Time-dependent Transformation Research Articles

Nonautonomous Hamiltonian quantum systems, operator equations, and representations of the Bender–Dunne Weyl-ordered basis under time-dependent canonical transformations

We solve the problem of integrating operator equations for the dynamics of nonautonomous quantum systems by using time-dependent canonical transformations. The studied operator equations essentially reproduce the classical integrability conditions at the quantum level in the basic cases of one-dimensional nonautonomous dynamical systems. We seek solutions in the form of operator series in the Bender–Dunne basis of pseudodifferential operators. Together with this problem, we consider quantum canonical transformations. The minimal solution of the operator equation in the representation of the basis at a fixed time corresponds to the lowest-order contribution of the solution obtained as a result of applying a canonical linear transformation to the basis elements.

Rapid heat treatment for anatase conversion of titania nanotube orthopedic surfaces

The amorphous to anatase transformation of anodized nanotubular titania surfaces has been studied by x-ray diffraction and transmission electron microscopy (TEM). A more rapid heat treatment for conversion of amorphous to crystalline anatase favorable for orthopedic implant applications was demonstrated. Nanotube titania surfaces were fabricated by electrochemical anodization of Ti6Al4V in an electrolyte containing 0.2 wt% NH4F, 60% ethylene glycol and 40% deionized water. The resulting surfaces were systematically heat treated in air with isochronal and isothermal experiments to study the temperature and time dependent transformation respectively. Energy dispersive spectroscopy shows that the anatase phase transformation of TiO2 in the as-anodized amorphous nanotube layer can be achieved in as little as 5 min at 350 °C in contrast to reports of higher temperature and much longer time. Crystallinity analysis at different temperatures and times yield transformation rate coefficients and activation energy for crystalline anatase coalescence. TEM confirms the (101) TiO2 presence within the nanotubes. These results confirm that for applications where amorphous titania nanotube surfaces are converted to crystalline anatase, a 5 min production flow-through heating process could be used instead of a 3 h batch process, reducing time, cost, and complexity.

The 2D time-dependent similarity transformation model as a tool for deformation monitoring

Besides the methodology of triangulation and geodetic networks nowadays, the permanent stations of satellite receivers exist, giving extra asset to geodetic daily practice. Permanent stations perform observations incessantly for the visible satellites. However, the coordinates of these stations are often changing over time due to geophysical and tectonic processes. Consequently, these changes are perceived to modern observations. So, along with the coordinates of geodetic points in a given epoch, their changes over time (e.g. the velocities of their movements) are also considered. Furthermore, any change to the reference system definition or/and to the network’s geometry can significantly impact the estimated coordinates and velocities. This paper investigates the reference datum definition problem (or datum problem, or zero order design problem) in a such network over time, which is later generalized for the study of the deformation control-networks. Emphasis is given to techniques of time-dependent 2D transformation models, with numerical tests on a simulation network.

An evaluation of colloidal and crystalline properties of CaCO3 nanoparticles for biological applications

Biodegradable calcium carbonate carriers are a promising and safe nanoparticle platform which might enable various applications as an engineered nanomaterial in health care, food and cosmetics. However, engineered nanoparticles can exhibit new forms of toxicity that must be carefully evaluated before being widely adopted in consumer products or novel drug delivery systems. To this end, we studied four common calcium carbonate particle systems (calcite nanoparticles, amorphous sub-micrometer and vaterite sub-micrometer and micrometer particles) and compared their behavior in biological medium and in cell culture experiments. The thermodynamically stable calcite phase is shown to maintain its morphological features as no phase transformation occurs. Size- and time-dependent phase transformation of the less stable vaterite particles are observed within 96h in cell medium. The protein serum albumin can be an effective inhibitor of phase-transition and it is shown to improve colloidal stability. The impact of the biological environment goes beyond protein-corona formation, as we observed rapid dissolution of amorphous particles in high ionic strength cell medium, but not in Millipore water. Cellular responses of human osteoblasts against CaCO3 particles indicate that increased intracellular calcium ions improve viability and that particle internalization is not size-dependent. Useful insights for designing CaCO3-based delivery systems are provided and also corroborate to the idea that intrinsic material properties as well as environmental conditions are of relevance for the successful implementation of dispersed CaCO3 particles in drug delivery systems and in other applications.

