Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

Relativistic velocity - potential hydrodynamics and stellar stability

The equations of relativistic, perfect-fluid hydrodynamics are cast in Eulerian form using six scalar "velocity-potential" fields, each of which has an equation of evolution. These equations determine the motion of the fluid through the equation

U_ʋ=µ^-1 (ø,_ʋ + αβ,_ʋ + ƟS,_ʋ).

Einstein's equations and the velocity-potential hydrodynamical equations follow from a variational principle whose action is

I = (R + 16π p) (-g)^1/2 d⁴x,

where R is the scalar curvature of spacetime and p is the pressure of the fluid. These equations are also cast into Hamiltonian form, with Hamiltonian density –T₀⁰ (-g^oo)^-1/2.

The second variation of the action is used as the Lagrangian governing the evolution of small perturbations of differentially rotating stellar models. In Newtonian gravity this leads to linear dynamical stability criteria already known. In general relativity it leads to a new sufficient condition for the stability of such models against arbitrary perturbations.

By introducing three scalar fields defined by

ρ ᵴ = ∇λ + ∇x(xi + ∇xɣi)

(where ᵴ is the vector displacement of the perturbed fluid element, ρ is the mass-density, and i, is an arbitrary vector), the Newtonian stability criteria are greatly simplified for the purpose of practical applications. The relativistic stability criterion is not yet in a form that permits practical calculations, but ways to place it in such a form are discussed.

Stability analysis and observer design for discrete-time SEIR epidemic models

This paper applies Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points is discussed for the discrete-time case. Afterwards, the design of a state observer for this discrete-time SEIR epidemic model is tackled. The analysis of the model along with the observer design is faced in an implicit way instead of obtaining first an explicit formulation of the system which is the novelty of the presented approach. Moreover, some sufficient conditions to ensure the asymptotic stability of the observer are provided in terms of a matrix inequality that can be cast in the form of a LMI. The feasibility of the matrix inequality is proved, while some simulation examples show the operation and usefulness of the observer.

On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.

On the stability of a rod adhering to a rigid surface: Shear-induced stable adhesion and the instability of peeling

Using variational methods, we establish conditions for the nonlinear stability of adhesive states between an elastica and a rigid halfspace. The treatment produces coupled criteria for adhesion and buckling instabilities by exploiting classical techniques from Legendre and Jacobi. Three examples that arise in a broad range of engineered systems, from microelectronics to biologically inspired fiber array adhesion, are used to illuminate the stability criteria. The first example illustrates buckling instabilities in adhered rods, while the second shows the instability of a peeling process and the third illustrates the stability of a shear-induced adhesion. The latter examples can also be used to explain how microfiber array adhesives can be activated by shearing and deactivated by peeling. The nonlinear stability criteria developed in this paper are also compared to other treatments. © 2012 Elsevier Ltd. All rights reserved.

Effects of annealing time and Si cap layer thickness on the Si/SiGe/Si heterostructures thermal stability

The effects of annealing time and Si cap layer thickness: on the thermal stability of the Si/SiGe/Si heterostructures deposited by disilane and solid-Ge molecule beam epitaxy were investigated. It is found that in the same strain state of the SiGe layers the annealing time decreases with increasing Si cap layer thickness. This effect is analyzed by a force-balance theory and an equation has been obtained to characterize the relation between the annealing time and the Si cap layer thickness. (C) 2001 Elsevier Science B.V. All rights reserved.

Electro-optical properties and temporal stability of the guest-host DCNP/PEK-c polymer thin film

The polyetherketone (PEK-c) guest-host system thin films in which the range of the weight percent of 3-(1,1-dicyanothenyl)-1-phenyl-4, 5- dihydro-1H-pryazole (DCNP) is from 20% to 50% were prepared. The predicted high value of electro-optical (EO) coefficient gamma(33) = 48.8 pm/V by using two-level model was obtained when the weight percent of DCNP in the polymer system is 40%, whereas EO coefficients are attenuated at higher chromophore loading then 40%. The temporal stability of the EO activity of the guest-host polymer was evaluated by probing the decay of the orientational order of the chromophores in the polymer system.

Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers

The analytic solutions of coupled-mode equations of four-wave mixings (FWMs) are achieved by means of the undepleted approximation and the perturbation method. The self-stability mechanism of the FWM processes is theoretically proved and is applicable to design a new kind of triple-wavelength erbium-doped fiber lasers. The proposed fiber lasers with excellent stability and uniformity are demonstrated by using a flat-near-zero-dispersion high-nonlinear photonic-crystal-fiber. The significant excellence is analyzed in theory and is proved in experiment. Our fiber lasers can stably lase three waves with the power ripple of less than 0.4 dB. (c) 2005 Elsevier B.V. All rights reserved.

Effects of annealing time and Si cap layer thickness on the Si/SiGe/Si heterostructures thermal stability

The effects of annealing time and Si cap layer thickness: on the thermal stability of the Si/SiGe/Si heterostructures deposited by disilane and solid-Ge molecule beam epitaxy were investigated. It is found that in the same strain state of the SiGe layers the annealing time decreases with increasing Si cap layer thickness. This effect is analyzed by a force-balance theory and an equation has been obtained to characterize the relation between the annealing time and the Si cap layer thickness. (C) 2001 Elsevier Science B.V. All rights reserved.

