Exponential Potential Model Research Articles

Investigation of bound state energy spectra for fermionic particles in the presence of ultra generalized exponential hyperbolic potential model

By considering the ultra generalized exponential hyperbolic potential, which covers many potential types, the solutions of the Dirac equation with spin/pseudo-spin symmetric limits are achieved. In both approaches, the relation giving the bound state energy eigenvalues is obtained in a closed form. By using these relations, the energy values are calculated numerically for both symmetry cases via the software program. In addition, it has been identified how the bound state energy eigenvalues depend on the parameters. Besides, the energy equations for the Schrödinger and Klein–Gordon particles in the limit states are derived.

Calibration-free pH long-time measurement method based on electrode potential drift dynamic compensation-applying self-adaptive dynamic optimization exponential smoothing method

The long-term in-situ accurate measurement of pH value is an urgent need for environmental water quality monitoring without calibration of pH electrodes. The nonlinearity and potential drift of pH electrode is the main problem which restricts long-term continuous monitoring. The characteristic rules including electrode potential, zero value, electrode slope coefficient, and electrode potential drift for pH electrode are analyzed in detail under the condition of long-term continuous use. The exponential smoothing potential drift prediction model with self-adaptive dynamic optimization smoothing order and smoothing coefficient is established. Combining electrode potential drift threshold judgment and Nernst equation, calibration-free dynamic calculation mathematical model of pH long-term monitoring is established. Indoor simulation and field test indicate that the measurement absolute error caused by electrode drift is within 0.01 pH and the specified measurement error for pH monitoring instrument is always within 0.1 pH. The proposed method is very suitable for the terminal of pH detector with the advantages of good portability for the MCU chip, small samples, high-precision and fast running speed. Furthermore, the life of pH electrode can be prolonged significantly. It is also proved that the proposed method has a good application prospect.

Rational Design of Nonbonded Point Charge Models for Divalent Metal Cations with Lennard-Jones 12-6 Potential.

Exploring a metal-involved biochemical process at a molecular level often requires a reliable description of metal properties in aqueous solution by classical nonbonded models. An additional C4 term for considering ion-induced dipole interactions was previously proposed to supplement the widely used Lennard-Jones 12-6 potential (known as the 12-6-4 LJ-type model) with good accuracy. Here, we demonstrate an alternative to modeling divalent metal cations (M2+) with the traditional 12-6 LJ potential by developing nonbonded point charge models for use with 11 water models: TIP3P, SPC/E, SPC/Eb, TIP4P-Ew, TIP4P-D, and TIP4P/2005 and the more recent OPC3, TIP3P-FB, OPC, TIP4P-FB, and a99SB-disp. Our designed models simultaneously reproduce the experimental hydration free energy, ion-oxygen distance, and coordination number in the first hydration shell accurately for most of the metal cations, an accuracy equivalent to that of the complex 12-6-4 LJ-type and double exponential potential models. A systematic comparison with the existing M2+ models is presented as well in terms of effective ion radii, diffusion constants, water exchange rates, and ion-water interactions. Molecular dynamics simulations of metal substitution in Escherichia coli glyoxalase I variants show the great potential of our new models for metalloproteins.

The Exact Solutions of a Class of Monotonic Exponential Potential Model

We studied a class of exponential potential model $$V(x)=-a\,e^{-b\,x}$$ ( $$a>0, b>0$$ ) and found that its solutions are given by the Bessel functions, but the energy spectra $$E=-b^2(n+1/2)^2/8$$ which are derived from the quantization condition do not correspond to any discrete bound states. The energy levels which are calculated by the boundary condition $$J_{\nu }(2\sqrt{2a}/b)=0$$ at the origin are in good agreement with the numerical results. We illustrate the wave functions through varying the potential parameters a, b and notice that they are pull back to the origin when the potential parameter a or b increases.