Numerical simulation of breakup and detachment of an axially stretching Newtonian liquid bridge with a moving contact line phase field method

The extensional, breakup and detachment dynamics of an axially stretching Newtonian liquid bridge are investigated numerically with a dynamic domain multiphase incompressible flow solver. The multiphase flow solver employs a Cahn–Hilliard phase field model to describe the evolution of the diffuse interface separating the liquid bridge fluid from the surrounding medium. The governing axisymmetric Navier–Stokes and Cahn–Hilliard phase field equations are discretized on a continuously expanding domain, the boundaries of which coincide with the planar solid surfaces containing the liquid bridge. The entire formulation, including the fast pressure correction for high density ratios and the semi-implicit discretization that overcomes the numerical stiffness of the fourth-order spatial operators, is performed on a fixed simplified computational domain using time-dependent transformation. Simulations reveal that the dynamic domain interface capturing technique effectively captures the deformation dynamics of the stretching liquid bridge, including the capillary wave formation, necking and interface evolution post breakup and detachment. It is found that the liquid bridge detachment is strongly influenced by the contact angle prescribed at the stationary and moving solid surfaces. At relatively small pulling speeds, the entire liquid is found to preferentially adhere to the less hydrophobic surface. When the prescribed contact angles are equal, however, the liquid bridge undergoes complete detachment so that no liquid resides either on the stationary or on the moving solid surface.

Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

In the geometric data model for spatio-temporal data, introduced by Chomicki and Revesz [1], spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities of the plane. To facilitate querying and animation of spatio-temporal data, we present a normal form for data in the geometric data model. We propose an algorithm for constructing this normal form via a spatio-temporal triangulation of geometric data objects. This triangulation algorithm generates new geometric data objects that partition the given objects both in space and in time. A particular property of the proposed partition is that it is invariant under time-dependent affine transformations, and hence independent of the particular choice of coordinate system used to describe the spatio-temporal data in. We can show that our algorithm works correctly and has a polynomial time complexity (of reasonably low degree in the number of input triangles and the maximal degree of the polynomial functions that describe the transformation functions). We also discuss several possible applications of this spatio-temporal triangulation. The application of our affine-invariant spatial triangulation method to image indexing and retrieval is discussed and an experimental evaluation is given in the context of bird images.

Surface characterization of insulin-coated Ti6Al4V medical implants conditioned in cell culture medium: An XPS study

Surface characterization of insulin-coated Ti6Al4V medical implants, after incubation in α-minimum essential medium (α-MEM), was done by X-ray photoelectron spectroscopy (XPS), in order to analyze the insulin behavior at the implant – α-MEM interface. In the absence of serum proteins in cell culture medium, the coated insulin layer remained intact, but experienced a time-dependent structural transformation exposing hydrophobic parts of the protein toward the solution. The presence of fetal bovine serum (FBS) in the medium resulted in partial substitution of insulin by serum proteins. In spite of some insulin release, the remaining coated layer demonstrated a direct surface effect by stabilizing the structure of protein competitors, and by supporting the accumulation of calcium and phosphate ions at the interface. A structurally stable protein layer with incorporated calcium and phosphate ions at the implant–tissue interface could be an important prerequisite for enhanced bone formation.

Equations of motion as constraints: superselection rules, Ward identities

The meaning of local observables is poorly understood in gauge theories, not to speak of quantum gravity. As a step towards a better understanding we study asymptotic (infrared) transformations in local quantum physics. Our observables are smeared by test functions, at first vanishing at infinity. In this context we show that the equations of motion can be seen as constraints, which generate a group, the group of space and time dependent gauge transformations. This is one of the main points of the paper. Infrared nontrivial effects are captured allowing test functions which do not vanish at infinity. These extended operators generate a larger group. The quotient of the two groups generate superselection sectors, which differentiate different infrared sectors. The BMS group changes the super-selection sector, a result long known for its Lorentz subgroup. It is hence spontaneously broken. Ward identities implied by the gauge invariance of the S-matrix generalize the standard results and lead to charge conservation and low energy theorems. Their validity does not require Lorentz invariance.