Structural stability of C-60 films under the bombardment of 1.95 GeV Kr ions

The structural stability of C-60 films under the bombardment of 1.95 GeV Kr ions is investigated. The irradiated C-60 films were analyzed by Fourier Transform Infrared (FTIR) spectroscopy and Raman scattering technique. The analytical results indicate that the irradiation induced a decrease of icosahedral symmetry of C-60 molecule and damage of C-60 films; different vibration modes of C-60 molecule have different irradiation sensitivities; the mean efficient damage radius obtained from experimental data is about 1.47 nm, which is in good agreement with thermal spike model prediction.

Effects of reinforcement filler and temperature on the stability of beta-crystal in glass bead filled polypropylene

The effects of crystallization temperature (T,), glass bead content and its size on the, formation of beta-crystal and structural stability of originally formed beta-crystal in glass bead filled polypropylene (PP) were examined. The differential scanning calorimetry (DSC) measurements indicated that the amount of beta-phase in PP crystals was a function of the crystallization temperature and glass bead content. For a constant crystallization temperature, it was observed that the amount of beta-crystal initially increased with increase in glass bead content up to 30 wt.%, and then decreased slightly with further increase in the filler content. From the DSC data, a disorder parameter (S) was derived to define the structural stability of originally formed beta-crystals. The structural stability of originally formed beta-crystals was enhanced with increase in either the crystallization temperature or the glass bead content. Also, the influence of glass bead size (4-66 mu m) on the formation and stability of beta-crystals in PP/glass bead blends was studied. Large glass bead particles suppressed the formation and decreased the stability of beta-crystals.

The solution properties of phenolphthalein poly(arylether sulfone) .1. The solubility behavior and determination of M-II equations

A series of narrow molecular weight distribution fractions of phenolphthalein polyarylether sulfone(PES-C) had been prepared, The <(M) over bar (w)> of these fractions were determined by conventional light scattering method. The [eta] and the Huggins slope constant k' in DMF, CHCl3 and 1,2-dichloroethane were also determined. The Huggins constants are greater than 0.5 in all of these solvents showing a special solubility behavior. The Mark-Houwink equations of PES-C in these solvents at 25 degrees C are [eta] = 2.79 x 10(-2) <(M) over bar (0.615)(w)> (DMF); [eta] = 3.96 x 10(-2) <(M) over bar (0.58)(w)> (CHCl3); [eta] = 7.40 x 10(-2) <(M) over bar (0.52)(w)> (CH2ClCH2Cl).

The stability zone of gas hydrate in the slope of East China Sea and neighboring trough basin area

We analyze the distribution of temperature and heat flow of the sea floor sediment in the area of East China Sea slope and West basin area of the Okinawa Trough. Based on the Sonar Buoy and OBS data, 6 velocity layers are recognized, each of which has velocity of 1.8(1.8 similar to 2.2) km/s,2.2(2.0 similar to 2.5)km/s,2.8 (2.7 similar to 3.2)km/s,3.4 similar to 3.6km/s,4.2(4.1 similar to 4.7)km/s and 5.1km/s, respectively. The upper velocity layer of 1.8 similar to 2.2 km/s corresponds to the Quaternary sediment stratum. The layer with velocity 3.4 similar to 4.2km/s is the Pliocene sediment stratum. The area that is suitable for stable existence of gas hydrate by the temperature and pressure is 70,000km(2) about 1/10 the total area of East China Sea. The thickness of the stability zone ranges from 400m (Middle Part of Okinawa Trough) to 1100m (North and South Part of Okinawa Trough). The Quaternary and Pliocene layers are suitable for stable exitence of gas hydrate. According to the tectonic stability and heat flow, the north part and south part of the Okinawa Trough are the most perspective area for the gas hydrate explorations.

Stability of alpine meadow ecosystem on the Qinghai-Tibetan Plateau

The meadow ecosystem on the Qinghai-Tibetan Plateau is considered to be sensitive to climate change. An understanding of the alpine meadow ecosystem is therefore important for predicting the response of ecosystems to climate change. In this study, we use the coefficients of variation (Cv) and stability (E) obtained from the Haibei Alpine Meadow Ecosystem Research Station to characterize the ecosystem stability. The results suggest that the net primary production of the alpine meadow ecosystem was more stable (Cv = 13.18%) than annual precipitation (Cv = 16.55%) and annual mean air temperature (Cv= 28.82%). The net primary production was insensitive to either the precipitation (E = 0.0782) or air temperature (E = 0.1113). In summary, the alpine meadow ecosystem on the Qinghai-Tibetan Plateau is much stable. Comparison of alpine meadow ecosystem stability with other five natural grassland ecosystems in Israel and southern African indicates that the alpine meadow ecosystem on the Qinghai-Tibetan Plateau is the most stable ecosystem. The alpine meadow ecosystem with relatively simple structure has high stability, which indicates that community stability is not only correlated with biodiversity and community complicity but also with environmental stability. An average oscillation cycles of 3-4 years existed in annual precipitation, annual mean air temperature, net primary production and the population size of consumers at the Haibei natural ecosystem. The high stability of the alpine meadow ecosystem may be resulting also from the adaptation of the ecosystem to the alpine environment.