Search

Fourier-transform microwave spectroscopy has been applied for the 13C/18O-substituted tropolone to observe tunneling-rotation transitions as well as pure rotational transitions. The tunneling-rotation transitions were observed between the 13C-4 and -6 forms as well as between 13C-3 and -7, between 13C-1 and -2, and between 18O-8 and -9 (we denote these tunneling pairs as 13C-46, etc., below) although they have an asymmetric tunneling potential due to the difference in the zero point energy (ZPE). From the observed tunneling splittings ΔEij (0.9800–1.6824 cm−1), the differences in ZPE Δij for the 13C-46, -37, -12, and 18O-89 species are derived to be −0.1104, 0.5652, −1.3682, and 1.3897 cm−1 to agree well with the DFT calculation. The state mixing ratio of the tunneling states decreases drastically from (44%:56%) to (8.7%:91.3%) for 13C-46 and 18O-89 with an increase in the asymmetry Δij of the tunneling potential function. The observed tunneling-rotation interaction constants Fij decrease from 16.001 to 9.224 cm−1 as the differences in ZPE Δij increase, while the diagonal tunneling-rotation interaction constants Fu increase from 1.767 to 13.70 cm−1, explained well by the mixing ratio of the tunneling states. [ABSTRACT FROM AUTHOR]

We present an approximate analytical approach to the adsorption problem of ABA triblock copolymers confined between two parallel plates in a θ solvent and give the expression of the propagator q(x, t) as a piece-wise function by solving the modified diffusion equation. In this way, the role of separation between the two plates, adsorption energy and block lengths on segment concentration profile, chain conformations, and interaction potential is then investigated, which agrees well with the numerical results. It is demonstrated that there are parallels between lengthening adsorbing A blocks and increasing surface affinity: strong adsorption and long adsorbing blocks favor the formation of loops and bridges, whereas more tails and free chains exist in the case of weak adsorption and short A blocks at large separations. For moderate and strong adsorptions, the bridging fraction begins to plummet at a separation larger than the end-to-end distance of non-adsorbing B block RB and becomes negligible at above 2RB owing to the entropy effect. The depth of the potential well in the interaction potential profile depends on the adsorption energy and A block length, while the location of the potential minimum corresponds to the onset of the sharp decrease in bridges. [ABSTRACT FROM AUTHOR]

The dynamics of (few) electrons dissolved in an ionic fluid—as when a small amount of metal is added to a solution while upholding its electronic insulation—manifests interesting properties that can be ascribed to nontrivial topological features of particle transport (e.g., Thouless' pumps). In the adiabatic regime, the charge distribution and the dynamics of these dissolved electrons are uniquely determined by the nuclear configuration. Yet, their localization into effective potential wells and their diffusivity are dictated by how the self-interaction is modeled. In this article, we investigate the role of self-interaction in the description of the localization and transport properties of dissolved electrons in non-stoichiometric molten salts. Although the account for the exact (Fock) exchange strongly localizes the dissolved electrons, decreasing their tunneling probability and diffusivity, we show that the dynamics of the ions and of the dissolved electrons are largely uncorrelated, irrespective of the degree to which the electron self-interaction is treated and in accordance with topological arguments. [ABSTRACT FROM AUTHOR]

We propose a generalization of the stochastic resetting mechanism for a Brownian particle diffusing in a one-dimensional periodic potential: randomly in time, the particle gets reset at the bottom of the potential well it was in. Numerical simulations show that in mirror asymmetric potentials, stochastic resetting rectifies the particle's dynamics, with a maximum drift speed for an optimal average resetting time. Accordingly, an unbiased Brownian tracer diffusing on an asymmetric substrate can rectify its motion by adopting an adaptive stop-and-go strategy. Our proposed ratchet mechanism can model the directed autonomous motion of molecular motors and micro-organisms. [ABSTRACT FROM AUTHOR]

We are considered with the following nonlinear Schrödinger equation: −Δu+(λa(x)+1)u=f(u),x∈V,$$ -\Delta u+\left(\lambda a(x)+1\right)u=f(u),x\in V, $$on a locally finite graph G=(V,E)$$ G=\left(V,E\right) $$, where V$$ V $$ denotes the vertex set, E$$ E $$ denotes the edge set, λ>1$$ \lambda >1 $$ is a parameter, f(s)$$ f(s) $$ is asymptotically linear with respect to s$$ s $$ at infinity, and the potential a:V→[0,+∞)$$ a:V\to \left[0,+\infty \right) $$ has a nonempty well Ω$$ \Omega $$. By using variational methods, we prove that the above problem has a ground state solution uλ$$ {u}_{\lambda } $$ for any λ>1$$ \lambda >1 $$. Moreover, we show that as λ→∞$$ \lambda \to \infty $$, the ground state solution uλ$$ {u}_{\lambda } $$ converges to a ground state solution of a Dirichlet problem defined on the potential well Ω$$ \Omega $$. [ABSTRACT FROM AUTHOR]

