Nonlinear Chain Research Articles

Managing the Blockchain-enabled digital transformation of the healthcare supply chain

Healthcare organisations are currently in an era of significant digital transformation further accelerated through the COVID-19 pandemic. Organisations are seeking to adapt within a globalised environment with the ever-increasing supply chain disruptions, complexity of care and regulatory requirements. To be successful in this new era, organisations must re-envision their supply chain to improve patient outcomes and reduce costs and be flexible and adaptable in their ability to respond to the competitive marketplace. The combination of traditional production and cyber-physical production will indicate the evolution from traditional business models to the emerging non-linear supply chains with a patient-centric focus. The aim of this article is to review the healthcare supply chain in the context of digitally enabled technologies such as hyperledger and Blockchain, which have the potential to extensively alter healthcare organisations. The management contributions include the development of a reusable hyperchain artifact, construct development and understanding of the shift from the traditional healthcare supply chain to the industry 4.0 digital healthcare model instantiation of the hyperchain.

Stochastic numerical investigations for nonlinear three-species food chain system

In this work, three-dimensional nonlinear food chain system is numerically treated using the computational heuristic framework of artificial neural networks (ANNs) together with the proficiencies of global and local search approaches based on genetic algorithm (GA) and interior-point algorithm scheme (IPAS), i.e. ANN–GA–IPAS. The three-dimensional food chain system consists of prey populations, specialist predator and top-predator. The formulation of an objective function using the differential system of three-species food chain and its initial conditions is presented and the optimization is performed by using the hybrid computing efficiency of GA–IPAS. The achieved numerical solutions through ANN–GA–IPAS to solve the nonlinear three-species food chain system are compared with the Adams method to validate the exactness of the designed ANN–GA–IPAS. The comparison of the results is presented to authenticate the correctness of the designed ANN–GA–IPAS for solving the nonlinear three-species food chain system. Moreover, statistical representations for 40 independent trials and 30 variables validate the efficacy, constancy and reliability of ANN–GA–IPAS.

Manipulation of wave motion in smart nonlinear phononic crystals made of shape memory alloys

Thanks to the functional role of shape memory alloys (SMAs) in controlling the mechanical behavior of structures, researchers have started investigating the possibility of manipulating wave motion in phononic crystals using SMAs. While SMAs were used before to tune the wave propagation in linear phononic crystals, in this work, we aim to extend their utilization to nonlinear lattices. For this purpose, SMA helical springs are used to manipulate the dispersion curves and the location of stop-bands in weakly nonlinear monoatomic and diatomic lattice chains. Using Brinson’s formulation to describe the thermo-mechanical behavior of SMA wires and Lindstedt-Poincaré method to solve the derived governing equations, closed-form nonlinear dispersion relations in monoatomic and diatomic lattice chains are obtained and the effects of temperature-induced phase transformation and stiffness nonlinearity on the wave propagation are investigated. The results reveal that the dispersion curves of a weakly nonlinear monoatomic chain are formed at lower frequencies through the austenite-to-martensite phase transformation. Similarly, both the acoustic and optical branches of a diatomic lattice are moved to lower frequencies during the phase transformation in the cooling process. Therefore, the generated stop-bands in nonlinear diatomic lattices are also moved to lower frequencies. In addition, using auxiliary SMA ground springs, new classes of nonlinear monoatomic and diatomic chains exhibiting additional low-frequency attenuation zones are introduced. These low-frequency stop-bands are tunable and their frequency range can be modulated by exploiting the temperature-induced phase transformation in the SMA springs. The results obtained from analytic formulations are verified by numerical calculations and an excellent agreement is observed. Such tunability and the potential for adding stop-bands in low frequencies reveal that SMAs can be very helpful in designing nonlinear phononic and acoustic devices, such as vibration mitigators and wave filters with pre-defined attenuation zones.

Kapitza resistance at a domain boundary in linear and nonlinear chains.

We explore Kapitza thermal resistance on the boundary between two homogeneous chain fragments with different characteristics. For a linear model, an exact expression for the resistance is derived. In the generic case of frequency mismatch between the domains, the Kapitza resistance is well defined in the thermodynamic limit. At the same time, in the linear chain, the resistance depends on the thermostat properties and therefore is not a local property of the considered domain boundary. Moreover, if the temperature difference at the ends of the chain is fixed, then neither the temperature drop at the domain boundary nor the heat flux depend on the system size; for the normal transport, one expects the scaling N^{-1} for both. For specific assessment, we consider the case of an isotopic boundary-only the masses in different domains are different. If the domains are nonlinear, but integrable (Toda lattice, elastically colliding particles), the anomalies are similar to the case of linear chain, with the addition of well-articulated thermal dependence of the resistance. For the case of elastically colliding particles, this dependence follows a simple scaling law R_{k}∼T^{-1/2}. For Fermi-Pasta-Ulam domains, both the temperature drop and the heat flux decrease with the chain length, but with different exponents, so the resistance vanishes in the thermodynamic limit. For the domains comprised of rotators, the thermal resistance exhibits the expected normal behavior.

