Periodic Potential Research Articles

A Two-Dimensional Transient Computational Multi-Physics Model for Analyzing Magnetic and Non-Magnetic Particle (Red Blood Cells and E. Coli Bacteria) Dynamics in a Traveling Wave Ferro-Magnetic Microfluidic Device for Potential Cell Separation and Sorting

Abstract This paper presents the theory and development, validation, and results of a transient computational multiphysics model for analyzing the magnetic field, particle dynamics, and capture efficiency of magnetic and nonmagnetic (e.g., Red Blood Cells and E. Coli bacteria) microparticles in a traveling wave ferromagnetic microfluidic device. This computational model demonstrates proof-of-concept of a method for greatly enhancing magnetic bioseparation in ferromicrofluidic systems using an array of copper conductive elements arranged in quadrature to create a periodic potential energy landscape. In contrast to previous works, our approach theoretically uses a microfluidic device with an electronic chip platform consisting of integrated copper electrodes that carry currents to generate programable magnetic field gradients locally. Alternating currents are applied to the electrodes in quadrature (using a 90 deg phase change from the neighboring electrode) to create a periodic magnetic field pattern that travels along the length of the microchannel. Our previous work evaluated magnetic and nonmagnetic particles in a static magnetic field within the same channel geometry. This work is a phase 2 study that expands on the previous work and analyzes the dynamics of magnetic and nonmagnetic entities characterized by material magnetic susceptibility in a transient magnetic field. This is an improvement over our previous work. The model, which is described in more detail in the methods section, combines a Eulerian-Lagrangian and two-way particle-fluid coupling CFD analysis with closed-form magnetic field analysis that is used to predict magnetic separation considering dominant magnetic and hydrodynamic forces similar to our previous works in magnetic drug targeting. The model was also validated with an experimental low frequency stationary flow study on separating nonmagnetic latex fluorescent particles in a water based ferrofluid. The results from the experimental study and the developed model demonstrate that the proposed device may potentially be used as an effective platform for microparticle and cellular manipulation and sorting. The developed multiphysics model could potentially be used as a design optimization tool for traveling wave ferromicrofluidic devices.

Langevin’s Equation of Motion: Dynamical States and Stochastic Resonance

In this present work, we numerically observe the existence of two dynamical states of trajectories in the underdamped motion of a particle in an inhomogeneous periodic bistable potential with high friction coefficient driven by a periodic force. The system is inhomogeneous in the sense that the coefficient of friction is periodic in space and with phase difference 'ϕ' with respect to the periodic bistable potential. Just like in sinusoidal potentials, the occurrence of stochastic resonance (SR) in the periodic bistable potential is due to the transitions between the dynamical states at an optimal (thermal) noise strength.

The spectrum theory of the discrete Schrödinger operator and its application

This paper introduces the spectrum theory of discrete Schrödinger operators with different kinds of potentials, including bounded, unbounded, periodic, or complex potentials. The paper also provides exponential estimates of the Green's function and eigenfunctions of the discrete Schrödinger operators. As an application, I review some of our results on standing wave solutions of discrete Schrödinger equations.

Moiré Synaptic Transistor for Homogeneous-Architecture Reservoir Computing

Reservoir computing has been considered as a promising intelligent computing paradigm for effectively processing complex temporal information. Exploiting tunable and reproducible dynamics in the single electronic device have been desired to implement the “reservoir” and the “readout” layer of reservoir computing system. Two-dimensional moiré materials, with an artificial lattice constant many times larger than the atomic length scale, are one type of most studied artificial quantum materials in community of material science and condensed-matter physics over the past years. These materials are featured with gate-tunable periodic potential and electronic correlation, thus varying the electric field allows the electrons in the moiré potential per unit cell to exhibit distinct and reproducible dynamics, showing great promise in robust reservoir computing. Here, we report that a moiré synaptic transistor can be used to implement the reservoir computing system with a homogeneous reservoir-readout architecture. The synaptic transistor is fabricated based on an h-BN/bilayer graphene/h-BN moiré heterostructure, exhibiting ferroelectricity-like hysteretic gate voltage dependence of resistance. Varying the magnitude of the gate voltage enables the moiré transistor to switch between long-term memory and short-term memory with nonlinear dynamics. By employing the short- and long-term memories as the reservoir nodes and weights of the readout layer, respectively, we construct a full-moiré physical neural network and demonstrate that the classification accuracy of 90.8% can be achieved for the MNIST (Modified National Institute of Standards and Technology) handwritten digits database. Our work would pave the way towards the development of neuromorphic computing based on moiré materials.

