Function Of Energy Difference Research Articles

Dynamics of Bose-Einstein condensation in an asymmetric double-well potential

Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.

Chaos of the Six-Dimensional Non-Autonomous System for the Circular Mesh Antenna

In the process of aerospace service, circular mesh antennas generate large nonlinear vibrations under an alternating thermal load. In this paper, the Smale horseshoe and Shilnikov-type multi-pulse chaotic motions of the six-dimensional non-autonomous system for circular mesh antennas are first investigated. The Poincare map is generalized and applied to the six-dimensional non-autonomous system to analyze the existence of Smale horseshoe chaos. Based on the topological horseshoe theory, the three-dimensional solid torus structure is mapped into a logarithmic spiral structure, and the original structure appears to expand in two directions and contract in one direction. There exists chaos in the sense of a Smale horseshoe. The nonlinear equations of the circular mesh antenna under the conditions of the unperturbed and perturbed situations are analyzed, respectively. For the perturbation analysis of the six-dimensional non-autonomous system, the energy difference function is calculated. The transverse zero point of the energy difference function satisfies the non-degenerate conditions, which indicates that the system exists Shilnikov-type multi-pulse chaotic motions. In summary, the researches have verified the existence of chaotic motion in the six-dimensional non-autonomous system for the circular mesh antenna.

Light field camera all-in-focus image acquisition based on angular information

Traditional light field all-in-focus image fusion algorithms are based on the digital refocusing technique. Multi-focused images converted from one single light field image are used to calculate the all-in-focus image and the light field spatial information is used to accomplish the sharpness evaluation. Analyzing the 4D light field from another perspective, an all-in-focus image fusion algorithm based on angular information is presented in this paper. In the proposed method, the 4D light field data are fused directly and a macro-pixel energy difference function based on angular information is established to accomplish the sharpness evaluation. Then the fused 4D data is guided by the dimension increased central sub-aperture image to obtain the refined 4D data. Finally, the all-in-focus image is calculated by integrating the refined 4D light field data. Experimental results show that the fused images calculated by the proposed method have higher visual quality. Quantitative evaluation results also demonstrate the performance of the proposed algorithm. With the light field angular information, the image feature-based index and human perception inspired index of the fused image are improved.

Measurement and analysis of blue shift on the helium 492.2 nm line in a liquid corona discharge

The helium singlet 1s4d-1s2p line (492.2 nm) has been measured in a corona discharge done in liquid helium at 4.2 K. A significant shift towards the blue direction is visible on the spectrum. Using an empirical model for the He-He* potential energy difference, we have performed a fitting of the line shape. The best-fit result is in good agreement with the experimental spectrum. It is shown that the blue shift is determined by the maximum of the potential energy difference function. Based on the fitting results, we give an estimate of this quantity.

Simple electronic model of enzymatic reactions

Electron transfers between active sites of the enzyme and the substrate (product) have been taken into account in kinetic equations for multistep enzymatic reactions with some reversible steps by introducing weak and strong chemisorption states for the intermediates based on Wolkenstein s electronic theory of catalysis originally developed for semiconductors. As a result, the expression for the reaction rate as a function of energy difference between the highest occupied molecular orbital (HOMO) of the active site of the enzyme and the bonding state of the substrate (product) adsorbed onto the surface of the enzyme has been obtained. The case of interaction between the LUMO of the enzyme and the HOMO of the substrate, as well as different factors impacting on the rate of enzymatic reactions have been also discussed.

Kinetics and optimization of microwave-assisted lignin fractionation with Protic low transition temperature mixture of Sesamum indicum straw for enhanced bioethanol production

Six novel low transition temperature mixtures were synthesized as two groups of ternary protic (tpLTTM) and binary amphiphilic (aLTTM) mixtures. The thermophysical assessment of these LTTMs was evaluated as a function of temperature. Sustainable delignification for sesame straw and Hansen solubility using kraft lignin was determined as a function of relative energy difference (RED). CLG exhibited lowest RED (0.86) implying elevated lignin affinity (63.2%). Pretreatment kinetics and optimization for lignin removal was defined as a function of time. The samples were observed prior to and after treatment under SEM. The treated biomass (78.3%) was subjected to enzymatic digestion with immobilized cellulase (Cellic CTec2) and fermentation was accomplished with the same (68.3%) to produce bioethanol (81.3%).

