Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an ``engineered'' initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.

Using space geodesy to constrain variations in seismogenic behavior on subduction megathrusts

The concept of seismogenic asperities and aseismic barriers has become a useful paradigm within which to understand the seismogenic behavior of major faults. Since asperities and barriers can be thought of as defining the potential rupture area of large megathrust earthquakes, it is thus important to identify their respective spatial extents, constrain their temporal longevity, and to develop a physical understanding for their behavior. Space geodesy is making critical contributions to the identification of slip asperities and barriers but progress in many geographical regions depends on improving the accuracy and precision of the basic measurements. This thesis begins with technical developments aimed at improving satellite radar interferometric measurements of ground deformation whereby we introduce an empirical correction algorithm for unwanted effects due to interferometric path delays that are due to spatially and temporally variable radar wave propagation speeds in the atmosphere. In chapter 2, I combine geodetic datasets with complementary spatio-temporal resolutions to improve our understanding of the spatial distribution of crustal deformation sources and their associated temporal evolution – here we use observations from Long Valley Caldera (California) as our test bed. In the third chapter I apply the tools developed in the first two chapters to analyze postseismic deformation associated with the 2010 Mw=8.8 Maule (Chile) earthquake. The result delimits patches where afterslip occurs, explores their relationship to coseismic rupture, quantifies frictional properties associated with inferred patches of afterslip, and discusses the relationship of asperities and barriers to long-term topography. The final chapter investigates interseismic deformation of the eastern Makran subduction zone by using satellite radar interferometry only, and demonstrates that with state-of-art techniques it is possible to quantify tectonic signals with small amplitude and long wavelength. Portions of the eastern Makran for which we estimate low fault coupling correspond to areas where bathymetric features on the downgoing plate are presently subducting, whereas the region of the 1945 M=8.1 earthquake appears to be more highly coupled.

Lightweight deformable mirrors for future space telescopes

This thesis presents a concept for ultra-lightweight deformable mirrors based on a thin substrate of optical surface quality coated with continuous active piezopolymer layers that provide modes of actuation and shape correction. This concept eliminates any kind of stiff backing structure for the mirror surface and exploits micro-fabrication technologies to provide a tight integration of the active materials into the mirror structure, to avoid actuator print-through effects. Proof-of-concept, 10-cm-diameter mirrors with a low areal density of about 0.5 kg/m² have been designed, built and tested to measure their shape-correction performance and verify the models used for design. The low cost manufacturing scheme uses replication techniques, and strives for minimizing residual stresses that deviate the optical figure from the master mandrel. It does not require precision tolerancing, is lightweight, and is therefore potentially scalable to larger diameters for use in large, modular space telescopes. Other potential applications for such a laminate could include ground-based mirrors for solar energy collection, adaptive optics for atmospheric turbulence, laser communications, and other shape control applications.

The immediate application for these mirrors is for the Autonomous Assembly and Reconfiguration of a Space Telescope (AAReST) mission, which is a university mission under development by Caltech, the University of Surrey, and JPL. The design concept, fabrication methodology, material behaviors and measurements, mirror modeling, mounting and control electronics design, shape control experiments, predictive performance analysis, and remaining challenges are presented herein. The experiments have validated numerical models of the mirror, and the mirror models have been used within a model of the telescope in order to predict the optical performance. A demonstration of this mirror concept, along with other new telescope technologies, is planned to take place during the AAReST mission.

An experimental assessment of the aquaculture potential of the brown mussel, Modiolus metcalfei

A study was conducted at Banate Bay, Iloilo, from November 1975 to March 1976. Trials were conducted using spat collectors of four types, but no Modiolus metcalfei spat settled on any of the experimental collectors during the entire study period. Instead they attached to the exposed posterior half of the living Modiolus collected for reproductive cycle studies. The aquaculture potential of the brown mussel is considered to be low. Improvement of its production potential should be approached along the line of resource management rather than aquaculture. This management should be aimed at two objectives: (1) maintenance of enough adults on settlement surfaces, and (2) provision of space to allow new recruitments to grow. A possible solution, therefore, is controlled harvesting or thinning after the peak in the settlement season. In this manner, the chances of the mussel bed recovering year after year may be enhanced.

The WISH pond: potential for development of aquaculture in northeast Cambodia

In Cambodia, fish provide a major source of animal protein for rural households. Capture fisheries have declined and aquaculture has been identified as playing an important role in food and nutritional security and rural income generation. In 2011, WorldFish, in partnership with the Stung Treng Fishery Administration Cantonment and the Culture and Environment Preservation Association, aimed at improving the uptake of small-scale aquaculture by communities with limited experience in fish culture in Stung Treng Province in northeast Cambodia. The system was given the name “WISH ponds,” derived from the combination of the words "water" and "fish" to reflect the integration of fish cultivation with water for storage and vegetable growing. It was targeted towards households with limited space to construct large aquaculture ponds, such as peri-urban households. The study indicated that WISH ponds can create an important learning platform for communities to address challenges associated with small-scale aquaculture development by using scientific data generated and owned by the participants. Results from this 2011 study provided important insights into the challenges and constraints for introducing small-scale aquaculture into rural households in Cambodia. In mid-2013, WorldFish won a Feed the Future Partnering for Innovation grant, funded by the United States Agency for International Development, to build upon its successful engagement with communities in northeast Cambodia where WISH ponds had already been introduced and investigate scaling this technology to establish more WISH ponds in these communities.