Vibrational resonance in a multistable system with position-dependent mass

The occurrence of vibrational resonance (VR) in a dual-frequency-driven multistable system with a spatially varying mass modelling particle with position-dependent mass (PDM) and evolving in a one-dimensional symmetric periodic potential has been investigated and reported in this paper. We numerically compute and analyze the response amplitude, the effects of the PDM parameters (m 0, a) on the potential structure, the occurrence of VR and the bifurcation of the equilibrium points. It is shown that the PDM parameters, besides controlling VR, can induce unconventional resonance patterns through the variation of the potential well depth. The resonant states can be influenced through the cooperation of the PDM parameters and the external forcing leading the system from multiresonance state into single and double resonance states. The contributions of the fixed rest mass m 0 on the VR and the PDM-induced resonance are determined by threshold conditions imposed by the magnitude of the mass nonlinear strength a.

Hamiltonian Ratchet for Matter-Wave Transport.

We report on the design of a Hamiltonian ratchet exploiting periodically at rest integrable trajectories in the phase space of a modulated periodic potential, leading to the linear nondiffusive transport of particles. Using Bose-Einstein condensates in a modulated one-dimensional optical lattice, we make the first observations of this spatial ratchet, which provides way to coherently transport matter waves with possible applications in quantum technologies. In the semiclassical regime, the quantum transport strongly depends on the effective Planck constant due to Floquet state mixing. We also demonstrate the interest of quantum optimal control for efficient initial state preparation into the transporting Floquet states to enhance the transport periodicity.

Energy bands in a three dimension simple cubic lattice of contact potential

In this work, we investigate energy bands in a three dimensional simple cubic lattice of contact potential. The energy bands in the first Brillouin Zone are obtained with Ewald’s summation method. In comparison with single point potential, the presence of lattice potential changes the existence condition of negative energy states near zero energy. It is found that the system always has negative energy states for an arbitrarily weak periodic potential. In addition, we prove that if an irreducible unitary representation is not a trivial representation of group of wave vector, the corresponding wave functions at lattice sites would be zero. With this theorem, the degeneracy of energy bands is explained with group theory. Furthermore, we find that there exists some energy bands which are not affected by the lattice potential. We call their corresponding eigenstates as dark states. The physical mechanism of the dark states is explained by explicitly constructing the standing wave-type Bloch wave functions.

The transition from used fuel container corrosion under oxic conditions to corrosion in an anoxic environment

AbstractThe conversion of copper oxide films on copper to copper sulfide has been investigated in sulfide‐containing chloride solutions. Single‐phase Cu2O films and duplex films consisting of Cu2O and CuO, and possibly Cu(OH)2, were prepared electrochemically on copper specimens at various applied potentials and characterized using Raman spectroscopy, scanning electron microscopy, and energy dispersive X‐ray analyses. The surface condition of the specimens subsequently exposed to a solution containing sulfide was monitored by measuring the corrosion potential (Ecorr) for various exposure periods, then cathodic stripping voltammetry was performed. Cuprite (Cu2O) was observed to be converted to Cu2S by chemical reaction with sulfide, while the conversion mechanism for the mixed deposit could comprise a galvanic process involving CuII reduction coupled to the formation of Cu2S by the reaction of sulfide with copper within pores in the Cu2O/CuO surface film and a chemical conversion of Cu2O to Cu2S. Cupric hydroxide was not converted to Cu2S on the time scale (24 h) of these experiments.