Estimating the Nucleation Ability of Various Surfaces Towards Isotactic Polypropylene via Light Intensity Induction Time Measurements

Crystallization of isotactic polypropylene (iPP) at the interface with crystalline films of two commercially employed nucleating agents (sodium benzoate (NaBz) and sodium 2,2’-methylene bis-(4,6-di-tert-butylphenyl)phosphate (NA-11)) and with a glass fiber (GF) was investigated using a polarized optical microscope. The analysis of the light intensity evolution during the crystallization process enabled the successful estimation of the time at which the crystal growth began, i.e., the induction time (ti), at various crystallization temperatures. Meaningful differences in the ti values were observed between the investigated systems. Moreover, the ti data have been analyzed according to different nucleation models proposed in the literature, which consider either the time to form the first crystalline layer in contact with the substrate or the time required to grow a cluster of critical size. It has been found that the two models are applicable in different temperature ranges depending on the efficiency of the given substrate. Therefore, in order to obtain the value of the surface free energy difference function, Δσ, which is directly related to the nucleation energy barrier and useful for the definition of a universal nucleating efficiency scale, a model that considers both the above-mentioned times was fitted to the overall data. The values of Δσ for the nucleation of iPP on the surface of the different substrates are thus obtained and discussed in the framework of the literature results.

Multi-Pulse Chaotic Dynamics of Circular Mesh Antenna with 1:2 Internal Resonance

The multi-pulse homoclinic orbits and chaotic dynamics of an equivalent circular cylindrical shell for the circular mesh antenna are investigated in the case of 1:2 internal resonance in this paper for the first time. Applying the method of averaging, the four-dimensional averaged equation in the Cartesian form is obtained. The theory of normal form is used to reduce the averaged equation to a simpler form. Based on the simplified system, the energy phase method is employed to investigate the homoclinic bifurcations and the Shilnikov type multi-pulse chaotic dynamics. First, the energy difference function and the zeroes of the energy difference function are obtained. Then, the existence of the Shilnikov type multi-pulse orbits is determined. The homoclinic trees are depicted to describe the relationship among the layers diameter, the pulse numbers and the phase shift. Finally, we need to verify the condition which makes sure that any multi-pulse orbit departing from a slow sink comes back to the domain of attraction of one of the sinks. The results obtained here show the existence of the Shilnikov type multi-pulse chaotic motions of the circular mesh antenna. Numerical simulations are used to find multi-pulse chaotic motions. The results of the theoretical analysis are in qualitative agreement with the results obtained using numerical simulation.

(Invited) A Fingerprint of Metal Oxide Powders: Characterization and Identification with Energy-Resolved Distribution of Electron Traps

Who can identify a powder, e.g., in an unlabeled bottle found in a laboratory? How can fluctuation in the quality of powder prepared by a routine procedure be evaluated? The X-ray diffraction (XRD) pattern may indicate the crystalline structure and composition, and nitrogen-adsorption and particle-size measurements may provide information on some physical/structural properties, but they are not sufficient for identification. This is in contrast to practical identification in the field of organic chemistry, i.e., showing a reasonable fit of elemental composition and the NMR pattern with theoretical/authentic ones. Such a difference in identification for molecules and particles must be due to the existence of surface on particles. For example, it is well known that numerous kinds of titania (titanium(IV) oxide) powders all assigned to anatase crystalline by XRD have different properties and reactivities in chemical reactions occurring on the surface. Here we propose a method for identification of metal-oxide powders with energy-resolved distribution of electron traps (ERDT), as a fingerprint, measured using newly developed reversed double-beam photoacoustic spectroscopy (RDB-PAS) [1]. RDB-PAS covers a sufficient energy range of ETs with higher resolution than that of the previously reported photochemical method [2]. As a brief explanation of the principle of RDB-PAS, the procedure involves (i) detecting a photoacoustic signal, by modulated LED light (625 nm), induced by accumulation of electrons filling ETs from a deep level to a shallow level under irradiation of scanned (from longer wavelengths to shorter wavelengths) continuous monochromatic light for excitation of valence-band electrons directly to ETs, (ii) differentiating the resultant spectra from the longer wavelength side and converting the signal intensity to absolute density of ETs with reference to results obtained by the photochemical method, (iii) plotting ERDT as a function of energy difference from the top of the VB (VBT) and (iv) comparing with the energy of the CB bottom (CBB), in reference to the VBT, which is estimated by conventional PA spectra (corresponding to photoabsorption spectra) . As a result, both ERDT and CBB are plotted as a function of energy difference from the VBT. The ERDT patterns and conduction-band bottom (CBB) positions, measured by ordinary photoacoustic spectroscopy, for more than 20 commercially available or non-profitably provided titanium(IV) oxide (titania) powders were different from each other depending on the kind of sample. Degrees of coincidence (ζ) of ERDT/CBB were evaluated for a given pair of samples as a product of coincidence of (a) ERDT-pattern matching, (b) total ET density and (c) CBB position. Samples collected from closed position in a bottle gave high ζ, but samples with different code names showed low ζ except for pairs of samples prepared in the same way but coded differently. Furthermore, it was shown that the higher the ζ, the higher the degree of coincidence of photocatalytic activity (ζpc) of titania samples, i.e., photocatalytic activity of titania samples may be governed by ERDT/CBB. Thus, ERDT/CBB data provide solely and exclusively the way of identification and characterization as well as the way of prediction of performance and/or reactivity of metal-oxide powders as e.g., catalysts or photocatalysts. [1] Nitta, A., Takase, M., Takashima, M., Murakami, N. and Ohtani, B. A fingerprint of metal oxide powders--Characterization and identification with energy-resolved distribution of electron traps., submitted . [2] Ikeda, S., Sugiyama, N., Murakami, S.-y., Kominami, H., Kera, Y., Noguchi, H., Uosaki, K., Torimoto, T. and Ohtani, B. Quantitative Analysis of Defective Sites in Titanium(IV) Oxide Photocatalyst Powders. Phys. Chem. Chem. Phys., 5, 778-783 (2003). Figure 1

