scholarly journals The Linear Stability of Time-Dependent Baroclinic Shear

2010 ◽  
Vol 40 (3) ◽  
pp. 568-581 ◽  
Author(s):  
F. J. Poulin
Keyword(s):  
Steady State ◽  
Linear Stability ◽  
Growth Rates ◽  
Shear Flows ◽  
Mathieu Equation ◽  
Extreme Case ◽  
Time Dependent ◽  
Time Variability ◽  
Bounded Noise ◽  
Wide Range

Abstract This article aims to advance the understanding of inherent randomness in geophysical fluids by considering the particular example of baroclinic shear flows that are spatially uniform in the horizontal directions and aperiodic in time. The time variability of the shear is chosen to be the Kubo oscillator, which is a family of time-dependent bounded noise that is oscillatory in nature with various degrees of stochasticity. The author analyzed the linear stability of a wide range of temporally periodic and aperiodic shears with a zero and nonzero mean to get a more complete understanding of the effect of oscillations in shear flows in the context of the two-layer quasigeostrophic Phillips model. It is determined that the parametric mode, which exists in the periodic limit, also exists in the range of small and moderate stochasticities but vanishes in highly erratic flows. Moreover, random variations weaken the effects of periodicity and yield growth rates more similar to that of the time-averaged steady-state analog. This signifies that the periodic shear flows possess the most extreme case of stabilization and destabilization and are thus anomalous. In the limit of an f plane, the linear stability problem is solved exactly to reveal that individual solutions to the linear dynamics with time-dependent baroclinic shear have growth rates that are equal to that of the time-averaged steady state. This implies that baroclinic shear flows with zero means are linearly stable in that they do not grow exponentially in time. This means that the stochastic mode that was found to exist in the Mathieu equation does not arise in this model. However, because the perturbations grow algebraically, the aperiodic baroclinic shear on an f plane can give rise to nonlinear instabilities.

scholarly journals Constitutive relations for compressible granular flow in the inertial regime

2019 ◽  
Vol 874 ◽  
pp. 926-951 ◽  
Author(s):  
D. G. Schaeffer ◽  
T. Barker ◽  
D. Tsuji ◽  
P. Gremaud ◽  
M. Shearer ◽  
...  
Keyword(s):  
Steady State ◽  
Granular Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Practical Interest ◽  
Time Dependent ◽  
Direct Result ◽  
Wide Range ◽  
Inertial Regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology that does not suffer from such defects is proposed. In the framework of compressible $I$-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.

scholarly journals Growth Rate of White Dwarf Mass in Binaries

1989 ◽  
Vol 114 ◽  
pp. 507-510
Author(s):  
Mariko Kato ◽  
Hideyuki Saio ◽  
Izumi Hachisu
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Star Formation ◽  
Neutron Star ◽  
Mass Loss ◽  
White Dwarf ◽  
Accretion Rate ◽  
Time Dependent ◽  
Type I ◽  
Wide Range

AbstractThe growth rate of a white dwarf which accretes hydrogen-rich or helium matter is studied. If the accretion rate is relatively small, unstable shell flash occurs and during which the envelope mass is lost. We have followed the evolutions of shell flashes by steady state approach with wind mass loss solutions to determined the mass lost from the system for wide range of binary parameters. The time-dependent models are also calculated in some cases. The mass loss due to the Roche lobe overflow are taken into account. This results seriously affects the existing scenarios on the origin of the type I supernova or on the neutron star formation induced by accretion.

scholarly journals Stability and solution of the time-dependent Bondi–Parker flow

2020 ◽  
Vol 493 (2) ◽  
pp. 2834-2840
Author(s):  
Eric Keto
Keyword(s):  
Steady State ◽  
Transonic Flow ◽  
Initial Conditions ◽  
Steady State Solution ◽  
State Solution ◽  
Time Dependent ◽  
Hamiltonian Description ◽  
Bernoulli’S Equation ◽  
Wide Range ◽  
Isothermal And Adiabatic Flows