Dynamical normal modes for time-dependent Hamiltonians in two dimensions

We present the theory of time-dependent point transformations to find independent dynamical normal modes for two-dimensional systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent modes can indeed be defined is identified, and a geometrical analogy is put forward. The results explain and unify recent work to design fast operations on trapped ions, needed to implement a scalable quantum-information architecture: Transport, expansions, and the separation of two ions, two-ion phase gates, as well as the rotation of an anisotropic trap for an ion, are treated and shown to be analogous to a mechanical system of two masses connected by springs with time-dependent stiffness.

Projectivity, affine, similarity and euclidean coordinates transformation parameters from ITRF to EUREF in Turkey

Abstract Today, in geodesy most practical applications is to use a datum to get three dimensional position of a particular point. The geodetic techniques generally provide time dependent coordinates in global datum. The difference between the global datum like international terrestrial reference frame (ITRF) to local datum like Europe fixed reference frame (EUREF) can be up to several centimeters due to different velocity rate of tectonic plates. To get high-precision measurements, there is an increasing need of time dependent transformations from the global level to local level. The present paper treats, this theoretical problem of geodesy by using mathematical dependency between two spatial coordinate systems whose common points are given in both systems. The paper describes four different (projective, affine, similarity and euclidean) modified methodologies for the transformation between global (ITRF) to local (EUREF) by using the Turkish permanent GPS network (TPGN) as an example. The time series from TPGN stations are used to review these transformations from ITRF 2008 to EUREF 2008. The transformation parameters in all cases shows that mostly transform coordinates depends on its counterparts (X to x and Y to y) and others coordinates have very less effect. Finally to show the validity of our model a comparative analysis with standard Bursa-Wolf and Molodensky-Badekas models has been presented. The test shows that our model error is equivalent to standard models, in this view the presented models are acceptable and can improve our understanding in coordinate transformation.

An explicit adaptive grid approach for the numerical solution of the population balance equation

Many engineering applications, such as the formation of soot in hydrocarbon combustion or the precipitation of nanoparticles from aqueous solutions, encompass a polydispersed particulate phase that is immersed in a reacting carrier flow. From a Eulerian perspective, the evolution of the particulate phase both in physical and in particle property space can be described by the population balance equation (PBE). In this article, we present an explicit solution-adaptive numerical scheme for discretizing the spatially inhomogeneous and unsteady PBE along a one-dimensional particle property space. This scheme is based on a space and time dependent coordinate transformation which redistributes resolution in particle property space according to the shapes of recent solutions for the particle property distribution. In particular, the coordinate transformation is marched in time explicitly. In comparison to many existing moving or adaptive grid approaches, this has the advantage that the semi-discrete PBE does not need to be solved in conjunction with an additional system of equations governing the movement of nodes in particle property space.By design, our adaptive grid technique is able to accurately capture sharp features such as peaks or near-discontinuities, while maintaining the semi-discrete system size and adhering to a uniform fixed grid discretization in transformed particle property space. This is particularly advantageous if the PBE is combined with a spatially and temporally fully resolved flow model and a standard Eulerian solution scheme is applied in physical space. In order to accommodate localized source terms and to control the grid stretching, we develop a robust scheme for modifying the coordinate transformation such that constraints on the resolution in physical particle property space are obeyed.As an example, we consider the precipitation of BaSO4 particles from an aqueous solution in a plug flow reactor. Our findings demonstrate that for a given accuracy of the numerical solution the explicit adaptive grid technique requires over an order of magnitude fewer grid points than a comparable fixed grid discretization scheme.