Electron-impact dissociative double ionization ofN2and CO: Dependence of transition probability on impact energy

We present an experimental and computational analysis of dissociative double ionization of ${\mathrm{N}}_{2}$ and CO molecules under electron impact. Experiments are performed at three energies, viz. 1, 3, and 5 keV, in order to observe the effect of impact energy on the dissociative ionization kinematics. We compare the kinetic energy release (KER) distributions of the charge symmetric dissociation channels of ${\mathrm{N}}_{2}^{2+}$ and ${\mathrm{CO}}^{2+}$ at these impact energies. An approximately linear trend between the transition energy and the expected KER values is inferred on the basis of the calculated potential energy curves of the dications. Experimentally, the normalized differential KER cross sections for these channels show an increasing trend in the low KER range and a decreasing trend in the high KER range as the electron-impact energy is increased. This observation indicates that the transition probability for excitation to different molecular ion states is not only a function of energy difference between the ground and excited states, but also a complicated function of the impact energy. In addition, nature of the observed trend in the differential KER cross sections differs significantly from their differential transition probability, which are calculated using inelastic collision model for fast-electron-impact case.

Mapping Substrate Surface Field Propagation in Block Polymer Thin Films

We isolated the key substrate–polymer interactions responsible for the propagation of substrate surface field effects in block polymer (BP) thin films through a modified approach to the Owens and Wendt interfacial energy formalism. This modification captured the influence of long-range surface energy components on through-film nanostructure orientation in BP thin films, and it provides a framework for manipulating BP thin film behavior without the need for extensive parameter space exploration. Optical microscopy (OM) of gradient thickness films on chlorosilane-modified substrates provided a high-throughput approach for identifying the critical propagation depth of substrate–polymer interfacial energy effects. Atomic force microscopy (AFM) was combined with OM to verify changes in free surface nanostructure as a function of film thickness. Using a model poly(methyl methacrylate-b-n-butyl acrylate) BP thin films system, we mapped the critical propagation depth as a function of interfacial energy difference...

Cage Effect in Poly(alkyl methacrylate) Thin Films Studied by Nile Red Single Molecule Fluorescence Spectroscopy

Interactions in a probe–polymer cage were monitored by spectral fluctuations in the emission spectroscopy of single molecules of Nile Red in poly(alkyl methacrylate) thin films (25–200 nm) in the 278–323 K temperature range. Three types of emission spectra were identified. The highest emission energy spectra show small amplitude fluctuations and a very low probability of changing their spectral emission features. On the other hand, the other two types of emission profiles exchange more frequently. The fluctuations are analyzed by the complementary cumulative distribution function of spectral emission energy difference between successive spectra in a time trace. The fluctuations show three components: two of them with zero mean average and distinctly different standard deviations and a third component with much lower frequency and an amplitude absolute value of 0.13–0.15 eV. This amplitude is the same in all conditions, pointing to a common feature of the probe–polymer cage as responsible for their presence: complex cage rearrangements, involving the carbonyl side chain of the polymer as the common actor are postulated to be the cause of these spectral fluctuations in the time range of seconds.

