Exact Analytical Model Research Articles

Dynamics of quantum droplets in an external harmonic confinement

Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross–Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov–Kolokolov (VK) criterion and are found stable.

On chain models for contact electrification

An exact analytical model of charge dynamics for a chain of atoms with asymmetric hopping terms is presented. Analytic and numeric results are shown to give rise to similar dynamics in both the absence and presence of electron interactions. The chain model is further extended to the case of two atoms per cell (a perfect alloy system). This extension is further applied to contact electrification between two different atomic chains and the effect of increasing the magnitude of the contact transfer matrix element is studied.

Synergy between the negative absolute temperature and the external trap for a Bose-Einstein condensate under optical lattices

We provide a generic but exact analytical model for realizing negative absolute temperature in ultracold atoms under a quasi-periodic optical lattice (bi-chromatic) and an expulsive trap. We keep freedom for maximum tunability for both kinds of trap profile, where bi-chromatic lattice is quasi-periodic except two tunable limits, from a pure optical lattice to another doubly periodic optical lattice. The expulsive trap can be tuned from zero to a stronger one. All the required conditions for achieving negative temperature domain have been explored by identifying appropriate trap parameters. Condensate density in each lattice site is controlled and Anderson-like localization is emphasized. A thorough study of a quantitative estimate of the temperature is performed in the negative domain by controlling the trap, where the roles of all the trap parameters are precisely identified. A numerical stability analysis by Fourier split-step method makes the study more useful and the proposed family of solution are found quite stable. This is also connected to the merit of negative temperature through mean deviation data with varied trap parameters.

Generalized Analysis of Dual-Output Mach-Zehnder Modulator With Applications to Photonic-Assisted Instantaneous Frequency Measurement

We propose a general and exact analytical model forintensity modulation and direct detection (IM/DD) fiber optic links using dual-output dual-drive Mach-Zehnder modulator (DO-MZM). This model extends previously published results relying on the small-signal approximation and infinite extinction ratio at the modulator outputs. In our treatment the output optical powers are calculated through analytical expressions taking into account the modulator electronic driver and directional coupler characteristics. Closed-form expressions, explicitly displaying the dependence of the link output power on the directional coupler transmission coefficients, optical modulation depth, and bias point, are obtained for output optical power, frequency chirp, extinction ratio and static characteristic MZM curves. We also propose an equivalent interferometric representation of each DO-MZM output in terms of virtual dual-drive Mach-Zehnder modulators (DD-MZMs) and show that each modulator output has distinct characteristic curves. The model is applied to a photonic-assisted instantaneous frequency measurement (IFM) based on frequency-to-power mapping, in which an amplitude comparison function (ACF) is generated by the power fading functions. We have obtained a generalized ACF through which both the frequency and amplitude of the input RF signal can be determined by a search procedure.

An order-splitting model for supplier selection and order allocation in a multi-echelon supply chain

This paper considers an integrated supplier selection and inventory control problem for a multi-echelon inventory system with an order-splitting policy. A buyer firm consisting of one warehouse and N identical retailers procures a type of product from a group of potential suppliers; the acquisition of the warehouse takes place when the inventory level depletes to a reorder point R, and the order Q is simultaneously split among m selected suppliers. We develop an exact analytical model for the order-splitting problem in a multi-echelon system, and formulate the supplier selection problem in a Mixed Integer Nonlinear Programming (MINLP) model. This model determines the optimal inventory policy that coordinates stock levels between each echelon of the systems while properly allocating orders among selected suppliers to maximize the expected profit. For verification and validation of the proposed mathematical model, we conduct several numerical analyses and implement simulation models which helps us demonstrate the model’s solvability and effectiveness.

