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.

Stability of Electrode-Electrolyte Interfaces during Charging in Lithium Batteries

In this thesis we study the growth of a Li electrode-electrolyte interface in the presence of an elastic prestress. In particular, we focus our interest on Li-air batteries with a solid electrolyte, LIPON, which is a new type of secondary or rechargeable battery. Theoretical studies and experimental evidence show that during the process of charging the battery the replated lithium adds unevenly to the electrode surface. This phenomenon eventually leads to dendrite formation as the battery is charged and discharged numerous times. In order to suppress or alleviate this deleterious effect of dendrite growth, we put forth a study based on a linear stability analysis. Taking into account all the mechanisms of mass transport and interfacial kinetics, we model the evolution of the interface. We find that, in the absence of stress, the stability of a planar interface depends on interfacial diffusion properties and interfacial energy. Specifically, if Herring-Mullins capillarity-driven interfacial diffusion is accounted for, interfaces are unstable against all perturbations of wavenumber larger than a critical value. We find that the effect of an elastic prestress is always to stabilize planar interfacial growth by increasing the critical wavenumber for instability. A parametric study results in quantifying the extent of the prestress stabilization in a manner that can potentially be used in the design of Li-air batteries. Moreover, employing the theory of finite differences we numerically solve the equation that describes the evolution of the surface profile and present visualization results of the surface evolution by time. Lastly, numerical simulations performed in a commercial finite element software validate the theoretical formulation of the interfacial elastic energy change with respect to the planar interface.

Hydrothermal experiments on the thermal stability of amino substances in sediments

Aspartic acid, threonine, serine and other thermally unstable amino acids have been found in fine-grained elastic sediments of advanced geologic age. The presence of these compounds in ancient sediments conflicts with experimental data determined for their simple thermal decomposition.

Recent and Late Miocene sediments and their humic acid extracts, known to contain essentially complete suites of amino acids, were heated with H₂O in a bomb at temperatures up to 500°C in order to compare the thermal decomposition characteristics of the sedimentary amino compounds.

Most of the amino acids found in protein hydrolyzates are obtained from the Miocene rock in amounts 10 to 100 times less than from the Recent sediment. The two unheated humic acids are rather similar despite their great age difference. The Miocene rock appears uncontaminated by Recent carbon.

Yields of amino acids generally decline in the heated Recent sediment. Some amino compounds apparently increase with heating time in the Miocene rock.

Relative thermal stabilities of the amino acids in sediments are generally similar to those determined using pure aqueous solutions. The relative thermal stabilities of glutamic acid, glycine, and phenylalanine vary in the Recent sediment but are uniform in the Miocene rock.

Amino acids may occur in both proteins and humic complexes in the Recent sediment, while they are probably only present in stabilized organic substances in the Miocene rock. Thermal decomposition of protein amino acids may be affected by surface catalysis in the Recent sediment. The apparent activation energy for the decomposition of alanine in this sediment is 8400 calories per mole. Yields of amino compounds from the heated sediments are not affected by thermal decomposition only.

Amino acids in sediments may only be useful for geothermometry in a very general way.

A better picture of the amino acid content of older sedimentary rocks may be obtained if these sediments are heated in a bomb with H₂O at temperatures around 150°C prior to HCl hydrolysis.

Leucine-isoleucine ratios may prove to be useful as indicators of amino acid sources or for evaluating the fractionation of these substances during diagenesis. Leucine-isoleucine ratios of the Recent and Miocene sediments and humic acids are identical. The humic acids may have a continental source.

The carbon-nitrogen and carbon-hydrogen ratios of sediments and humic acids increase with heating time and temperature. Ratios comparable to those in some kerogens are found in the severely heated Miocene sediment and humic acid.

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a Stable nonlinear system. It is shown that the instability of the zeros of the linear System can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This paper analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Linear stability of miscible two-fluid flow down an incline

We show that miscible two-layer free-surface flows of varying viscosity down an inclined substrate are different in their stability characteristics from both immiscible two-layer flows, and flows with viscosity gradients spanning the entire flow. New instability modes arise when the critical layer of the viscosity transport equation overlaps the viscosity gradient. A lubricating configuration with a less viscous wall layer is identified to be the most stabilizing at moderate miscibility (moderate Peclet numbers). This also is in contrast with the immiscible case, where the lubrication configuration is always destabilizing. The co-existence that we find under certain circumstances, of several growing overlap modes, the usual surface mode, and a Tollmien-Schlichting mode, presents interesting new possibilities for nonlinear breakdown. © 2013 AIP Publishing LLC.