Mechanism of energy limit equilibrium of rock burst in coal mine

With the increase of mining depth, the effect of rock burst on coal mining is becoming more and more obvious and the rock burst mechanism becomes more and more complicated. Scholars from many countries had put forward different mechanisms, but no one gave a reasonable explanation to the mechanism of rock burst. In this paper, based on the energy theories, we studied the energy limit equilibrium (ELE) of coal mine rock burst. The coal seam with rock burst is divided into energy limit equilibrium zone (ELEZ) (A) and elastic zone (B); we also determined the position where the rock burst occurs, including the roof and floor of coal seams; in addition, we derived the limit width of ELEZ and the mathematic relationship between the limit width and occurrence mechanism of rock burst: the energy difference function (EDF), w( x) = w j − w p , because first-order derivative w′( x), is less than 0. So EDF is a monotonically decreasing function. The graph of the energy difference function was also determined, through which we analysed the occurrence mechanism of rock burst.

Transcrystallization kinetics at the poly(3-hydroxybutyrate-co-3-hydroxyvalerate)/hemp fibre interface

Abstract Transcrystallization of poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) on hemp fibres was investigated using polarized optical microscopy. Nucleation and growth of crystals of the transcrystalline region (TCR) were measured during isothermal treatments of samples located in a hot stage. The nucleation rate, nucleation density at saturation and growth rate of the TCR, were determined at crystallization temperatures between 320 and 363 K. The growth rate of crystals in the TCR is the same as that of spherulites in the bulk. Nucleation at the hemp fibres was properly described in terms of the heterogeneous nucleation theory and the transcrystalline growth agrees with the kinetics theory of polymer crystallization. From the empirical data we determined that the interfacial free energy difference function of PHBV on hemp fibres is Δσ = 4.4 erg/cm2, lower than the one in the bulk. This indicates that the substrate is not neutral but contributes to the formation of the TCR. From the intensity of the depolarization light, measured under different cooling rates, we determined the activation energies for crystallization in the bulk and transcrystallization.

A signal subspace approach for speech modelling and classification

In this paper, a speech classifier inspired by the signal subspace approach is developed. A novel signal subspace speech model is initially obtained via a rank reducing subspace decomposition algorithm that is based on the SVD. Motivated by the assumption that the speech signal comprises of short term dynamics that are slowly changing, it follows that the signal subspace of the speech signal is likewise slowly changing. The proposed signal subspace model aims to characterize the subspace dynamics using a family of subspace trajectories. In particular, each subspace trajectory is a sequence of vectors that traces the dynamics of a rank-one subspace in time. An assembly of these trajectories, henceforth, specifies the progression of the embedded signal subspace. To construct the signal subspace classifier, prototype elements in the form of the signal subspace models are determined for every signal class. A minimum-distance rule with a distance measure that resembles an energy difference function is subsequently applied in the actual classification task. Simulation of the proposed signal subspace classifier in an isolated digit speech recognition problem reveals promising results.

Numerical renormalization group studies of SU(4) Kondo effect in quantum dots

We theoretically study an enhancement of the Kondo effect in quantum dots with two orbitals and spin 1 2 . The Kondo temperature and conductance are evaluated as functions of energy difference Δ between the orbitals, using the numerical renormalization group method. The Kondo temperature is maximal around the degeneracy point ( Δ = 0 ) and decreases with increasing | Δ | following a power law, T K ( Δ ) = T K ( 0 ) ( T K ( 0 ) / | Δ | ) γ , which is consistent with the scaling analysis. The conductance at T = 0 is almost constant 2 e 2 / h . Both the orbitals contribute to the conductance around Δ = 0 , whereas the current through the upper orbital is negligibly small when | Δ | ≳ T K ( 0 ) . These are characteristics of SU(4) Kondo effect.