The parameter space of graphene chemical vapor deposition on polycrystalline Cu

A systematic study of the parameter space of graphene chemical vapor deposition (CVD) on polycrystalline Cu foils is presented, aiming at a more fundamental process rationale in particular regarding the choice of carbon precursor and mitigation of Cu sublimation. CH 4 as precursor requires H 2 dilution and temperatures ≥1000 °C to keep the Cu surface reduced and yield a high-quality, complete monolayer graphene coverage. The H 2 atmosphere etches as-grown graphene; hence, maintaining a balanced CH 4/H 2 ratio is critical. Such balance is more easily achieved at low-pressure conditions, at which however Cu sublimation reaches deleterious levels. In contrast, C 6H 6 as precursor requires no reactive diluent and consistently gives similar graphene quality at 100-150 °C lower temperatures. The lower process temperature and more robust processing conditions allow the problem of Cu sublimation to be effectively addressed. Graphene formation is not inherently self-limited to a monolayer for any of the precursors. Rather, the higher the supplied carbon chemical potential, the higher the likelihood of film inhomogeneity and primary and secondary multilayer graphene nucleation. For the latter, domain boundaries of the inherently polycrystalline CVD graphene offer pathways for a continued carbon supply to the catalyst. Graphene formation is significantly affected by the Cu crystallography; i.e., the evolution of microstructure and texture of the catalyst template form an integral part of the CVD process. © 2012 American Chemical Society.

Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Radar interferometer measurements of space debris using the Evpatoria RT-70 transmitter

The ability of the Evpatoria RT-70 radar complex to perform research on space debris was investigated in four trial experiments during 2001-2003. The echo-signals of 25 objects at geostationary, highly elliptical and medium-altitude orbits were recorded on magnetic tapes at radio telescopes in Russia, Italy, China and Poland. The multi-antenna system configuration gives potential to supplement the classic radar data with precise angular observations using the technique of Very Long Baseline Interferometry. The first stage of such processing was fulfilled by the correlator in N. Novgorod, Russia. The cross-correlation of transmitted and received signals was obtained for the 11 objects on the Evpatoria-Bear Lakes, Evpatoria-Urumqi and Evpatoria-Noto baselines. This activity also promoted developing the optical observations of geostationary objects, conducted for the improvement of the radar target ephemerides. (C) 2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

Inner structure of Spin(c)(4) gauge potential on 4-dimensional manifolds

The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

Surface pigments,algal biomass profiles,and potential production of the euphotic layer:Relationships reinvestigated in view of remote-sensing applications

Maps of surface chlorophyllous pigment (Chl a + Pheo a) are currently produced from ocean color sensors. Transforming such maps into maps of primary production can be reliably done only by using light-production models in conjuction with additional information about the column-integrated pigment content and its vertical distribution. As a preliminary effort in this direction. $\ticksim 4,000$ vertical profiles pigment (Chl a + Pheo a) determined only in oceanic Case 1 waters have been statistically analyzed. They were scaled according to dimensionless depths (actual depth divided by the depth of the euphotic layer, $Z_e$) and expressed as dimensionless concentrations (actual concentration divided by the mean concentration within the euphotic layer). The depth $Z_e$ generally unknown, was computed with a previously develop bio-optical model. Highly sifnificant relationships were found allowing $\langle C \rangle_tot$, the pigment content of the euphotic layer, to be inferred from the surface concentration, $\bar C_pd$, observed within the layer of one penetration depth. According to their $\bar C_pd$ values (ranging from $0.01 to > 10 mg m^-3$), we categorized the profiles into seven trophic situations and computed a mean vertical profile for each. Between a quasi-uniform profile in eutrophic waters and a profile with a strong deep maximum in oligotrophic waters, the shape evolves rather regularly. The wellmixed cold waters, essentially in the Antarctic zone, have been separately examined. On average, their profiles are featureless, without deep maxima, whatever their trophic state. Averaged values their profiles are featureless, without deep maxima, whatever their trophic state. Averaged values their profiles are featureless, without deep maxima, whatever their trophic state. Averaged values of $ρ$, the ratio of Chl a tp (Chl a + Pheo a), have also been obtained for each trophic category. The energy stored by photosynthesizing algae, once normalized with respect to the integrated chlorophyll biomass $\langle C \rangle _tot $ is proportional to the available photosythetic energy at the surface via a parameter $ψ∗$ which is the cross-section for photosynthesis per unit of areal chlorophyll. By tanking advantage of the relative stability of $ψ∗.$ we can compute primary production from ocean color data acquired from space. For such a computation, inputs are the irradiance field at the ocean surface, the "surface" pigment from which $\langle C \rangle _tot$ can be derived, the mean $ρ value pertinent to the trophic situation as depicted by the $\bar C_pd or $\langle C \rangle _tot$ values, and the cross-section $ψ∗$. Instead of a contant $ψ∗.$ value, the mean profiles can be used; they allow the climatological field of the $ψ∗.$ parameter to be adjusted through the parallel use of a spectral light-production model.

Potential energy landscape and robustness of a gene regulatory network: Toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers.

Crystallization behaviors of n-nonadecane in confined space: Observation of metastable phase induced by surface freezing

Crystallization and phase transition behaviors of n-nonadecane in microcapsules with a diameter of about 5 mu m were studied with the combination of differential scanning calorimetry ( DSC) and synchrotron radiation X-ray diffraction ( XRD). As evident from the DSC measurement, a surface freezing monolayer, which is formed in the microcapsules before the bulk crystallization, induces a novel metastable rotator phase ( RII), which has not been reported anywhere else. We argue that the existence of the surface freezing monolayer decreases the nucleating potential barrier of the RII phase and induces its appearance, while the lower free energy in the confined geometry turns the transient RII phase to a " long- lived" metastable phase.