Theoretical investigation on the phase stability of Nd2Fe14B and site preference of V, Cr, Mn, Zr and Nb

The stability of the excellent permanent magnetic compound Nd2Fe14B and substitution of Fe in the compound by V, Cr, Mn, Zr and Nb are investigated by using interatomic pair potentials which are converted from lattice-inversion method. Calculation shows that the substitution always makes the cell volume larger, and the increase of the volume is almost linear with substituent concentration. The calculated cohesive energy shows that the preferential order of substitution of Fe is Nb, V, Cr, Mn, Zr. Nevertheless, all the five substituting elements should most preferentially replace Fe in the j(2)' site, which has the greatest space among all six Fe sites. (C) 2005 Elsevier B.V. All rights reserved.

Side radical influence on the nonlinear optical properties and thermal stability of poled polymer films

Films of polyetherketone doped with the chromophores Disperse Red 1 (DR1) and Disperse Red 13 (DR13) were prepared by spin-coating method. By the in situ Second-harmonic Generation (SHG) signal intensity measurement, the optimal poling temperatures were obtained. For the investigated polyetherketone polymer doped with DR1 (DR1/PEK-c) and polyetherketone polymer doped with DR13 (DR13/PEK-c) films, the optimal poling temperatures were 150degreesC and 140degreesC, respectively. Under the optimal poling conditions, the high second-order nonlinear optical coefficient chi(33)((2)) = 11.02 pm/V has been obtained for the DR1/PEK-c; and for DR13/PEK-c at the same conditions the coefficient is 17.9 pm/V. The SHG signal intensity DR1/PEK-c could maintain more than 80% of its initial value when the temperature was under 100degreesC, and the SHG signal intensity of the DR13/PEK-c could maintain more than 80% of its initial value when the temperature was under 135degreesC. (C) 2002 Kluwer Academic Publishers.

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.

On the acid-base stability of Keggin Al-13 and Al-30 polymers in polyaluminum coagulants

The acid-base stabilities of Al-13 and Al-30 in polyaluminum coagulants during aging and after dosing into water were studied systematically using batch and flow-through acid-base titration experiments. The acid decomposition rates of both Al-13 and Al-30 increase rapidly with the decrease in solution pH. The acid decompositions of Al-13 and Al-30 with respect to H+ concentration are composed of two parallel first-order and second-order reactions, and the reaction orders are 1.169 and 1.005, respectively. The acid decomposition rates of Al-13 and Al-30 increase slightly when the temperature increases from 20 to ca. 35 A degrees C, but decrease when the temperature increases further. Al-30 is more stable than Al-13 in acidic solution, and the stability difference increases as the pH decreases. Al-30 is more possible to become the dominant species in polyaluminum coagulants than Al-13. The acid catalyzed decomposition and followed by recrystallization to form bayerite is one of the main processes that are responsible for the decrease of Al-13 and Al-30 in polyaluminum coagulants during storage. The deprotonation and polymerization of Al-13 and Al-30 depend on solution pH. The hydrolysis products are positively charged, and consist mainly of repeated Al-13 and Al-30 units rather than amorphous Al(OH)(3) precipitates. Al-30 is less stable than Al-13 upon alkaline hydrolysis. Al-13 is stable at pH < 5.9, while Al-30 lose one proton at the pH 4.6-5.75. Al-13 and Al-30 lose respective 5 and 10 protons and form [Al-13] (n) and [Al-30] (n) clusters within the pH region of 5.9-6.25 and 5.75-6.65, respectively. This indicates that Al-30 is easier to aggregate than Al-13 at the acidic side, but [Al-13] (n) is much easier to convert to Alsol-gel than [Al-30] (n) . Al-30 possesses better characteristics than Al-13 when used as coagulant because the hydrolysis products of Al-30 possess higher charges than that of Al-13, and [Al-30] (n) clusters exist within a wider pH range.

Global stability of Hopfield neural networks

This paper gives a condition for the global stability of a continuous-time hopfield neural network when its activation function maybe not monotonically increasing.