Methane dehydrogenation on 3d 13-atom transition-metal clusters: A density functional theory investigation combined with Spearman rank correlation analysis

The rational use of non-renewable energy sources such as methane (CH4) has been considered a promising alternative to several high-value chemicals. Therefore, there is a considerable effort to identify the main physical-chemical features for modulating CH4 dehydrogenation, in particular, at the nanoscale regime, where new effects could promote the breaking of the C–H bond. Thus, at this work, we report a theoretical investigation of the dehydrogenation of CH4 based on a step-by-step process on 3d 13-atom transition-metal (TM) clusters (TM = Fe, Co, Ni, Cu) through ab initio density functional theory calculations combined with the Spearman rank correlation analysis and the unity bond index-quadratic exponential potential (UBI-QEP) model. Our results revealed that the adsorption/interaction of CH4 and its dehydrogenated species (CH3, CH2, CH, and C) is guided by three factors, namely, (i) charge transfer from the TM13 clusters to the CHn species, (ii) enhancement of the sp-d coupling between the electronic states of the CHn species (sp-) and TM13 (d-states) systems, (iii) number of unpaired electrons in the CHn species, in which (ii) and (iii) increases by decreasing n, which is consistent with the tendency of the C atom to restore its 4-fold coordination. The H co-adsorption promotes an increasing in the adsorption/interaction energy as it promotes an enhancement of sp-d hybridization, which has a maximum for, Fe13 and Co13 and minimum for Cu13. From the Spearman correlation analysis, we identified that the effective coordination number, the Hirshfeld charge on the C atom, and the distance between the CHn and TM13 systems drive the magnitude of the adsorption energy, in particular, at the H co-adsorption regime. The thermodynamic and kinetic properties obtained via the UBI-QEP model indicates that the CH4 dehyrogenation is slightly favorable on Ni13 cluster, while kinetically CH4 dehydrogenation process would take place much easier on Ni13, Fe13, and Co13 rather than on the Cu13 cluster.

Position-dependent mass Schrödinger equation for exponential-type potentials.

In quantum chemical calculations, there are two facts of particular relevance: the position-dependent mass Schrödinger equation (PDMSE) and the exponential-type potentials used in the theoretical study of vibrational properties for diatomic molecules. Accordingly, in this work, the treatment of exactly solvable PDMSE for exponential-type potentials is presented. The proposal is based on the exactly solvable constant mass Schrödinger equation (CMSE) for a class of multiparameter exponential-type potentials, adapted to the position-dependent-mass (PDM) kinetic energy operator in the O von Roos formulation. As a useful application, we consider a PDM distribution of the form [Formula: see text], where the different parameters can be adjusted depending on the potential under study. The principal advantage of the method is that solution of different specific PDM exponential potential models are obtained as particular cases from the proposal by means of a simple choice of the involved exponential parameters. This means that is not necessary resort to specialized methods for solving second-order differential equations as usually done for each specific potential. Also, the usefulness of our results is shown with the calculation of s-waves scattering cross-section for the Hulthén potential although this kind of study can be extended to other specific potential models such as PDM deformed potentials.

Dissociative Adsorption, Dissolution, and Diffusion of Hydrogen in Liquid Metal Membranes. A Phenomenological Model

There is only limited experimental data and theoretical treatment available in the literature on hydrogen sorption and diffusion in liquid metals, in stark contrast with that in solid metals. This paper utilizes our predictive phenomenological model requiring minimal input, the Pauling Bond Valence-Modified Morse Potential (PBV-MMP) model, for estimating the thermodynamic and kinetic parameters of hydrogen solution and diffusion in liquid metals treated as quasi-crystalline. The PBV-MMP model is a refinement of the Unity Bond Index-Quadratic Exponential Potential (UBI-QEP) model for estimating the energetics of solid metal surface reactions. The sequential kinetic steps of hydrogen dissociative surface adsorption on the feed side, subsurface penetration, and atomic interstitial diffusion in the bulk, followed by these steps in reverse on the permeate side, are thus treated via the PBV-MMP model within Eyring’s transition-state theory framework, while the entropic changes are evaluated via Eyring’s free vo...