Carbon source priority and availability limit bidirectional electron transfer in freshwater mixed culture electrochemically active bacterial biofilms

This study investigated, if a mixed electroactive bacterial (EAB) culture cultivated heterotrophically at a positive applied potential could be adapted from oxidative to reductive or bidirectional extracellular electron transfer (EET). To this end, a periodic potential reversal regime between − 0.5 and 0.2 V vs. Ag/AgCl was applied. This yielded biofilm detachment and mediated electroautotrophic EET in combination with carbonate, i.e., dissolved CO2, as the sole carbon source, whereby the emerged mixed culture (S1) contained previously unknown EAB. Using acetate (S2) as well as a mixture of acetate and carbonate (S3) as the main carbon sources yielded primarily alternating electrogenic organoheterotropic metabolism with the higher maximum oxidation current densities recorded for mixed carbon media, exceeding on average 1 mA cm−2. More frequent periodic polarization reversal resulted in the increase of maximum oxidative current densities by about 50% for S2-BES and 80% for S3-BES, in comparison to half-batch polarization. The EAB mixed cultures developed accordingly, with S1 represented by mostly aerobes (84.8%) and being very different in composition to S2 and S3, dominated by anaerobes (96.9 and 96.5%, respectively). S2 and S3 biofilms remained attached to the electrodes. There was only minor evidence of fully reversible bidirectional EET. In conclusion the three triplicates fed with organic and/or inorganic carbon sources demonstrated two forms of diauxie: Firstly, S1-BES showed a preference for the electrode as the electron donor via mediated EET. Secondly, S2-BES and S3-BES showed a preference for acetate as electron donor and c-source, as long as this was available, switching to CO2 reduction, when acetate was depleted.Graphical

Single-file transport of binary hard-sphere mixtures through periodic potentials.

Single-file transport occurs in various scientific fields, including diffusion through nanopores, nanofluidic devices, and cellular processes. We here investigate the impact of polydispersity on particle currents for single-file Brownian motion of hard spheres when they are driven through periodic potentials by a constant drag force. Through theoretical analysis and extensive Brownian dynamics simulations, we unveil the behavior of particle currents for random binary mixtures. The particle currents show a recurring pattern in dependence of the hard-sphere diameters and mixing ratio. We explain this recurrent behavior by showing that a basic unit cell exists in the space of the two hard-sphere diameters. Once the behavior of an observable inside the unit cell is determined, it can be inferred for any diameter. The overall variation of particle currents with the mixing ratio and hard-sphere diameters is reflected by their variation in the limit where the system is fully covered by hard spheres. In this limit, the currents can be predicted analytically. Our analysis explains the occurrence of pronounced maxima and minima of the currents by changes in the effective potential barrier for the center-of-mass motion.

Differences in the electrochemical behavior of Vulcan XC-72 carbon black and glassy carbon after prolonged potential cycling

The electrochemical characteristics of a carbon carrier play an important role in catalyst investigations. The evolution of the electrochemical characteristics of Vulcan XC-72 carbon black and a glassy carbon disk electrode was studied under prolonged electrochemical action. The electrochemical action was performed by repeated application of a sawtooth periodic potential to the electrodes in the range from 0.05 to 1 V vs. RHE and back at a scan rate of 50 mV/s. The EDL charging current, the cyclic current–voltage curves, the equilibrium electrode potential, and the dissolved oxygen reduction current in potentiostatic mode at 0.05 V vs. RHE were recorded periodically. Carbon black was characterized by helium pycnometry, SEM, TEM, X-ray diffraction, and Raman spectroscopy. The currents on the carbon black were several orders of magnitude higher than those on the glassy carbon. The differences in the dynamics of electrochemical characteristics are discussed.

Stochastic resetting-induced reentrance phenomena of inertial Brownian particle in the rough periodic potential

Stochastic resetting-induced reentrance phenomena of inertial Brownian particle in the rough periodic potential

Information in feedback ratchets.