ABSTRACT Bondi and Parker derived a steady-state solution for Bernoulli’s equation in spherical symmetry around a point mass for two cases, respectively, an inward accretion flow and an outward wind. Left unanswered were the stability of the steady-state solution, the solution itself of time-dependent flows, whether the time-dependent flows would evolve to the steady state, and under what conditions a transonic flow would develop. In a Hamiltonian description, we find that the steady-state solution is equivalent to the Lagrangian implying that time-dependent flows evolve to the steady state. We find that the second variation is definite in sign for isothermal and adiabatic flows, implying at least linear stability. We solve the partial differential equation for the time-dependent flow as an initial-value problem and find that a transonic flow develops under a wide range of realistic initial conditions. We present some examples of time-dependent solutions.

scholarly journals Three-dimensional stability of an elliptical vortex in a straining field

1984 ◽  
Vol 142 ◽  
pp. 451-466 ◽  
Author(s):  
A. C. Robinson ◽  
P. G. Saffman
Keyword(s):  
Steady State ◽  
Linear Stability ◽  
Cross Section ◽  
Dimensional Stability ◽  
Growth Rates ◽  
Finite Strain ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Elliptical Cross ◽  
Dimensional Instability

The three-dimensional linear stability of a rectilinear vortex of elliptical cross-section existing as a steady state in an irrotational straining field is studied numerically in the case of finite strain. It is shown that the instability predicted analytically for weak strain persists for finite strain and that the weak-strain results continue to be quantitatively valid for finite strain. The dependence of the growth rates of the unstable modes on the strain and the axial-disturbance wavelength is discussed. It is also shown that a three-dimensional instability is always more unstable than a two-dimensional instability in the range of parameters of most interest.

The rheology of non-dilute dispersions of highly deformable viscoelastic particles in Newtonian fluids

2014 ◽  
Vol 763 ◽  
pp. 386-432 ◽  
Author(s):  
Reza Avazmohammadi ◽  
Pedro Ponte Castañeda
Keyword(s):  
Steady State ◽  
Simple Shear ◽  
Shear Flows ◽  
Rheological Behaviour ◽  
Time Dependent ◽  
Simple Shear Flow ◽  
Average Particle ◽  
Special Cases ◽  
Constitutive Properties ◽  
Extensional Flows

AbstractWe present a model for the rheological behaviour of non-dilute suspensions of initially spherical viscoelastic particles in viscous fluids under uniform Stokes flow conditions. The particles are assumed to be neutrally buoyant Kelvin–Voigt solids undergoing time-dependent finite deformations and exhibiting generalized neo-Hookean behaviour in their purely elastic limit. We investigate the effects of the shape dynamics and constitutive properties of the viscoelastic particles on the macroscopic rheological behaviour of the suspensions. The proposed model makes use of known homogenization estimates for composite material systems consisting of random distributions of aligned ellipsoidal particles with prescribed two-point correlation functions to generate corresponding estimates for the instantaneous (incremental) response of the suspensions, together with appropriate evolution laws for the relevant microstructural variables. To illustrate the essential features of the model, we consider two special cases: (i) extensional flow and (ii) simple shear flow. For each case, we provide the time-dependent response and, when available, the steady-state solution for the average particle shape and orientation, as well as for the effective viscosity and normal stress differences in the suspensions. The results exhibit shear thickening for extensional flows and shear thinning for simple shear flows, and it is found that the volume fraction and constitutive properties of the particles significantly influence the rheology of the suspensions under both types of flows. In particular, for extensional flows, suspensions of particles with finite extensibility constraints are always found to reach a steady state, while this is only the case at sufficiently low strain rates for suspensions of (less realistic) neo-Hookean particles, as originally reported by Roscoe (J. Fluid Mech., vol. 28, 1967, pp. 273–293) and Gao et al. (J. Fluid Mech., vol. 687, 2011, pp. 209–237). For shear flows, viscoelastic particles with high viscosities can experience a damped oscillatory motion of decreasing amplitude before reaching the steady state.

Spectroscopic Studies of Asparaginyl-tRNA Synthetase from Entamoeba histolytica

2019 ◽  
Vol 26 (6) ◽  
pp. 435-448
Author(s):  
Priyanka Biswas ◽  
Dillip K. Sahu ◽  
Kalyanasis Sahu ◽  
Rajat Banerjee
Keyword(s):  
Circular Dichroism ◽  
Steady State ◽  
Entamoeba Histolytica ◽  
Protein Concentration ◽  
Trna Synthetase ◽  
Solvent Exposure ◽  
Steady State Fluorescence ◽  
State Process ◽  
Wide Range ◽  
Circular Dichroïsm