Exact analytical solutions with great computational efficiency to three-dimensional multispecies advection-dispersion equations coupled with a sequential first-order reaction network

This study presents novel exact analytical solutions to a set of simultaneous three-dimensional advection-dispersion equations coupled with a sequential first-order degradation reaction network involving distinct retardation factor values among individual species. The analytical solutions to the coupled partial differential equation system subject to both the first - and third -type inlet source boundary conditions are derived by consecutive application of the three integral transformations in combination with sequential substitutions. The correctness of the developed analytical solutions is confirmed through numerical comparisons of three verification examples between our derived exact analytical solutions and a three-dimensional single-species analytical model in a semi-infinite domain, a two-dimensional multispecies exact analytical model in a finite domain and a three-dimensional multispecies semi-analytical model in a semi-infinite domain of the previous studies, respectively. The advantage of the derived analytical solutions is that its computational efficiency is 104 times the computational efficiency of two-dimensional multispecies analytical solutions for a finite domain when two solutions are simultaneously used to solve a two-dimensional multispecies transport problem. The developed analytical solutions are then used to evaluate the performance of the public domain BIOCHLOR model that simulates aquifer remediation by natural attenuation of dissolved multispecies at a chlorinated-solvent contaminated site provided by the Center for Subsurface Modeling Support (CSMoS) of USEPA. Results show that the BIOCHLOR model that was developed based on three-dimensional analytical model assuming a single retardation factor value for all dissolved species would not be suitable for simulating most multispecies plume migration at contaminated sites where each contaminant has its own retardation factor value. The effects of the inlet source boundary conditions on the multispecies plume migration are also investigated. The high computational efficiency of the developed analytical model in this current study renders it a very efficient tool for executing a probabilistic health risk assessment involving a large number of simulations required for problems of multispecies transport of dissolved chlorinated solvent in groundwater at a contaminated site with uncertainties in many different variables.

Analytical magnetic field calculation for flat permanent-magnet linear machines with dual-rotor by using improved two-dimensional hybrid analytical method

PurposeThis paper aims to propose an improved two-dimensional hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain technique and the magnetic equivalent circuit (MEC).Design/methodology/approachThe magnetic field solution is obtained by coupling an exact analytical model (AM), calculated in all regions having relative permeability equal to unity, with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff’s current law) in ferromagnetic regions. The AM and MEC are connected in both axes (x, y) of the (non-)periodicity direction (i.e. in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead of the MEC characterized by an equivalent magnetomotive force (MMF) located in slots, teeth and yokes.FindingsIt is found that whatever the iron core relative permeability, the developed HAM gives accurate results for no- and on-load conditions. The finite-element analysis demonstrates excellent results of the developed technique.Originality/valueThe main objective of this paper is to make a direct coupling between the AM and MEC in both directions (i.e. x- and y-edges). The current density distribution is modeled by using Maxwell’s equations instead of the MEC and characterized by an MMF.

Photonic time-stretch based on phase modulation for sub-octave applications.

Photonic time-stretch (PTS) has been extensively studied due to its great potential in analog-to-digital converters. Here, we propose and demonstrate a PTS system based on phase modulation for sub-octave applications. Different from the PTS system using a Mach-Zehnder modulator (MZM), the PTS system, which uses a phase modulator (PM), has an operation bandwidth within an octave and is more suitable for preprocessing of sub-octave signals. Within the sub-octave band, the system is free of all second-order spurious signals. Because there is no direct current bias in a PM, the problem of bias drift, as well as the nonlinear distortion caused by it, can be thoroughly avoided. In addition, based on phase modulation and direct detection, the proposed PTS system has higher stability and a more simplified structure than that based on coherent detection. An exact analytical model has been established, and some compact expressions have been derived to fully characterize all frequency components of the PM-based PTS system. System properties, including the power transfer function, 3-dB bandwidth, and nonlinear distortion have been discussed, and numerical and experimental results on the performance of the PM-based PTS have been presented. In addition, a dual-channel PTS that employs a PM and a push-pull MZM has been proposed to extend the operation bandwidth to multi-octave.

Two-dimensional hybrid model for magnetic field calculation in electrical machines: exact subdomain technique and magnetic equivalent circuit