Transition Probability of Neutralization Process of +2 Ion Scattered on a Metal Surface

We examine the transition probability in the neutralizing process of +2 ion such as Be +2 , Ca +2 and Ba +2 through the electron transfer between the ion and a metal surface, using an impurity Anderson Hamiltonian. Within second order perturbation theory with respect to the transfer integral, an analytical expression of the transition probability is derived and numerically calculated. From the numerical results, the neutralization process of +2 ion on the metal surface seems to occur more easily with decreasing the atomic number of an ion. The transition probability depends on not only the initial kinetic energy of the moving ion but also its species of ions. In addition, the plot of the transition probability as a function of the initial velocity of ions theoretically suggests the presence of an optimized initial velocity for the neutralization process. From the contour map of the transition probability plotted as functions of energy difference E a - E F ( E a : energy of localized electron, E F : Fermi ...

Effective three-band model for double perovskites

We start from a six-band model describing the transition-metal t2g orbitals of half-metallic double perovskite systems, such as Sr2FeMoO6, in which only one of the transition metal ions (Fe) contains important intratomic repulsion Ufe. By eliminating the Mo orbitals using a low-energy reduction similar to that used in the cuprates, we construct a Hamiltonian which contains only effective t2g Fe orbitals. This allows to treat exactly Ufe, and most of the Fe-Mo hopping. As an application, we treat the effective Hamiltonian in the slave-boson mean-field approximation and calculate the position of the metal-insulator transition and other quantities as a function of pressure or on-site energy difference.

Interfacial crystallization of isotactic polypropylene molded against the copper surface with various surface roughnesses prepared by an electrochemical process

The influence of surface topography of copper (Cu) sheet on the heterogeneous nucleation of isotactic polypropylene (iPP) at the iPP/Cu interface had been investigated mainly using polarized optical microscope with hot stage. Various textures of Cu surfaces prepared by sandpaper polishing and electrochemical anodizing had been made and they were utilized to induce interfacial nucleation of iPP upon supercooling. This process enables us to change the topological feature of the copper surface without changing their chemical compositions. The pretreated surfaces were quantitatively characterized by a surface texture instrument in terms of RMS roughness (Ra). Copper surface with higher surface roughness induced more nuclei of iPP and led to a thicker transcrystalline layer in the interfacial region upon supercooling over the temperature range 128°C < Tc < 134°C. Based on the theory of heterogeneous nucleation, it was found that the induction time correlates well with the nucleation rate in determining the interfacial free energy difference function Δσ of iPP. The ratio of Δσ at the interface to that in the bulk matrix (ΔσTCL/Δσbulk) for the polished surface (Ra = 0.09 μm) is 2.89, implying the transcrystallization growth is unfavorable from a thermodynamic point of view. The ratio of ΔσTCL/Δσbulk becomes smaller as the current density for anodizing increases, indicating the transcrystallization growth is getting favorable. Moreover, induction times and nucleation rates were also measured to characterize quantitatively the nucleating ability of various Cu surfaces.

Effect of the surface roughness of sulfuric acid-anodized aluminum mold on the interfacial crystallization behavior of isotactic polypropylene

The influence of the surface topography of aluminum alloy (Al) on the heterogeneous nucleation of isotactic polypropylene (iPP) at the iPP/Al interface has been investigated using a polarized optical microscope (POM) with a hot stage. Different textures of the Al surface were prepared by electrochemical processes, including polishing and anodizing, and utilized to induce interfacial nucleation upon supercooling. This process enabled the topological features of the aluminum surface to be controlled without altering their chemical composition by such a procedure. The pretreated surfaces were investigated by scanning electron microscopy and quantitatively characterized by a surface texture instrument in terms of RMS roughness (R a). The Al surface with a higher surface roughness induced more nuclei of iPP and led to a transcrystalline layer (TCL) in the interfacial region upon supercooling over the temperature range 128°C < T c < 154°C. Based on the theory of heterogeneous nucleation, it was found that the induction time correlates well with the nucleation rate in determining the interfacial free energy difference function Δσ of iPP. The ratio of Δσ at the interface to that in the bulk matrix (ΔσTCL/Δσ bulk) for the polished surface (R a = 0.38 μm) is 4.45, implying that transcrystallization growth is unfavorable from a thermodynamic point of view. On the other hand, the Δσ TCL/Δσ bulk ratio decreases as the current density for anodizing increases, indicating that transcrystallization growth becomes favorable. The induction times and nucleation rates were also measured to characterize quantitatively the nucleating ability of various Al surfaces. The oxide porosity was filled in when sealing treatment by hydration was carried out. This resulted in Δσ TCL/Δσ bulk being slightly higher as the surface roughness decreased.