Feedback control uses the state information of the system to actuate on it. The information used implies an effective entropy reduction of the controlled system, potentially increasing its performance. How to compute this entropy reduction has been formally shown for a general system and has been explicitly computed for spatially discrete systems. Here, we address a relevant example of how to compute the entropy reduction by information in a spatially continuous feedback-controlled system. Specifically, we consider a feedback flashing ratchet, which constitutes a paradigmatic example for the role of information and feedback in the dynamics and thermodynamics of transport induced by the rectification of Brownian motion. A Brownian particle moves in a periodic potential that is switched on and off by a controller. The controller measures the position of the particle at regular intervals and performs the switching depending on the result of the measurement. This system reaches a long-time dynamical regime with a nonzero mean particle velocity, even for a symmetric potential. Here, we calculate the efficiency at maximum power in this long-time regime, computing all the required contributions. We show how the entropy reduction can be evaluated from the entropy of the non-Markovian sequence of control actions, and we also discuss the required sampling effort for its accurate computation. Moreover, the output power developed by the particle against an external force is investigated, which-for some values of the system parameters-is shown to become larger than the input power provided by the switching of the potential. The apparent efficiency of the ratchet thus becomes higher than one, if the entropy reduction contribution is not considered. This result highlights the relevance of including the entropy reduction by information in the thermodynamic balance of feedback-controlled devices, specifically when writing the second principle. The inclusion of the entropy reduction by information leads to a well-behaved efficiency over all the range of parameters investigated.

Continuous families of non-Hermitian surface solitons.

We show that surface solitons form continuous families in one-dimensional complex optical potentials of a certain shape. This result is illustrated by non-Hermitian gap-surface solitons at the interface between a uniform conservative medium and a complex periodic potential. Surface soliton families are parameterized by a real propagation constant. The range of possible propagation constants is constrained by the relation between the continuous spectrum of the uniform medium and the bandgap structure of the periodic potential.

Twisted-bilayer FeSe and the Fe-based superlattices

We derive BM-like continuum models for the bands of superlattice heterostructures formed out of Fe-chalcogenide monolayers: (I) a single monolayer experiencing an external periodic potential, and (II) twisted bilayers with long-range moire tunneling. A symmetry derivation for the inter-layer moire tunnelling is provided for both the \GammaΓ and MM high-symmetry points. In this paper, we focus on moire bands formed from hole-band maxima centered on \GammaΓ, and show the possibility of moire bands with C=0C=0 or ±1±1 topological quantum numbers without breaking time-reversal symmetry. In the C=0C=0 region for \theta→0θ→0 (and similarly in the limit of large superlattice period for I), the system becomes a square lattice of 2D harmonic oscillators. We fit our model to FeSe and argue that it is a viable platform for the simulation of the square Hubbard model with tunable interaction strength.

Fast Ewald summation for Stokes flow with arbitrary periodicity

A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for Stokes flow to periodic boundary conditions in any number (three, two, one, or none) of the spatial directions, in a unified framework. The periodic potential is split into a short-range and a long-range part, where the latter is treated in Fourier space using the fast Fourier transform. A crucial component of the method is the modified kernels used to treat singular integration. We derive new modified kernels, and new improved truncation error estimates for the stokeslet and stresslet. An automated procedure for selecting parameters based on a given error tolerance is designed and tested. Analytical formulas for validation in the doubly and singly periodic cases are presented. We show that the computational time of the method scales like O(Nlog⁡N) for N sources and targets, and investigate how the time depends on the error tolerance and window function, i.e. the function used to smoothly spread irregular point data to a uniform grid. The method is fastest in the fully periodic case, while the run time in the free-space case is around three times as large. Furthermore, the highest efficiency is reached when applying the method to a uniform source distribution in a primary cell with low aspect ratio. The work presented in this paper enables efficient and accurate simulations of three-dimensional Stokes flow with arbitrary periodicity using e.g. boundary integral and potential methods.