PurposeThe purpose of this paper is to propose a two-dimensional (2-D) hybrid analytical model (HAM) in polar coordinates, combining a 2-D exact subdomain (SD) technique and magnetic equivalent circuit (MEC), for the magnetic field calculation in electrical machines at no-load and on-load conditions.Design/methodology/approachIn this paper, the proposed technique is applied to dual-rotor permanent magnet (PM) synchronous machines. The magnetic field is computed by coupling an exact analytical model (AM), based on the formal resolution of Maxwell’s equations applied in subdomains, in regions at unitary relative permeability with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff's current law), in ferromagnetic regions. The AM and MEC are connected in both directions (i.e. r- and theta-edges) of the (non-)periodicity direction (i.e. in the interface between teeth regions and all its adjacent regions as slots and/or air-gap). To provide accurate solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead to MEC and characterized by an equivalent magnetomotive force (MMF) located in the slots, teeth and yoke.FindingsIt is found that whatever the iron core relative permeability, the developed HAM gives accurate results for both no-load and on-load conditions. Finite element analysis demonstrates the excellent results of the developed technique.Originality/valueThe main objective of this paper is to achieve a direct coupling between the AM and MEC in both directions (i.e. r- and theta-edges). The current density distribution is modeled by using Maxwell’s equations instead to MEC and characterized by an MMF.

8-16-4 graphyne: Square-lattice two-dimensional nodal line semimetal with a nontrivial topological Zak index

An unprecedented graphyne allotrope with square symmetry and nodal line semimetallic behavior has been proposed in the two-dimensional (2D) realm. The emergence of the Dirac loop around the high-symmetry points in the presence of both the inversion and time-reversal symmetries is a predominant feature of the electronic band structure of this system. Besides, the structural stability in terms of the dynamic, thermal, and mechanical properties has been critically established for the system. Following the exact analytical model based on the real-space renormalization group scheme and tight-binding approach, we have inferred that the family of 2D nodal line semimetals with square symmetry can be reduced to a universal four-level system in the low-energy limit. This renormalized lattice indeed explains the underlying mechanism responsible for the fascinating emergence of 2D square nodal line semimetals. Besides, the analytical form of the generic dispersion relation of these systems is well supported by our density-functional theory results. Finally, the nontrivial topological properties have been explored for the predicted system without breaking the inversion and time-reversal symmetry of the lattice. We have obtained that the edge states are protected by the nonvanishing topological index, i.e., Zak phase.

An Exact Analytical Model for an IoT Network with MMPP Arrivals

Analytical modeling of the Internet of Things (IoT) networks is challenging. This is due to the presence of a large number of devices in these networks and the complexity of the priorities between different types of traffic. Taking these aspects into account, the objective of this paper is to analyze the performance of an IoT network where the IoT devices work independently of one another. To this end, we developed a novel multi-dimensional Continuous-Time Markov Chain (CTMC) model with threshold-based preemption. In this model, each IoT device is modeled as a Markov Modulated Poisson Process (MMPP) that can transmit regular and alarm packets. Alarm packets have higher priority over regular packets. To measure access to the channel between alarm and regular packets, we introduced a threshold parameter where the threshold is the number of packets in the alarm queue that indicates when preemption starts. The performance measures include blocking probability, the average delay of regular packets and alarm packets, discard rate , and success probability of regular packets. Comprehensive numerical analysis was conducted. Our results indicate that impact of the threshold on performance measures is higher on the boundary values of the threshold. The model was proven to be efficient in analyzing the performance of IoT networks on a wide range of parameter values. These results may be used in the future to develop and assess a protocol that utilizes a scheduling algorithm with a dynamic preemption threshold to optimize the performance of the IoT network.

New calculation method for tube cross-flow heat exchangers

A new method for thermal calculations of the cross-flow tube heat exchangers was proposed. The temperature of both fluids and the wall temperature are determined. The heat exchanger is divided into control volumes, in which outlet fluid temperatures are calculated by closed analytical formulas. Two examples of the application of the method for the calculation of two-pass cross-co-current and cross-countercurrent superheaters were presented. An exact analytical model was also developed for both superheaters to estimate the accuracy of the proposed method. The results of the superheater calculations using the developed method are in good agreement with the results obtained by the exact analytical models. The proposed method can be used to calculate heat exchangers with a complicated flow system in which the physical properties of fluids are temperature-dependent.