Field-controlled micromanipulation represents a pivotal technique for handling microparticles, yet conventional methods often risk physical damage to targets. Here, we discovered a completely new mechanism for true noncontact manipulation through photothermal effects, called thermal-optical tweezers. We employ a laser self-assembly photothermal waveguide (PTW) for dynamic microparticle manipulation. This waveguide demonstrates superior photothermal conversion and precision control, generating a nonisothermal temperature field. The interaction of thermal convection and thermophoresis within this field creates a microfluidic potential well, enabling noncontact and nondestructive particle manipulation. By varying the path of PTWs in lithography and manipulating laser loading modes, diverse manipulation strategies, such as Z-shaped migration, periodic oscillation, and directional transport, are achievable. Our innovative noninvasive micromanipulation technology minimizes not only physical damage to target objects but also enables precise and diverse manipulation of micro entities, opening up new avenues for the photothermal control of cells and biomolecules. [ABSTRACT FROM AUTHOR]

This article is about the following Kirchhoff–Schrödinger–Poisson system with steep potential well 1.1 −(a+b∫ℝ3|∇u|2dx)△u+λV(x)u+μϕ(x)u=f(x,u)+h(x)|u|αinℝ3,−△ϕ=u2,inℝ3,$$ \left\{\begin{array}{ll}-\left(a&#x0002B;b{\int}_{{\mathrm{\mathbb{R}}}&#x0005E;3}{\left&#x0007C;\nabla u\right&#x0007C;}&#x0005E;2 dx\right)\triangle u&#x0002B;\lambda V(x)u&#x0002B;\mu \phi (x)u&#x0003D;f\left(x,u\right)&#x0002B;h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{\alpha }& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}&#x0005E;3,\\ {}-\triangle \phi &#x0003D;{u}&#x0005E;2,& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}&#x0005E;3,\end{array}\right. $$ where a,b,λ>0$$ a,b,\lambda >0 $$ are constants, μ>0$$ \mu >0 $$, and 0<α<1,f∈C(ℝN×ℝ,ℝ)$$ 0<\alpha <1,f\in C\left({\mathrm{\mathbb{R}}}&#x0005E;N\times \mathrm{\mathbb{R}},\mathrm{\mathbb{R}}\right) $$. By using the variational principle, we overcome the difficulties caused by Poisson's term and obtain system (1.1) that has two nontrivial solutions under certain assumptions. Moreover, we study the concentration of solutions and obtain new conclusions of system (1.1). Finally, we present the case where the solution to system (1.1) does not exist. [ABSTRACT FROM AUTHOR]

We use post Hartree–Fock advanced electronic structure computations to investigate the lowest electronic states of the AlO3+ trication. These computations confirm the existence of metastable AlO3+ ions in gas phase. At least three electronic states (13Π, 11Δ, 11Σ+) with potential wells are identified. These potential wells have depths of several hundreds of meV, which are deep enough to support several rovibrational levels where this trication may be found. Besides, we estimate the adiabatic triple ionisation energy of AlO at ∼55 eV. Furthermore, the current confirmation of the meta-stability of AlO3+ in gas phase should motivate the search for this aluminium oxide with Al(+V) in liquids and in solid state, in particular at high-pressure/high-temperature phases of alumina polymorphs and of aluminosilicates. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variable coefficient viscoelastic semilinear wave equation with logarithmic source term and acoustic boundary conditions in domains with non‐locally reacting boundary. By potential well method, we get the global existence of solution and through several important lemmas, we prove the general energy decay estimate of the system. [ABSTRACT FROM AUTHOR]

In this paper, we study multi-bump solutions of the following Kirchhoff type equation: - M ∫ R 2 | ∇ u | 2 d x Δ u + μ V (x) + h (x) u = λ f (u) in R 2 , where M is continuous with inf R + M > 0 , V ≥ 0 and its zero set has several disjoint bounded components, μ , λ are positive parameters, f has exponential critical growth. When V decays to zero at infinity, we use variational methods to obtain the existence and concentration behavior of multi-bump solutions. [ABSTRACT FROM AUTHOR]

This paper explores the use of the approximation of isolated resonance method for determining the safe basins (SBs) in the problem of escape from a potential well. This study introduces a novel approach to capture the location and shape of the SBs and establish their erosion profiles. This research highlights the concept of "true" safe basins, which remain invariant with phase shifts, a critical factor often faced in real-world applications. A cubic polynomial potential serves as the benchmark to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

This study demonstrates a significant enhancement in the performance of thin-film transistors (TFTs) in terms of stability and mobility by combining indium–tungsten oxide (IWO) and zinc oxide (ZnO). IWO/ZnO heterojunction structures were fabricated with different channel thickness ratios and annealing environments. The IWO (5 nm)/ZnO (45 nm) TFT, annealed in O2 ambient, exhibited a high mobility of 26.28 cm2/V·s and a maximum drain current of 1.54 μA at a drain voltage of 10 V, outperforming the single-channel ZnO TFT, with values of 3.8 cm2/V·s and 28.08 nA. This mobility enhancement is attributed to the formation of potential wells at the IWO/ZnO junction, resulting in charge accumulation and improved percolation conduction. The engineered heterojunction channel demonstrated superior stability under positive and negative gate bias stresses compared to the single ZnO channel. The analysis of O 1s spectra showed OI, OII, and OIII peaks, confirming the theoretical mechanism. A bias temperature stress test revealed superior charge-trapping time characteristics at temperatures of 25, 55, and 85 °C compared with the single ZnO channel. The proposed IWO/ZnO heterojunction channel overcomes the limitations of the single ZnO channel and presents an attractive approach for developing TFT-based devices having excellent stability and enhanced mobility. [ABSTRACT FROM AUTHOR]