Background: Aminoacyl-tRNA synthetases play an important role in catalyzing the first step in protein synthesis by attaching the appropriate amino acid to its cognate tRNA which then transported to the growing polypeptide chain. Asparaginyl-tRNA Synthetase (AsnRS) from Brugia malayi, Leishmania major, Thermus thermophilus, Trypanosoma brucei have been shown to play an important role in survival and pathogenesis. Entamoeba histolytica (Ehis) is an anaerobic eukaryotic pathogen that infects the large intestines of humans. It is a major cause of dysentery and has the potential to cause life-threatening abscesses in the liver and other organs making it the second leading cause of parasitic death after malaria. Ehis-AsnRS has not been studied in detail, except the crystal structure determined at 3 Å resolution showing that it is primarily α-helical and dimeric. It is a homodimer, with each 52 kDa monomer consisting of 451 amino acids. It has a relatively short N-terminal as compared to its human and yeast counterparts. Objective: Our study focusses to understand certain structural characteristics of Ehis-AsnRS using biophysical tools to decipher the thermodynamics of unfolding and its binding properties. Methods: Ehis-AsnRS was cloned and expressed in E. coli BL21DE3 cells. Protein purification was performed using Ni-NTA affinity chromatography, following which the protein was used for biophysical studies. Various techniques such as steady-state fluorescence, quenching, circular dichroism, differential scanning fluorimetry, isothermal calorimetry and fluorescence lifetime studies were employed for the conformational characterization of Ehis-AsnRS. Protein concentration for far-UV and near-UV circular dichroism experiments was 8 µM and 20 µM respectively, while 4 µM protein was used for the rest of the experiments. Results: The present study revealed that Ehis-AsnRS undergoes unfolding when subjected to increasing concentration of GdnHCl and the process is reversible. With increasing temperature, it retains its structural compactness up to 45ºC before it unfolds. Steady-state fluorescence, circular dichroism and hydrophobic dye binding experiments cumulatively suggest that Ehis-AsnRS undergoes a two-state transition during unfolding. Shifting of the transition mid-point with increasing protein concentration further illustrate that dissociation and unfolding processes are coupled indicating the absence of any detectable folded monomer. Conclusion: This article indicates that GdnHCl induced denaturation of Ehis-AsnRS is a two – state process and does not involve any intermediate; unfolding occurs directly from native dimer to unfolded monomer. The solvent exposure of the tryptophan residues is biphasic, indicating selective quenching. Ehis-AsnRS also exhibits a structural as well as functional stability over a wide range of pH.

scholarly journals Identification of DC Thermal Steady-State Differential Inductance of Ferrite Power Inductors

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3854
Author(s):  
Salvatore Musumeci ◽  
Luigi Solimene ◽  
Carlo Stefano Ragusa
Keyword(s):  
Steady State ◽  
Input Voltage ◽  
Switching Frequency ◽  
Ohmic Losses ◽  
Steady State Temperature ◽  
Wide Range ◽  
Average Current ◽  
Power Inductors ◽  
Saturable Inductor ◽  
Thermal Steady State

In this paper, we propose a method for the identification of the differential inductance of saturable ferrite inductors adopted in DC–DC converters, considering the influence of the operating temperature. The inductor temperature rise is caused mainly by its losses, neglecting the heating contribution by the other components forming the converter layout. When the ohmic losses caused by the average current represent the principal portion of the inductor power losses, the steady-state temperature of the component can be related to the average current value. Under this assumption, usual for saturable inductors in DC–DC converters, the presented experimental setup and characterization method allow identifying a DC thermal steady-state differential inductance profile of a ferrite inductor. The curve is obtained from experimental measurements of the inductor voltage and current waveforms, at different average current values, that lead the component to operate from the linear region of the magnetization curve up to the saturation. The obtained inductance profile can be adopted to simulate the current waveform of a saturable inductor in a DC–DC converter, providing accurate results under a wide range of switching frequency, input voltage, duty cycle, and output current values.

scholarly journals Spatiotemporal linear stability of viscoelastic free shear flows: Nonaffine response regime

2021 ◽  
Vol 33 (5) ◽  
pp. 054106
Author(s):  
D. Bansal ◽  
D. Ghosh ◽  
S. Sircar
Keyword(s):  
Linear Stability ◽  
Shear Flows

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

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