Stochastic Resonance in Second-Order Underdamped System With Exponential Bistable Potential for Bearing Fault Diagnosis

Stochastic resonance (SR) as effective approach for weak signal detection has been widely used in bearing fault signal diagnosis. In this paper, a new method was proposed to detect fault signals, which consists of an exponential bistable potential model generalized by using a harmonic Potential (HP) model, a Gaussian potential (GP) model and second-order underdamped system. As the classical bistable SR (CBSR) has the disadvantage of output saturation, which will suppress the optimal signal-to-noise ratio (SNR) of the system, therefore, underdamped SR with exponential potential (UESR) and underdamped SR with classical bistable potential (UCSR) are applied to detect fault signal, respectively. Under the adiabatic condition, the analytical expression of the SNR is calculated for the UESR system driven by Gaussian white noise and periodic signal. Then, the effects of system parameters and the damping factor on analytical expression of SNR as a function of noise intensity for different parameters are studied, respectively. Finally, the proposed method is applied to detect simulated fault signals and actual bearing fault signals. The experimental results show that the proposed UESR method is superior to the UCSR method in fault signal diagnosis, such as larger output SNR and higher spectrum peaks at fault characteristic frequencies.

Uniform Airy Approximation for Nonadiabatic Transitions in a Curve-Crossing Weak-Coupling Case

Abstract This work suggests a connection between Landau-Zener transition probabilities between two crossing potentials in the classically accessible WKB regime and Landau-Lifshitz transition probabilities in the classically inaccessible WKB regime. It is based on the uniform Airy (UAi) approximation which represents a generalization of quantum transition probabilities for linear crossing potentials with constant coupling. The performance of the UAi approximation is tested by comparison with distorted-wave probabilities for an exponential potential model and illustrated for potentials that determine the intersection of two ab initio vibronic potential surfaces of the NO-Ar system.

Non-deformed singular and non-singular exponential-type potentials

The canonical transformation method applied to the Schrödinger equation to transform it into a second-order differential equation of hypergeometric-type is presented. Starting from there, those exactly solvable multiparameter exponential-type (ME-T) potentials with hypergeometric wavefunctions that belong to the families of radial (singular) and one-dimensional (non-singular) potentials, are obtained. Furthermore, we show how the choice of the involved parameters leads, as particular cases, to different deformed or non-deformed potential models already used in the study of electronic properties of diatomic molecules. Also, the analysis of parameters lets us identify the couple of potential partners (singular/non-singular) that correspond to each choice of the parameters appearing in the ME-T potential. As a useful application of the proposal, the most important non-deformed exponential potential models are considered for which it can be viewed as a unified treatment with the following advantages: (1) It is not necessary to use a special method to solve the Schrödinger equation for a specific potential model because solution is obtained as particular case by the simple choice of the involved parameters; (2) The families of singular and non-singular potentials are straightforward identified; (3) The corresponding associated partners, between radial and one-dimensional non-deformed potentials, are found; (4) New potentials, as interesting alternatives for quantum applications, are obtained. In addition, from the conditions that parameters must meet to have physically acceptable solutions, we establish the requirements for the existence or not of singular/non-singular potential partners.

Minimally coupled scalar field cosmology in anisotropic cosmological model

We study a spatially homogeneous and anisotropic cosmological model in the Einstein gravitational theory with a minimally coupled scalar field. We consider a non-interacting combination of scalar field and perfect fluid as the source of matter components which are separately conserved. The dynamics of cosmic scalar fields with a zero rest mass and an exponential potential are studied, respectively. We find that both assumptions of potential along with the average scale factor as an exponential function of scalar field lead to the logarithmic form of scalar field in each case which further gives power-law form of the average scale factor. Using these forms of the average scale factor, exact solutions of the field equations are obtained to the metric functions which represent a power-law and a hybrid expansion, respectively. We find that the zero-rest-mass model expands with decelerated rate and behaves like a stiff matter. In the case of exponential potential function, the model decelerates, accelerates or shows the transition depending on the parameters. The isotropization is observed at late-time evolution of the Universe in the exponential potential model.