AbstractThis article continues the series of works by the authors on the approximation of the electronic terms of a diatomic molecules and their vibrational structure by the Morse formula, which is the simplest anharmonic approximation of the real term U(r). Depending on the choice of parameters, the approximation has two alternative solutions M1(r) and M2(r), with different patterns of deviations from the real term and its vibrational structure; some typical deviations for M1(r) and M2(r) are described. The difference δ(r)=U(r)−M(r) quantitatively shows the changes in the shape of the terms during approximation and can serve as a reference point when choosing its type for solving a specific problem. We introduced an empirical anharmonicity function −2ωex(v), which characterizes the positions of vibrational levels in the potential well; it demonstrates the distortion of the vibrational structure of the term U(r) during the approximation. Based on the data from literature, the functions δ(r) and −2ωex(v) were constructed for more than 20 molecules and a preliminary classification of electronic terms according to their characteristic features is described. Here we present a group of simple terms with minimal deviations from the Morse shape. [ABSTRACT FROM AUTHOR]

An edge-confined single-species plasma will relax to create a potential energy hill that climbs from the boundary. This hill represents a potential well for species of the opposite sign and can be a means to confine the second species. With this ultimate application in mind, we have studied the relation between the plasma temperature, the number of confined particles, and the electrostatic potential well that forms in a fully non-neutral plasma of electrons in a trapping volume with an artificially structured boundary (ASB). An ASB is a structure that produces periodic short-range static electric and magnetic fields for confining a plasma. To perform a detailed analysis on this topic, simulations using a particle-in-cell code have been performed. By varying the configurational elements of the ASB, such as the bias on the boundary electrodes and the internal radius of the structure, coupled with a course thermalization process and a prescribed threshold for particle leakage, potential well values were determined for a range of plasma temperatures and confinement conditions. Maximum well depths were observed below a threshold plasma temperature in each configuration. This study gives insight into the limitations of primary particle confinement with this type of structure and optimal conditions for the formation of a potential well that might be utilized to confine a second species. [ABSTRACT FROM AUTHOR]

Analysis of the performance degradation for W-band lossy ceramic-loaded gyrotron traveling wave tubes (gyro-TWTs) caused by ionization of the released gas molecules is presented in this paper. The gas is released from the lossy ceramics during high average or continuous wave operation and ionized by colliding with the high-energy gyrating electrons. A potential well will be formed by the diffusion and accumulation of the ionization particles after the collision and then degrade the gyro-TWT performance. This process has been simulated based on a simplified model by introducing an equivalent ionization source combining ions and electrons. With a vacuum of 5.1 × 10 - 5 Pa, the theoretically calculated initial energy and equivalent ionization current are 0.01 eV and 0.5 A, respectively. It leads to a deterioration in the output power stability of the gyro-TWT. The performance degradation including spectrum and field pattern caused by gas ionization is also given and analyzed. One of the primary causes is the quality (pitch factor and velocity spread) degradation of the electron beam. According to the simulation and hot test experiments, the vacuum should be maintained below 2.1 × 10 - 6 Pa for stabilizing the amplified operation. [ABSTRACT FROM AUTHOR]

This paper considers a class of higher-order nonlocal parabolic equations with special coefficient. We apply the Faedo-Galerkin approximation method and cut-off technique to obtain the local solvability. Furthermore, based on the framework of the modified potential well, we get the global existence, asymptotic behavior, and blow-up of the weak solutions by the Hardy-Sobolev inequality when the initial energy is subcritical J(u0) < d. In the critical case of J(u0) = d, the above results have also been obtained. Finally, we utilize some new processing methods to gain the blow-up criterion in finite time with supercritical initial energy J(u0) > 0. [ABSTRACT FROM AUTHOR]

In this paper, we study the following Kirchhoff-type equation:... where M ∈ C(R+,R+) is a general function, V ≥ 0 and its zero set may have several disjoint connected components, μ > 0 is a parameter, K is permitted to be unbounded above, and f has exponential critical growth. By using the truncation technique and developing some approaches to deal with Kirchhofftype equations with critical growth in the whole space, we get the existence and concentration behavior of solutions. The results are new even for the case M ≡ 1. [ABSTRACT FROM AUTHOR]

In this paper, we use the modified potential well method and the Galerkin method to study the following mixed local and nonlocal parabolic equation:$ \begin{align} \begin{cases} u_t-\Delta u+(-\Delta)^{s} u = |u|^{p-2}u & \text { in } \Omega \times \mathbb{R}^{+}, \\ u(x, 0) = u_{0}(x)&\text { in } \Omega, \\ u(x, t) = 0 &\text { in } \mathbb{R}^N\backslash \Omega \times \mathbb{R}_{0}^{+}, \ \end{cases} \end{align} $where $ \Delta $ is the Laplace operator, $ (-\Delta)^{s} $ is the fractional Laplace operator, $ \Omega\subset \mathbb{R}^N $ is a bounded domain with Lipschitz boundary $ \partial\Omega $, $ N>2s $, $ 2