Time-dependent shear transformation zone in thin film metallic glasses revealed by nanoindentation creep

The holding time effect on the mechanical property, creep behavior and shear transformation zone has been systematically investigated by performing a series of nanoindentation creep measurements on magnetron-sputtered La-Co-Al, Zr-Cu-Ni-Al, Ni-Nb and W-Ru-B thin film metallic glasses. When the variation of contact stiffness with indentation depth is considered, the hardness, Young's modulus and strain rate have been found to decrease with increasing holding time. Meanwhile, strain rate sensitivity (m), and the volume and activation energy of shear transformation zone (STZ) have been analyzed, according to the cooperative shear model, at different stages of creep to explain the time-dependent mechanical behavior and properties. The higher strain rate results in few potential STZs with larger volume and activation energy, and the lower plastic stability of deformation manifested by smaller m, at the primary creep stage, as compared with those at apparent steady-state creep. Therefore, easier STZ activation, at longer holding time and lower strain rate, conduces to profuse operation of STZs and larger critical size for deformation mode transition from highly-localized to non-localized.

Employing an interaction picture to remove artificial correlations in multilayer multiconfiguration time-dependent Hartree simulations

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method is implemented in the interaction picture to allow a more effective description of correlation effects. It is shown that the artificial correlation present in the original Schrödinger picture can be removed with an appropriate choice of the zeroth-order Hamiltonian. Thereby, operators in the interaction picture are obtained through time-dependent unitary transformations, which have negligible computational cost compared with other parts of the ML-MCTDH algorithm. The efficiency of the method is demonstrated by application to a model of vibrationally coupled charge transport in molecular junctions.

Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes

The Bessel process with parameter D > 1 and the Dyson model of interacting Brownian motions with coupling constant β > 0 are extended to the processes in which the drift term and the interaction terms are given by the logarithmic derivatives of Jacobi’s theta functions. They are called the elliptic Bessel process, eBES(D), and the elliptic Dyson model, eDYS(β), respectively. Both are realized on the circumference of a circle [0, 2πr) with radius r > 0 as temporally inhomogeneous processes defined in a finite time interval [0, t∗), t∗ < ∞. Transformations of them to Schrödinger-type equations with time-dependent potentials lead us to proving that eBES(D) and eDYS(β) can be constructed as the time-dependent Girsanov transformations of Brownian motions. In the special cases where D = 3 and β = 2, observables of the processes are defined and the processes are represented for them using the Brownian paths winding round a circle and pinned at time t∗. We show that eDYS(2) has the determinantal martingale representation for any observable. Then it is proved that eDYS(2) is determinantal for all observables for any finite initial configuration without multiple points. Determinantal processes are stochastic integrable systems in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single continuous function called the spatio-temporal correlation kernel.

DEVELOPMENT OF A TIME-DEPENDENT 3-PARAMETER HELMERT DATUM TRANSFORMATION MODEL: A CASE STUDY FOR MALAYSIA

Abstract. This paper aims to develop a time-dependent 3-parameter Helmert datum transformation model for Malaysia as a proposed solution to the current non-geocentric issue of the Geocentric Datum of Malaysia 2000 (GDM2000). Methodologically, the datum transformation models is categorised into three parts; firstly, the time-dependent aspect of the datum transformation model is determined using the tectonic motion velocities computed from linear least squares regression of the long-term time series of MyRTKnet stations positions from year December 2004 to 2014; whereby the station positions are obtained from high-precision daily double-difference processing of MyRTKnet and IGS stations via Bernese 5.0. Secondly, the 3 Helmert translation-only parameters, are derived between the original GDM2000 and GDM2000@2013 – the new datum coordinates which refers to ITRF2008 at epoch 3/7/2013 – via Bernese 5.0 software. Thirdly, a distortion model is computed in order to minimise the coordinate residuals between the ‘processed’ and ‘transformed’ new datum. The datum transformation model is then validated to determine the reliability of the model. The validation results show that the datum transformation model is within centimetre-level accuracy, i.e., below 3 cm, over Malaysia for forward transformations to year 2014 and 2015. Therefore, this study anticipates that it will contribute as a feasible solution for the GDM2000 issue with consideration of the core concern: the complex tectonic motion of Malaysia.

Unique Fock quantization of a massive fermion field in a cosmological scenario

It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive to this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a non trivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set.