Dynamics of a magnetic pendulum in the presence of an oscillating conducting plate

AbstractA pendulum with an attached permanent magnet moving near a conductor is a typical experiment for the demonstration of electromagnetic braking. When the conductor itself moves, it can transfer energy to the pendulum. We study a simple but exact analytical model where the conductor is a horizontally unbounded flat plate. For this geometry, eddy currents and induced Lorentz force due to the motion of a magnetic dipole are known analytically in the quasistatic limit. A vertical oscillation of such a horizontal plate located beneath the magnet is considered. In this setup, the vertical position of the pendulum is an equilibrium point when the magnetic moment of the magnet is perpendicular to its plane of motion. Depending on the strength of the magnetic dipole moment, the frequency and amplitude of the plate as well as the distance between plate and magnet, the plate oscillation can destabilize the equilibrium. The stability limits for weak electromagnetic coupling are computed analytically using the harmonic balancing method. For stronger coupling, the stability limits are obtained numerically using Floquet analysis. Chaotic motions with finite amplitudes are also found.

A Fast Optimization Scheme of Coaxial Magnetic Gears Based on Exact Analytical Model Considering Magnetic Saturation

This article presents a harmonic modeling method (HMM) for coaxial magnetic gears (CMGs) by considering the nonlinear B – H curve for soft-magnetic material. CMGs are divided into several annular layers, where Maxwell equation is solved. A convolution matrix of permeability is introduced to obtain the relationship between the magnetic flux density and magnetic field strength, and the continuous boundary conditions can be further satisfied. Subsequently, the magnetic field distribution and electromagnetic performance of CMGs can be calculated by solving the system equations. The computation time and accuracy of HMM are compared with those of finite element analysis (FEA) and subdomain method. The results show that the HMM is relatively fast and precise, and its computation time is about 80% of that of FEA. Then, the parameters of CMGs are optimized based on the HMM and non-dominated sorting genetic algorithm II (NSGA-II) combined optimization method. Particularly, the modulator is divided into multilayers, so its saturation can be modeled more precisely, and its shape can be further optimized. Finally, two optimal cases are evaluated and compared, and the result proves the effectiveness of the integrated optimization method.

Parametric instability of a magnetic pendulum in the presence of a vibrating conducting plate

A pendulum with an attached permanent magnet swinging in the vicinity of a conductor is a typical experiment for the demonstration of electromagnetic braking and Lenz’ law of induction. When the conductor itself moves, it can transfer energy to the pendulum. An exact analytical model of such an electromagnetic interaction is possible for a flat conducting plate. The eddy currents induced in the plate by a moving magnetic dipole and the resulting force and torque are known analytically in the quasistatic limit, i.e., when the magnetic diffusivity is sufficiently high to ensure an equilibrium of magnetic field advection and diffusion. This allows us to study a simple pendulum with a magnetic dipole moment in the presence of a horizontal plate oscillating in vertical direction. Equilibrium of the pendulum in the vertical position can be realized in three cases considered, i.e., when the magnetic moment is parallel to the rotation axis, or otherwise, its projection onto the plane of motion is either horizontal or vertical. The stability problem is described by a differential equation of Mathieu type with a damping term. Instability is only possible when the vibration amplitude and the distance between plate and magnet satisfy certain constraints related to the simultaneous excitation and damping effects of the plate. The nonlinear motion is studied numerically for the case when the magnetic moment and rotation axis are parallel. Chaotic behavior is found when the eigenfrequency is sufficiently small compared to the excitation frequency. The plate oscillation typically has a stabilizing effect on the inverted pendulum.

3-D Diffusive Molecular Communication With Two Fully-Absorbing Receivers: Hitting Probability and Performance Analysis

Exact analytical channel models for molecular communication via diffusion (MCvD) systems involving multiple fully absorbing receivers (FARs) in a three-dimensional (3-D) medium are hard to obtain due to the mathematical intractability of corresponding diffusion equations. Therefore, this work considers an MCvD system with two spherical FARs in a 3-D diffusion-limited medium and develop several insights using an approximate analytical expression for the hitting probability of information molecule (IM). Further, based on the hitting probability, a novel approximate closed-form analytical expression for the area under the receiver operating characteristic curve (AUC) is derived to analyze the detection performance at each FAR in the presence of other FAR. Finally, simulation results are presented to validate the analytical results using the particle-based and Monte-Carlo simulations and to yield important insights into the MCvD system performance with two FARs.