In this paper, we study a viscoelastic Kirchhoff equation with fractional Laplacian. We first prove local existence and uniqueness of solutions. By using the theory of potential wells, we further obtain the global existence of solutions. Moreover, in the case where the Kirchhoff function takes a common form, we obtain asymptotic behavior and blow-up of solutions. [ABSTRACT FROM AUTHOR]

In this article, we invite the reader to join us in developing a culturally situated understanding of mental health at work in the Global South. Basing our analysis within the context of Peru, we situate depression as a feminist‐inspired “Public Feelings project,” whereby embodied experiences such as depression are inseparable from historical, social, and political structures of oppression (Cvetkovich, 2007). Through methodologically engaging in a mode of Nguyen et al.’s (2016) epistemic friendship, we explore the experiences of 12 Peruvian working women who self‐identify as having depression. Using interviews and arts‐based methods; specifically, Peruvian‐inspired portraiture, as a potential well for hope, healing, and humanity, we consider the narratives, experiences, feelings, and other embodied forms of knowing around depression and work in Peru. Working with the in vivo concept of “being loco,” we develop two art‐works presenting in dialogue with findings that explore the potential of how a Public Feelings lens might open up theoretical and methodological vistas for exploring in situ health experiences as constituted in particular geohistorical and gendered landscapes. [ABSTRACT FROM AUTHOR]

The growth kinetics of colloidal lead halide perovskite nanomaterials are an integral part of their applications, remains poorly understood due to complex nucleation processes and lack of in situ size monitoring method. Here we demonstrated that absorption spectra can be used to observe in situ growth processes of ultrathin CsPbBr3 nanowires in solution with reference to the effective mass infinite deep square potential well model. By means of this method, we have found that the ultrathin nanowires, fabricated by hot injection method, were firstly formed within one minute. Subsequently, they merge with each other into a thicker structure with increasing reaction time. We revealed that the nucleation, growth, and merging of the CsPbBr3 nanowires are determined by the acid concentration and ligand chain length. At lower acidity, the critical nucleation size of the nanowire is smaller, while the shorter the ligand chain length, the faster the merging among the nanowires. Moreover, the merging mode between nanowires changed with their nucleation size. This growth kinetics of CsPbBr3 nanowires provides a reference for optimizing the synthesis conditions to obtain the one-dimensional CsPbBr3 with desired size, thus enabling accurate control of the nanowire shape. [ABSTRACT FROM AUTHOR]

Currently, the focus of stochastic resonance (SR) research is primarily on bistable systems, and classical bistable SR systems have the problems of low dimension, inconvenient parameter adjustment, and high threshold for SR effects. In this paper, based on the classic bistable system, a class of multi-dimensional single potential well SR systems without transition threshold is proposed and applied to signal processing. Firstly, the mechanism of double potential well SR and single potential well SR is studied. On this basis, a kind of multi-dimensional single potential well SR system is defined and its theoretical conditions are analyzed. Then a specific four-dimensional single potential well SR system is constructed, and the dynamics of the system is analyzed. The gain range and the approximate relationship between the system input and the four-dimensional output are derived. Finally, the four-dimensional single potential well SR system is applied to the processing of various signals. The experimental results show that the constructed system has good noise reduction and feature amplification effects on noisy signals through the advantages of multi-dimensional output, and can be used to highlight the fault feature frequency in bearing fault signals. [ABSTRACT FROM AUTHOR]

We study a class of damped p$$ p $$‐ biharmonic$$ biharmonic $$ type wave equation with homogeneous Dirichlet boundary condition. First of all, we prove the local existence of weak solutions by Galerkin method. Besides, when the energy level is low E(0)

Context. Recent measurements of gas velocity in the outer parts of high redshift galaxies suggest that steeply falling rotation curves may be common or even universal in these galaxies, in contrast to the near universal flat, non-declining rotation curves in nearby galaxies. Aims. The aim was to investigate the implications of these postulated steeply falling rotation curves for the role of dark matter in galaxy formation. Methods. Using an established computer code, the collapse of dark matter and baryonic matter together, starting with a variety of initial conditions, was simulated for comparison with the observed rotation curves. A simulation of collapsing baryonic matter on its own without dark matter was also carried out. The masses of the protogalaxies were chosen to produce a stellar disc in the same mass range as the observed galaxies at roughly the same redshift. Results. As soon as a smooth stellar disc was formed in the baryonic matter, with properties similar to the observed high redshift galaxies, the computed rotation curves were without exception relatively flat to large radius in the gas disc. Only a simulation without a dark matter halo was able to reproduce the observed rotation curves. Conclusions. This implies that if the high redshift steeply falling rotation curves turn out to be common, then the standard scenario of galaxy formation by baryonic matter falling into the potential well of a massive dark matter halo must be wrong, unless there is pressure support via velocity dispersion significantly higher than has so far been observed or resulted from our simulations. It would also imply that for these galaxies the flat rotation curves at low redshift must be due to dark matter which has subsequently fallen into the galactic potential well, or there must be some other explanation for their contemporary flat rotation curves other than dark matter. [ABSTRACT FROM AUTHOR]

