two-level system as well as for the case of a large energy difference between the levels. It can be demonstrated that the asymmetric dichotomous perturbation favors the coherent transfer in the case of an energetically degenerated two-level system and does not result in an asymmetric steady-state population for the non-degenerated case.

Chiral non-racemic C 60 derivatives: A proposed sector rule for fullerene absolute configuration

A number of higher fullerenes as well as carbon nanotubes have been predicted to be chiral. Our lab has recently reported the resolution and CD spectra of several enantiomeric C 60 derivatives. It appears that chromatographic resolutions using Whelk-O columns are rather general. Using optically active enones and dienes, non-racemic C 60 adducts can also be formed. Recently we have discovered that fullerene CD spectra appear to arise from a UV band diagnostic for reaction at the CC bond between two six membered rings, the most common site for mono-addition. A Cotton effect is observed in the CD associated with this chromophore and allows proposal of a sector rule for fullerene chirality. Preparation of chiral (non-racemic) fullerene adducts of known absolute configuration allows assignment of the sign to each of the sectors. These CD bands are due to asymmetric perturbation of an intrinsically symmetric chromophore and provide a new tool for a priori determination of absolute configuration.

Stability of a thermal plasma jet

The stability of a slab model of a jet moving in an external plasma is investigated, assuming the configuration to be characterized by a general heat-loss function. Numerical results are obtained for the growth rates of unstable modes, both for symmetric and asymmetric perturbations for equal parallel magnetic fields along or transverse to the propagation vector in the wide and slender jet approximations. Special configurations of an incompressible jet moving past a thermal plasma and also of a thermal plasma moving past an incompressible static plasma are also considered.

Structural basis for ligand discrimination and response initiation in the heme-based oxygen sensor FixL.

FixL is a multiple-domain bacterial O2-sensing protein that modulates the activity of its kinase domain in response to O2 concentration. The kinase activity is coupled, via phosphoryl transfer, to transcriptional activation by a response-regulating protein, FixJ. Heme ligation resulting in a transition from high to low spin inhibits the kinase through an, as yet, ill-defined mechanism. This report presents spectroscopic, kinetic, and thermodynamic data on various complexes of two deletion derivatives of Rhizobium meliloti FixL, FixLN (the heme domain) and a functional heme kinase, FixL*. Resonance Raman characterization of metFixLN and metFixL* indicates that the heme core is smaller than that observed in metmyoglobin and is indicative of a five-coordinate high-spin heme in metFixLs. Resonance Raman spectra of FixL-CO adducts reveal that the Fe-C = O unit and/or its electrostatic environment in FixL*-CO is distorted relative to that in FixLN-CO. The 1H NMR spectra of the met forms further support the model of an asymmetric perturbation of the heme pocket structure associated with the presence of the kinase domain in FixL*. Observation of equivalent Fe-imidazole stretching vibrations for deoxyFixLN and deoxyFixL* (212 cm-1) indicates that the source of this perturbation in the heme pocket of FixL* does not lie on the proximal side of the heme. The equivalent Fe-imidazole stretching frequencies for deoxyFixLN and FixL* indicate that the presence of the kinase domain does not alter the relative strength of the proximal Fe-imidazole bond and that the proximal imidazole ligand is weakly H-bonded, probably to a backbone carbonyl group. Kinetic and thermodynamic data for the reactions of cyanide and fluoride ions with FixL are consistent with shape selectivity due to steric and/or an anisotropic electrostatic field in the distal heme pocket being responsible for the unique reactivities (or lack thereof) of FixL with ligands, i.e., O2, CO, CN-, F-, N3-, and SCN-. While the rate constants for binding of CN- to metFixLN and metFixL* are an order of magnitude slower than that for metMb, the stabilities of these complexes and metMb-CN are nearly the same. Neither N3- nor SCN- binds to the heme with measurable affinity. Since other ferric heme proteins form stable adducts with these ligands, the inability of FixL to form analogous complexes suggests that the ligand selectivity of this protein is rooted in insurmountable activation barriers to the binding of ligands containing more than two atoms and for ligands whose lowest-energy coordination geometries are linear. This allows the natural O2 ligand to compete kinetically with other naturally occurring ligands that form stable complexes with unencumbered hemes. Moreover, the rate constant for binding of CN- to the functional heme-kinase (metFixL*) is smaller than its metFixLN counterpart and the stability of metFixL*-CN is measurably lower than that of metFixLN-CN. This indicates that the contacts between the heme and kinase domains of FixL* impose more stringent geometric constraints on ligand binding than FixLN. The kinase is thus implicated in a possible mechanism for phosphate-dependent feedback control over ligand affinity of the heme.