The two-state reversible kinetics of a long polymer molecule in solution with a delocalized coupling term. An exact analytical model

We develop a mathematical recipe for calculating the exact delocalized rate constant, for the end loop motion of a long polymer. It undergoes reversible reaction between two disjunct states, the open and the closed state, due to the effect of the surrounding solvent. The Smoluchowski-like equation mathematically represents the diffusion of the end monomers of the open polymer chain and the closed chain in terms of a free particle performing random motion under different harmonic potentials. The coupling term between the two potentials is assumed to be represented by a delocalized coupling term. For a favorable disposition towards the more realistic experimental behavior, the rate constant have effect incorporated from all the bond making and bond breaking phenomenon of the chemical reactions different from the end loop formation. It not only involves the end looping but can evaluate for reactions where only one of the ends of the open-chain is involved.

Anomalous elastic response of a 3D anti - tetrachiral metamaterial

The elastic modulus and Poisson's ratio of a 3D anti-tetrachiral (3ATC) metamaterial design was investigated using an exact analytical model, finite element simulations and experiments on additively manufactured Ti6Al4V lattices. The 3ATC structure was found to undergo a unique symmetric-to-asymmetric transition as the number of unit cells in the lattice decreases, an observation that has not been reported to date. A reduced lattice size also increases the influence of shear forces introduced by the fixed boundary conditions, which can lead to a higher elastic modulus in certain orientations and reduce it in others. These shear forces also drive the joints in small lattices into an out-of-plane rotation that causes the Poisson's ratio of such structures to range from -1.2 to 1 for different relative densities, in contrast to a constant value of -0.5 for bulk 3ATC lattices that do not undergo this joint twisting. Our results strongly indicate that the 3ATC structure belongs to a new ‘rotation-dominated’ geometric class in the Ashby framework for cellular materials, in addition to the well-established bending- and stretch- dominated topologies. The main contributor of strain for this class of materials is rigid joint rotation, with novel, distinctive traits such as a nonlinear elastic stress-strain response and multiple relative modulus vs. relative density relationships. For the 3ATC structure, one of these relations is linear, similar to stretch-dominated structures, while the other is disjointed and does not follow the power law, which is atypical of a cellular material.

Geometrically exact three-dimensional modeling of cable-driven parallel manipulators for end-effector positioning

A geometrically exact analytical model of cable-driven parallel manipulators operating in a three-dimensional space is formulated and discussed in this work. The model aims at investigating the exact positioning of a rigid body in a Cartesian space by a m-cables-driven parallel manipulator taking into account the cables mass, their elasticity and, consequently, the sag effect. The direct kinematic problem is formulated by means of 3(m+1) nonlinear equations expressing compatibility and equilibrium in the same number of unknowns, namely, 3m components of the constraint reactions and 3 finite rotations. A novel approach to the solution of the inverse kinematic problem is formulated by adding a set of m target equations to obtain 4m+3 nonlinear algebraic equations solved in terms of an equal number of unknowns. The latter are defined by the 3(m+1) increments of the variables of the direct problem and m additional unknowns, i.e., the increments of the cable unstretched lengths. The elastostatic problem of point mass end-effector is then derived. Consequently, the direct and the inverse kinematic problems are formulated by means of 3m and 4m nonlinear equations, respectively, in the equal number of unknowns. Examples with an increasing number of cables are considered, showing that, although solving the inverse kinematic problem may imply very slack cables configurations, the proposed approach allows to find a solution.

SmarTrafo: A Probabilistic Predictive Tool for Dynamic Transformer Rating

Operating electrical networks by Dynamic Transformer Rating (DTR) unlocks the capacity of grids and allows to increase the exploitation of distributed generation and renewables. However, there is risk associated with the operation of transformers by DTR. Energy dispatch and/or load curtailment must be scheduled before the actual energy delivery, thus DTR and load should be predicted prior the actual transformer loading. Since both are random variables, this problem is prone to be addressed by stress-strength analysis. In this paper, the novel comprehensive probabilistic tool “SmarTrafo” is presented. It allows predicting the probability of the DTR to be greater than the load (i.e., the probability of success) through an exact analytic stress-strength model, and formulating an alarm-setting strategy in order to establish a warning if the expected probability is greater than a threshold. Specifically, the threshold is optimized in a multi-objective formulation, exploiting three different indices which differently evaluate the predictive skill of alarm-setting strategy. Numerical experiments based on actual data confirm the suitability of the proposal in predicting the probability of success and in establishing high-performance alarms based on such predictions.