Exciton–polaritons, which are bosonic quasiparticles with an extremely low mass, play a key role in understanding macroscopic quantum effects related to Bose–Einstein condensation (BEC) in solid-state systems. The study of trapped polaritons in a potential well provides an ideal platform for manipulating polariton condensates, enabling polariton lasing with specific formation in k-space. Here, we realize quantized microcavity polariton lasing in simple harmonic oscillator (SHO) states based on spatial localized excitons in InGaN/GaN quantum wells (QWs). Benefiting from the high exciton binding energy (90 meV) and large oscillator strength of the localized exciton, room-temperature (RT) polaritons with large Rabi splitting (61 meV) are obtained in a strongly coupled microcavity. The manipulation of polariton condensates is performed through a parabolic potential well created by optical pump control. Under the confinement situation, trapped polaritons are controlled to be distributed in the selected quantized energy sublevels of the SHO state. The maximum energy spacing of 11.3 meV is observed in the SHO sublevels, indicating the robust polariton trapping of the parabolic potential well. Coherent quantized polariton lasing is achieved in the ground state of the SHO state and the coherence property of the lasing is analyzed through the measurements of spatial interference patterns and g(2)(τ). Our results offer a feasible route to explore the manipulation of macroscopic quantum coherent states and to fabricate novel polariton devices towards room-temperature operations. [ABSTRACT FROM AUTHOR]

In this work, we are looking at the generalized quasilinear Schrödinger equations with critical growth and a steep potential well: −divg2(u)∇u+g(u)g′(u)|∇u|2+(λV(x)+1)u=|u|αp−2u+|u|α2∗−2u,x∈ℝN,$$ -\operatorname{div}\left({g}&#x0005E;2(u)\nabla u\right)&#x0002B;g(u){g}&#x0005E;{\prime }(u){\left&#x0007C;\nabla u\right&#x0007C;}&#x0005E;2&#x0002B;\left(\lambda V(x)&#x0002B;1\right)u&#x0003D;{\left&#x0007C;u\right&#x0007C;}&#x0005E;{\alpha p-2}u&#x0002B;{\left&#x0007C;u\right&#x0007C;}&#x0005E;{\alpha {2}&#x0005E;{\ast }-2}u,\kern0.30em x\in {\mathrm{\mathbb{R}}}&#x0005E;N, $$ where λ>0,α∈[1,2],20,\alpha \in \left[1,2\right],2

Considered herein is a Cauchy problem for a system of Schrödinger equations with second‐order derivative‐type and combined power‐type nonlinearities. Through the effective combination of potential well theory, conservation laws, and vector‐valued Gargliardo–Nirenberg inequality, we establish the uniform boundedness in H$H$‐norm on [0,T)$[0,T)$ and corresponding decay rate estimate. Moreover, we also prove the existence of corresponding ground‐state solutions for this problem. Finally, we mainly investigate three different sharp thresholds for blowup and uniform bound of solutions in H$H$‐norm on [0,T)$[0,T)$ by using potential well theory, variational method, and some transformation techniques. [ABSTRACT FROM AUTHOR]

A class of complex breather and soliton solutions to both KdV and mKdV equations are identified with a Pöschl-Teller type P T -symmetric potential. However, these solutions represent only the unbroken- P T phase owing to their isospectrality to an infinite potential well in the complex plane having real spectra. To obtain the broken- P T phase, an extension of the potential satisfying the s l 2 , R potential algebra is mandatory that additionally supports non-trivial zero-width resonances. [ABSTRACT FROM AUTHOR]

The study focuses on the model reduction of an internally damped chain of particles confined within a weakening potential well subjected to polyharmonic excitation to investigate the chain's escape dynamics. The chain features strong linear coupling between particles and nonnegligible viscous damping forces arising from their relative motion. The potential well is modeled to have no energy dissipation, which means that damping arises solely from the internal interactions among particles and not from their motion through a resisting medium. Polyharmonic excitation frequencies are chosen to excite both the center of mass of the chain and at least one of the internally resonant frequencies, which are significantly higher than the linearized angular eigenfrequency of the center of mass within the well. The relative motion of the particles quickly reaches a steady state because of the non-small internal damping, allowing for the derivation of an efficient force field for the center of mass. Eliminating fast dynamics reduces the system's degrees of freedom to one, employing a probabilistic approach based on the relative motion's probability density function. The reduced 1 DoF model is appropriate for further investigation using various methods established in the literature. [ABSTRACT FROM AUTHOR]

We developed in this paper the used methodology to describe the Lennard-Jones potential of two atoms in rare gas. In this treatment we supposed that one atom could be described by a harmonic oscillator. The interaction potential is developed at short and long ranges. The results showed that the obtained physico-chemical parameters such as the oscillator frequency, the atom mass, and the atom charge well reproduce the Lennard-Jones potential. Then the potential well depth and the effective equilibrium diameter are expressed in function of the oscillator frequency, the atom mass and charge. [ABSTRACT FROM AUTHOR]