宽广温度压强下Rb<sub>x</sub>C<sub>60</sub> (x = 3,4,6)的热力学性质

本文基于自由体积理论(FVT)应用解析平均场近似的方法对RbxC60 (x = 3,4,6)的热力学性质进行研究。根据双指数势模型和文献中的压缩实验数据，拟合得到三套势参数，并对相应的势函数曲线进行了比较分析。在宽广温度和压强下对三种碱金属掺杂富勒烯RbxC60 (x = 3,4,6)的热力学量，包括热膨胀、体积模量、等容热容量、亥姆霍兹自由能进行了计算和分析。我们采用的方法不仅计算简单而且结果与文献中实验数据非常一致。 Based on the free volume theory (FVT), the thermodynamic properties of RbxC60 (x = 3,4,6) are studied by means of analytic mean field approximation. According to the double exponential po-tential model and the compression experimental data in the literature, three sets of potential pa-rameters are obtained, and the corresponding potential function curves are compared and ana-lyzed. The thermodynamic properties of three alkali metal doped fullerene RbxC60 (x = 3,4,6), in-cluding thermal expansion, bulk modulus, constant volume heat capacity and Helmholtz free en-ergy, were calculated and analyzed under wide temperature and pressure. Our method is not only simple in calculation, but also in good agreement with the experimental data in the literature.

Klein-Gordon equation particles in exponential-type molecule potentials and their thermodynamic properties in D dimensions

In this paper we use the Nikiforv-Uvarov method to obtain the approximate solutions of the Klein-Gordon equation with deformed five parameter exponential type potential (DFPEP) model. We also obtain the solutions of the Schr\"odinger equation in the presence of the DFPEP in the non-relativistic limits. In addition, we calculate in the nonrelativistic limits the thermodynamics properties such as vibrational mean energy U, free energy F and the specific heat capacity C . Special cases of the potential are also discussed.

Spatial correlation of productive component for peach palm crop and some physical attributes of Eutrochrept soil

Currently, Brazil sells around 300 million dollars per year of peach palms (Bactris gasipaes), wherein this country is responsible for being the largest worldwide producer, exporter and consumer. In crop year of 2014, productive components of peach palms were analyzed according to soil physical properties in Registro, SP, Brazil. The objectives were to evaluate the variability of the soil attributes and define a linear and spatial correlation between the crop productive components and the soil physical properties. Geostatistical grid was installed to collect data from soil and plant, with 54 sampling points in a total area of approximately 10,000 m2. With regard to linear point of view, stem diameter and palm height was explained by direct and exponential potential model, which was highly significant due to mechanical resistance to penetration.

Planck2013 results. XXII. Constraints on inflation

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to $n_s = 0.9603 \pm 0.0073$, ruling out exact scale invariance at over 5 $\sigma$. Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V" < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n > 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining $d n_s/d ln k = -0.0134 \pm 0.0090$. Several analyses dropping the slow-roll approximation are carried out, including detailed model comparison and inflationary potential reconstruction. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit $\chi^2$ by ~ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with bounds on $f_\mathrm{NL}$ measured by Planck. The fractional primordial contribution of CDM isocurvature modes in the curvaton and axion scenarios has upper bounds of 0.25% or 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelation can improve $\chi^2$ by approximatively 4 as a result of slightly lowering the theoretical prediction for the $\ell<40$ multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.

Unified semiclassical theory for the two-state system: An analytical solution for general nonadiabatic tunneling

Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.

Dark energy exponential potential models as curvature quintessence

It has been recently shown that, under some general conditions, it is always possible to find a fourth-order gravity theory capable of reproducing the same dynamics as a given dark energy model. Here, we discuss this approach for a dark energy model with a scalar field evolving under the action of an exponential potential. In the absence of matter, such a potential can be recovered from a fourth-order theory via a conformal transformation. Including the matter term, the function f(R) entering the generalized gravity Lagrangian can be reconstructed according to the dark energy model.