Arsinothricin, a novel organoarsenic species produced by a rice rhizosphere bacterium

Environmental contextRice is a major human dietary source of arsenic. We identified a novel organoarsenic species, arsinothricin, produced by a bacterium in the rice rhizosphere. This result suggests diverse biochemical dynamics and microbial biodiversity of arsenic metabolism in the rice rhizosphere. AbstractMethylated arsenic compounds in rice grains originate from the action of soil bacteria in the rice rhizosphere. Here, we investigated the chemical structures of arsenic compounds produced by a bacterium, Burkholderia gladioli strain GSRB05, in the rice rhizosphere. When cultured in liquid R2A medium containing arsenite (AsIII), strain GSRB05 produced two unknown novel arsenic compounds that were later identified as arsinothricin (AST, 2-amino-4-(hydroxymethylarsinoyl)butanoic acid), an arsenic mimetic of the herbicide phosphinothricin, and a probable hydroxyl precursor of AST, termed AST-OH (2-amino-4-(dihydroxyarsonoyl)butanoic acid). The chemical structure of AST was determined by means of liquid chromatography–high-resolution tandem mass spectrometry and NMR analyses, whereas that of AST-OH was estimated by means of ultra-high-performance liquid chromatography–tandem mass spectrometry. Time-dependent AsIII transformation by strain GSRB05 showed that AST was produced after AST-OH. Compared with AsIII, AST showed higher absorption by, and was more toxic to, Escherichia coli DH5α cells in M9 minimal medium, which lacks amino acids. These findings have implications for the environmental transfer of arsenic, and human health consequences in terms of our dietary burden of arsenic.

Novel Phasor Transformation for Feedback Control Design of Induction Heating Systems With Experimental Results

For analyzing the transients of induction heating (IH) systems, time-dependent phasor transformations were proposed so far in the literature. Applying these transformations to linear R, L, C circuit equations leads to differential equations in the complex domain from which equivalent circuits modeling the envelopes of sinusoidal waveforms were derived. This paper proposes a phasor transformation, which is based on fictitiously replacing the real voltage and current signals of a system by complex voltage and current signals. It leads to transformed system equations in the real domain where instantaneous amplitudes, phases, and frequencies explicitly appear, which makes the transformed equations suitable for the feedback control design. The methodology is applied to a parallel IH system to design a sliding-mode controller. The theory is supported by simulations, experiments, and comparisons.

Phase Diagram and Sweep Dynamics of a One-Dimensional Generalized Cluster Model

We numerically study quantum phase transitions and dynamical properties in the one-dimensional cluster model with several interactions by using the time-evolving block decimation method for infinite systems and the exact diagonalization. First, boundaries among several quantum phases of the model are determined from energy gap and each phase is characterized by order parameters and the entanglement spectrum (ES). We confirm that in the model with open boundary condition the degeneracy of the lowest levels in the ES corresponds to that of the ground states. Then, using the time-dependent Bogoliubov transformation with open boundary condition, we investigate dynamical properties during an interaction sweep through the critical point which separates two topological phases involving four-fold degeneracy in the ground state. After a slow sweep across the critical point, we observe spatially periodic structures in the string correlation functions and the entanglement entropy. It is shown that the periodicities stem from the Bogoliubov quasiparticles generated near the critical point.

Coincidence of quantum-classical orbits for periodically driven two-dimensional anisotropic oscillator—Berry phase and Hannay angle

In this paper we study quantum–classical correspondence of a periodically driven two-dimensional (2D) anisotropic-oscillator. In terms of the time-dependent canonical transformation the stationary Lissajous orbits are found along with the Hannay’s angle. On the other hand, the stationary wave functions are derived analytically with the help of the generalized gauge transformation. The Berry phase in the original gauge is found to be times the nonadiabatic Hannay’s angle with the integer number n being the eigenstate index. By using the SU(2) coherent superposition of degenerate 2D-eigenstates for a fixed energy we construct the stationary wave function, the probability cloud of which is shown to coincide perfectly with the classical orbits.