In this investigation, a three-dimensional (3D) axisymmetric potential well-based nonlinear piezoelectric energy harvester is proposed to increase the broadband frequency response under low-strength planar external excitation. Here, a two-dimensional (2D) planar bi-stable Duffing potential is generalized into three dimensions by utilizing axial symmetry. The resulting axisymmetric potential well has infinitely many stable equilibria and one unstable equilibria at the highest point of the potential barrier for this cantilevered oscillator. Dynamics of such a 3D piezoelectric harvester with axisymmetric multi-stability are studied under planar circular excitation motion. Bifurcations of average power harvested from the two pairs of piezoelectric patches are presented against the frequency variation. The results show the presence of several branches of large-amplitude cross-well type period-1 and subharmonic solutions. Subharmonics involved in such responses are verified from the Fourier spectra of the solutions. The identified subharmonic solutions perform interesting patterns of curvilinear oscillations, which do not cross the potential barrier through its highest point. These solutions can completely or partially avoid the climbing of the potential barrier, thereby requiring low input excitation energy for barrier crossing. The influence of excitation amplitude on the bifurcations of normalized power is also investigated. Through multiple solution branches of subharmonic solutions, producing comparable power to the period-1 branch, broadband frequency response characteristics of such a 3D axisymmetically multi-stable harvester are highlighted. [ABSTRACT FROM AUTHOR]

Optically levitated multiple nanoparticles have emerged as a platform for studying complex fundamental physics such as non-equilibrium phenomena, quantum entanglement, and light–matter interaction, which could be applied for sensing weak forces and torques with high sensitivity and accuracy. An optical trapping landscape of increased complexity is needed to engineer the interaction between levitated particles beyond the single harmonic trap. However, existing platforms based on spatial light modulators for studying interactions between levitated particles suffered from low efficiency, instability at focal points, the complexity of optical systems, and the scalability for sensing applications. Here, we experimentally demonstrated that a metasurface which forms two diffraction-limited focal points with a high numerical aperture (∼0.9) and high efficiency (31 %) can generate tunable optical potential wells without any intensity fluctuations. A bistable potential and double potential wells were observed in the experiment by varying the focal points' distance, and two nanoparticles were levitated in double potential wells for hours, which could be used for investigating the levitated particles' nonlinear dynamics, thermal dynamics and optical binding. This would pave the way for scaling the number of levitated optomechanical devices or realizing paralleled levitated sensors. [ABSTRACT FROM AUTHOR]

The dependence of the transparency coefficient of a five-layer two-barrier structure on the electron energy and the ratio of the widths of two neighboring potential barriers is calculated. It is shown that the extremum of the transparency coefficient significantly depends on the geometric dimensions of the structure layers. In a symmetric five-layer two-barrier semiconductor structure, the condition for the occurrence of "resonant" electron transitions is defined. It is demonstrated that the mechanism of such (resonant) transitions is explained by the interference of de Broglie waves of electrons in the potential well, where the phases of de Broglie waves are determined by the geometric dimensions of the structure, and their amplitudes - by the ratio of the carrier energy to the height of the potential barrier. It has been established that with an increase in the effective mass of charge carriers, the number of intersections of the quantities fR (ξ) and ((1-2ξ))/(√(ξ-ξ2) increases. These intersections determine the dimensionally-quantized levels where electrons are localized.

Desorption of a self-propelling filament from an attractive surface is studied by computer simulations and the influence of activity, chain length, and chain rigidity is explored. For the flexible filament, we find three scaling regimes of desorption time vs activity with various scaling exponents. At low activity, the scaling law results from the spiral-like detachment kinetics. And at high activity, by theoretical analysis, the desorption is reminiscent of the escaping mechanism of a super-diffusive blob from a potential well at a short time scale. Additionally, the desorption time decreases first and then increases with chain length at low activity, since it is hard to form a spiral for short filaments due to the limited volume repulsion. For high activities, the desorption time approximately scales with chain length, with a scaling exponent ∼ 0.5 , which can be explained by the theory and numerically fitting scaling law between the end-to-end distance of the "globule-like" filament and chain length. Furthermore, a non-monotonic behavior is observed between the desorption time and the chain stiffness. Desorption time slightly decreases first and then rapidly increases with stiffness due to the opposed effects of increasing rigidity on headiing-up time and leaving-away time. In contrast to traditional polymers, the scaling behavior suggests unique desorption characteristics of active polymers. [ABSTRACT FROM AUTHOR]

The main goal of this work is to investigate an initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation. Under the different initial energy, we study the existence, uniqueness and asymptotic behavior of the global solution and the blow up phenomenon of the weak solution. Moreover, we obtain lower and upper bound estimates for the blow-up time and rate in different initial energy cases. [ABSTRACT FROM AUTHOR]

This paper deals with the coupled fourth-order parabolic equations, subject to Dirichlet or Navier boundary conditions. We combine the generalized potential well method, the concave method, with the auxiliary methods to classify the initial energy about the existence of blow-up solutions and global solutions. Moreover, the decay estimate of global solutions and the bounds of blow-up time and rate are determined, respectively. [ABSTRACT FROM AUTHOR]