CONFORMAL SCALING GAUGE SYMMETRY AND INFLATIONARY UNIVERSE

Considering the conformal scaling gauge symmetry as a fundamental symmetry of nature in the presence of gravity, a scalar field is required and used to describe the scale behavior of the universe. In order for the scalar field to be a physical field, a gauge field is necessary to be introduced. A gauge invariant potential action is constructed by adopting the scalar field and a real Wilson-like line element of the gauge field. Of particular, the conformal scaling gauge symmetry can be broken down explicitly via fixing gauge to match the Einstein–Hilbert action of gravity. As a nontrivial background field solution of pure gauge has a minimal energy in gauge interactions, the evolution of the universe is then dominated at earlier time by the potential energy of background field characterized by a scalar field. Since the background field of pure gauge leads to an exponential potential model of a scalar field, the universe is driven by a power-law inflation with the scale factor a(t)~tp. The power-law index p is determined by a basic gauge fixing parameter gF via [Formula: see text]. For the gauge fixing scale being the Planck mass, we are led to a predictive model with gF=1 and p≃62.

UBI-QEP Analysis for the Mechanism of Fischer-Tropsch Synthesis

The unity bond index-quadratic exponential potential(UBI-QEP) model is used to evaluate the heat of chemisorption of adsorbed species and activation barriers for the elementary reactions in the mechanisms for Fischer-Tropsch synthesis (FTS) reaction over a model catalyst Co(0001), including carbide mechanism, hydroxycarbene mechanism, and Co insertion mechanism. It is demonstrated that the reaction pathway for the formation of hydrocarbons proposed in the carbide mechanism is energetically favorable. The insertion of CO is the pathway for the formation of oxygenations. Dissociation of adsorbed CO and hydrogenation of C(subscript ads) have higher activation barriers than other elementary steps in the reaction pathway. The energetically preferred pathway to initiate the carbon chain growth is via insertion of CH(subscript 2, ads) intermediate into the carbon-metal bond of CH(subscript 3, ads) or CH(subscript 2, ads) group. The activation barrier for termination of carbon chain propagation by β-H elimination is lower than hydrogenation. The olefins and oxygenates in the primary products during FTS are apt to conduct the secondary reaction via readsorption on the catalyst surface because of its low active energies. Compared with Fe/W(110), the activation barriers for CH(subscript x, ads) hydrogenations and CH(subscript 2, ads) insertion are lower on Co(0001), which results in higher selectivity of methane and more yield of heavy hydrocarbons.

Quintessence in a brane world

We reanalyze a new quintessence scenario in a brane world model, assuming that a quintessence scalar field is confined in our 3-dimensional brane world. We study three typical quintessence models : (1) an inverse-power-law potential, (2) an exponential potential, and (3) kinetic-term quintessence ($k$-essence) model. With an inverse power law potential model ($V(\phi) = \mu ^{\alpha + 4} \phi^{- \alpha}$), we show that in the quadratic dominant stage, the density parameter of a scalar field $\Omega_\phi$ decreases as $a^{-4(\alpha-2)/(\alpha+2)}$ for $2<\alpha < 6$, which is followed by the conventional quintessence scenario. This feature provides us wider initial conditions for a successful quintessence. In fact, even if the universe is initially in a scalar-field dominant, it eventually evolves into a radiation dominant era in the $\rho^2$-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, resulting that $\alpha\geq 4$ is required. This constraint also restricts the value of the 5-dimensional Planck mass, e.g. $4 \times 10^{-14}m_4 \lsim m_5 \lsim 3 \times 10^{-13}m_4$ for $\alpha=5$. For an exponential potential model $V=\mu^4\exp(-\lambda \phi/m_4)$, we may not find a natural and successful quintessence scenario as it is. While, for a kinetic-term quintessence, we find a tracking solution even in $\rho^2$-dominant stage, rather than the $\Omega_\phi$-decreasing solution for an inverse-power-law potential. Then we do find a little advantage in a brane world. Only the density parameter increases more slowly in the $\rho^2$-dominant stage, which provides a wider initial condition for a successful quintessence.