Study of the Free Randomly Moving Electron Transport Peculiarities in Metals

In this study, we review some aspects of the application of free randomly moving (RM) electron density and its probability density function distribution to the main free electron transport characteristics of elemental metals. It is shown that metal atom thermal vibrations not only produce free RM electrons, but also produce the same number of electronic defects (weakly shielded ions). The general expressions for the drift mobility, diffusion coefficient, and mean free path of randomly moving electrons are presented. It is shown that the scattering of free RM electrons is mainly due to electronic defects, which cause the distortion of the periodic potential (or the charge density) distribution in the periodic lattice. The resistivity of the elemental metal is caused by electronic defect scattering, taking into account the exchange in the thermal energies between phonons and free RM electrons. Special attention is paid to the analysis of the Hall effect measurement data: the Hall coefficient is presented for two types of RM electrons and holes, taking into account electron-like and hole-like densities of states. The paramagnetism and diamagnetism of the free RM electrons are simply explained using the definition of free RM electron density.

Band structures and contact points in phosphorene superlattice

We study the band structures and the associated contact points for a phosphorene superlattice made up of two periodic potential. We use the boundary conditions to extract an equation describing the dispersion relation after obtaining the eigen-wavefunctions. We explore two scenarios, equal and unequal barrier heights and well widths, and analyze their effects on the critical potential VBc and the positioning of the Dirac points. We show that energy transforms into linear behavior near contact points, and fermions move at different speeds along x- and y- directions. It was discovered that the periodic potential caused additional Dirac points, which we located in k-space by establishing their positions. Furthermore, we demonstrate that manipulating the height and width of the barriers can alter the energy gap and the locations of the contact points. It might be that our findings will be useful in the development of phosphorene-based electronic devices.

Untwisting Moiré Physics: Almost Ideal Bands and Fractional Chern Insulators in Periodically Strained Monolayer Graphene.

Moiré systems have emerged in recent years as a rich platform to study strong correlations. Here, we will propose a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of twisted moiré heterostructures-but without introducing a twist. We consider a monolayer graphene sheet subject to a C_{2}-breaking periodic strain-induced pseudomagnetic field with period L_{M}≫a, along with a scalar potential of the same period. This system has almost ideal flat bands with valley-resolved Chern number ±1, where the deviation from ideal band geometry is analytically controlled and exponentially small in the dimensionless ratio (L_{M}/l_{B})^{2}, where l_{B} is the magnetic length corresponding to the maximum value of the pseudomagnetic field. Moreover, the scalar potential can tune the bandwidth far below the Coulomb scale, making this a very promising platform for strongly interacting topological phases. Using a combination of strong-coupling theory and self-consistent Hartree-Fock, we find quantum anomalous Hall states at integer fillings. At fractional filling, exact diagonaliztion reveals a fractional Chern insulator at parameters in the experimentally feasible range. Overall, we find that this system has larger interaction-induced gaps, smaller quasiparticle dispersion, and enhanced tunability compared to twisted graphene systems, even in their ideal limit.

Tunneling Mechanism for Changing the Motion Direction of a Pulsating Ratchet. Temperature Effect

A pulsating ratchet with a spatially periodic double-well potential profile undergoing shift fluctuations for half a period is considered. The motion direction in such a ratchet is determined by the probability of overcoming which of the barriers surrounding the shallow potential well is greater. At relatively high temperatures, in accordance with the Arrhenius law, the probabilities of overcoming the barriers are determined by their heights, and at temperatures close to absolute zero, when the ratchet moves according to the tunnel mechanism, the barrier shapes are also important. Therefore, for narrow high and low wide barriers, the overcoming mechanism may turn out to be different and, moreover, dependent on temperature. As a result, a temperature-induced change in the direction of the ratchet motion is possible. A simple interpolation theory is presented to illustrate this effect. Simple criteria are formulated for the shape of the potential relief, using which one can experimentally observe motion reversal.