We electrically characterized melt-quenched amorphized Ge2Sb2Te5 (GST) phase-change memory cells of 20 nm thickness, ∼66–124 nm width, and ∼100–600 nm length with and without photoexcitation in the 80–275 K temperature range. The cells show distinctly different current–voltage characteristics in the low-field (≲19 MV/m), with a clear response to optical excitation by red light, and high-field (≳19 MV/m) regimes, with a very weak response to optical excitation. The reduction in carrier activation energy with photoexcitation in the low-field regime increases from ∼10 meV at 80 K to ∼50 meV at 150 K (highest sensitivity) and decreases again to 5 meV at 275 K. The heterojunctions at the amorphous–crystalline GST interfaces at the two sides of the amorphous region lead to formation of a potential well for holes and a potential barrier for electrons with activation energies in the order of 0.7 eV at room temperature. The alignment of the steady state energy bands suggests the formation of tunnel junctions at the interfaces for electrons and an overall electronic conduction by electrons. When photoexcited, the photo-generated holes are expected to be stored in the amorphous region, leading to positive charging of the amorphous region, reducing the barrier for electrons at the junctions and hence the device resistance in the low-field regime. Holes accumulated in the amorphous region are drained under a high electric field. Hence, the potential barrier cannot be modulated by photogenerated holes, and the photo-response is significantly reduced. These results support the electronic origin of resistance drift in amorphous GST. [ABSTRACT FROM AUTHOR]

This paper deals with the infinite blow‐up phenomena for a class of damped plate equations with logarithmic nonlinearity under the Navier boundary condition. Combining potential well method and modified differential inequality technique, we establish the infinite blow‐up result of solutions with arbitrary initial energy. In particular, it is not necessary to suppose that the initial velocity and the initial displacement should have the same sign in the sense of the L2${L^2}$ inner product, that is, the solution may blow up at infinity even ∫Ωu0u1dx<0$\int _\Omega {{u_0}{u_1}dx} < 0$, more precisely, ∫Ωu0u1dx>−12u0∗2$\int _\Omega {{u_0}{u_1}dx} > - \frac{1}{2}\left\Vert {{u_0}} \right\Vert _*^2$. [ABSTRACT FROM AUTHOR]

The localization and scattering properties of potential wells or barriers uniformly moving on a lattice are strongly dependent on the drift velocity, owing to a violation of the Galilean invariance of the discrete Schrödinger equation. Here a type of localization–delocalization phase transition of algebraic type is unraveled, which does not require any kind of disorder and arises when a power‐law potential well drifts fast on a lattice. While for an algebraic exponent α$\alpha$ lower than the critical value αc=1$\alpha _{\text{c}}=1$ dynamical delocalization is observed, for α>αc$\alpha > \alpha _{\text{c}}$ asymptotic localization, corresponding to asymptotic frozen dynamics, is instead realized. At the critical phase transition point α=αc=1$\alpha _=\alpha _{\text{c}}=1$ an oscillatory dynamics is found, corresponding to Bloch oscillations. An experimentally accessible photonic platform for the observation of the predicted algebraic phase transition, based on light dynamics in synthetic mesh lattices, is suggested. [ABSTRACT FROM AUTHOR]

The aim of this paper is to deal with the standing wave problems in coupled nonlinear fractional Klein–Gordon equations. First, we establish the constrained minimizations for a single nonlinear fractional Laplace equation. Then we prove the existence of a standing wave with a ground state using a variational argument. Next, applying the potential well argument and the concavity method, we obtain the sharp criterion for blowing up and global existence. Finally, we show the instability of the standing wave. [ABSTRACT FROM AUTHOR]

We propose a probabilistic representation of the ground states of massive and massless Schrödinger operators with a potential well in which the behaviour inside the well is described in terms of the moment-generating function of the first exit time from the well and the outside behaviour in terms of the Laplace transform of the first entrance time into the well. This allows an analysis of their behaviour at short to mid-range from the origin. In a first part, we derive precise estimates on these two functionals for stable and relativistic stable processes. Next, by combining scaling properties and heat kernel estimates, we derive explicit local rates of the ground states of the given family of non-local Schrödinger operators both inside and outside the well. We also show how this approach extends to fully supported decaying potentials. By an analysis close-by to the edge of the potential well, we furthermore show that the ground state changes regularity, which depends qualitatively on the fractional power of the non-local operator. [ABSTRACT FROM AUTHOR]

The formation process of core–shell structure from multiple graphdiyne‐like chains and carbon nanotube is investigated by a molecular dynamics simulation. Multiple graphdiyne‐like chains self‐curl into helical structures located inside carbon nanotubes. The entire process involves two steps: sliding and twisting. A detailed analysis is conducted on the formation mechanism. Both the van der Waals potential well and the π–π stacking interaction between carbon nanotube and graphdiyne‐like chains play a major role in the self‐assemble process. Furthermore, the influence factors such as the number of graphdiyne‐like chains, the diameter of carbon nanotube, the length of carbon nanotube, the length of graphdiyne‐like chains, and the simulation temperature is also investigated. The research results are an important theoretical basis for manufacturing high‐quality carbon nanomaterials and other novel nanostructures. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of fourth-order dispersive wave equations with exponential source term. Firstly, by applying the contraction mapping principle, we establish the local existence and uniqueness of the solution. In the spirit of the variational principle and mountain pass theorem, a natural phase space is precisely divided into three different energy levels. Then we introduce a family of potential wells to derive a threshold of the existence of global solutions and blow up in finite time of solution in both cases with sub-critical and critical initial energy. These results can be used to extend the previous result obtained by Alves and Cavalcanti (Calc. Var. Partial Differ. Equ. 34 (2009) 377–411). Moreover, an explicit sufficient condition for initial data leading to blow up result is established at an arbitrarily positive initial energy level. [ABSTRACT FROM AUTHOR]

In this work, we deal with the higher-order hyperbolic-type equation. Firstly, we prove the global existence and blow up of solutions with the subcritical initial energy. Later, we prove the global existence and blow up of solutions with the critical initial energy. [ABSTRACT FROM AUTHOR]

This paper is concerned with the well-posedness and asymptotic behavior for a singular epitaxial thin-film growth equation with logarithmic nonlinearity under the Navier boundary condition. Based on the technique of cut-off and combining with Hardy-Sobolev inequality, the technique of Faedo-Galerkin, and multiplier, we establish the local solvability. Meantime, by virtue of the family of potential wells, we obtain the threshold between the existence and nonexistence of the global solution (including the critical case) and give the upper bound of lifespan and the estimate of blow-up rate. Furthermore, the results of blow-up with arbitrary initial energy and the lifespan are derived. [ABSTRACT FROM AUTHOR]

In this article, the diffusion Monte Carlo (DMC) method is applied to the study of the quantum states of a hydrogen atom confined into a cylindrical potential well. We present an independent reproduction of previous studies based on different methods, in particular the energy eigenvalues for ground and selected excited states and the polarizability of the ground state, both for finite and infinite cylinders. The static field ionization of ground and excited states of the confined atom is discussed, including the determination of the potential energy surface and equilibrium position of the proton. This study provides a further demonstration of the versatility of the DMC method for this and analogous problems. [ABSTRACT FROM AUTHOR]

Featured Application: The findings presented in this work will allow the calculation of the electronic density states as well as the electrical and optical properties of complex one-dimensional coupled periodic potential wells without using expensive licensed software. The analytical generalization for N periodic potential wells coupled to a probe rectangular-like potential and a zero potential is extremely important in the study of one-dimensional periodic potentials in solid state physics, e.g., in the calculation of transport, optical, and magnetic properties. These findings raise the possibility of calculating equations for the generalization of N arbitrary potentials related to any potential V (x) using special functions as a solution. In this work, a novel analytical generalization of the transcendental energy equation, group velocity, and effective mass for N-coupled potentials to a probe one-dimensional potential V = V (x) was proposed. Initially, two well-known linear periodic potentials V = V (x) were employed to obtain analytical solutions for rectangular-like and Dirac-delta potentials. Python libraries were used to easily represent the equations for one or two rectangular-like potentials coupled with an arbitrary potential, highlighting the transcendental energy, group velocity, and effective mass. The results showed that the group velocity behavior changed its orientation due to the sign of the potential, whereas the width of the potential V (x) strongly influenced the group velocity behavior. The effective mass was also modified by the potential shapes, and their combinations, both effective mass and group velocity, exhibited similar physical behaviors to those found in ordinary rectangular-like potentials. [ABSTRACT FROM AUTHOR]

This paper proposes an asymmetric hybrid tri-stable piezoelectric energy harvester for rotational motion (RHTPEH). The device features an asymmetric tri-stable piezoelectric cantilever beam positioned at the edge of a rotating disk. This beam is uniquely configured with an asymmetric arrangement of magnets. Additionally, an elastic amplifier composed of a vertical and a rotating spring connects the beam's fixed end and the disk. This setup enhances both the rotational amplitude and vertical displacement of the beam during motion. A comprehensive dynamical model of the RHTPEH was developed using Lagrange's equations. This model facilitated an in-depth analysis of the system's behavior under various conditions, focusing on the influence of key parameters such as the asymmetry in the potential well, the stiffness ratio of the amplifier springs, the radius of the disk, and the disk's rotational speed on the nonlinear dynamic response of the system. The results show that the asymmetric hybrid tri-stable piezoelectric energy harvester makes it easier to harvest the vibration energy in rotational motion and has excellent power output performance compared with the symmetric tri-stable piezoelectric energy harvester. The output power magnitude of the system at higher rotational speeds increases as the radius of rotation expands, but when the rotational speed is low, the steady-state output power magnitude of the system is not sensitive to changes in the radius of rotation. Theoretical analysis and numerical simulations validate the effectiveness of the proposed asymmetric RHTPEH for energy harvesting in low-frequency rotating environments. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global existence and finite time blow-up of solution for the Cauchy problem of one-dimensional fifth-order Boussinesq equation with logarithmic nonlinearity. Fist we prove the existence and uniqueness of local mild solutions in the energy space by means of the contraction mapping principle. Further under some restriction on the initial data, we establish the results on existence and uniqueness of global solutions and finite time blow-up of solutions by using the potential well method. Moreover, the sufficient and necessary conditions of global existence and finite time blow-up of solutions are given. [ABSTRACT FROM AUTHOR]