Dispersion curves of electromagnetically actuated nonlinear monoatomic and mass-in-mass lattice chains

Including nonlinearity can lead to fascinating wave propagation behavior in phononic crystals, broadening their possible applications in acoustic engineering. The current work aims to benefit from the exclusive properties of nonlinear chains, on one hand, and electromagnetic actuation, on the other hand, to actively control and deliberately manipulate propagating waves in monoatomic and mass-in-mass chains. First, the governing equations are derived and analytic dispersion relations for the nonlinear propagation of waves are provided using the modified Lindstedt-Poincare method. Then, the effects of electromagnetic actuation on the dispersion curves as well as wave-filtering capabilities of nonlinear lattice chains are investigated. Furthermore, a detailed analysis of the effects of electromagnetic actuation on the stop-bands with local resonance (LR) nature in mass-in-mass chains is performed. The results reveal that successful implementation of the electromagnetic actuation to the studied systems can efficiently manipulate their wave-propagation characteristics, providing about 25% tunability in the stop-band frequency range of monoatomic chains and about 15% in mass-in-mass chains. Also, additional controllable low-frequency stop-bands can be generated as a result of applying electromagnetic actuation leading to higher tunability of wave propagation/attenuation in nonlinear phononic chains.

Analytical study of two nonlinear Schrödinger equations via optical soliton solutions

In this study, we investigate two nonlinear Schrödinger equations (NLSEs) which point out the evolution of disturbances in dynamics. The first one is the nonlinear Heisenberg ferromagnetic spin chain equation of (2+1)-dimensional and the second one is (1+1)-dimensional cubic NLSE that govern the dynamics of modulated compressional dispersive Alfvén (CDA) envelope. The ([Formula: see text]-expansion method is adopted to carry out this target in a straightforward way. A diversity of new hyperbolic and periodic solitary wave solutions are acquired. The obtained solutions with some constraint conditions show the validity and effectiveness of the method.

Vibrations in a Growing Nonlinear Chain

A one-dimensional chain describing the linear statistical increment of growing homogeneous atoms was arbitrarily built and investigated using an energy potential function. The analytic form of the considered potential has two exponential terms which describes chaotic behavior when the chain was excited. In order to investigate the dynamics of statistical attachment of individual atoms in the slender gold chain, the total energy of the entire system was changed by increasing the kinetic energy upon increment of homogeneous atoms in the chain. This resulted in a corresponding increase of the total energy in the system. On the other hand, the potential energy of the system on increment of homogeneous atoms equals zero, because the distance between corresponding atoms equals to the molecular distance (minimum potential distance). We considered the dynamical system with linear damping and without linear damping. \\ Different initial points were investigated to obtain trends of vibration that includes chaotic and regular oscillations. At some initial point(s), the attached atom experiences an infinite jump which means it falls off the nonlinear slender chain and the chain was broken. The interpretation of this phenomenon means the gold chain will result into an unstable nanostructure. We compared the numerical simulation of the system with different built-in ordinary differential equation solvers of various computer algebra software. Numerical simulation were carried out by plotting the system of growing atoms' displacement against time. The system of linearly attached atoms were numerically simulated and inferences were stated from the study. In all cases considered, we inferred that amplitude of oscillation significantly increased at the end of the chain (terminal point) as compared to the initial point the oscillation started.

Two decades of INO research on laser arrays

We summarize in this work the salient points of the studies carried out at the National Institute of Optics (INO) in Florence in the vast field of coherent laser arrays. The research began in the early 90s under the push of Tito Arecchi with the study of coupled laser oscillators. These systems stimulated Tito's curiosity by representing an accessible sample of nonlinear oscillator chains. In the following years at INO we continued our research in this field, obtaining numerical and experimental results both with the realization of laser arrays and in the field of their possible application. Of particular importance for obtaining a fruitful application was the development of optical phase filtering techniques aimed at increasing the optical quality of the beam emitted from these sources, which is actually far from having a traditional geometry.

Lattice approximations of the first-order mean field type differential games

The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the approximations of the value function of the first-order mean field type differential game using solutions of model finite-dimensional differential games. The model game appears as a mean field type continuous-time Markov game, i.e., the game theoretical problem with the infinitely many agents and dynamics of each agent determined by a controlled finite state nonlinear Markov chain. Given a supersolution (resp. subsolution) of the Hamilton–Jacobi equation for the model game, we construct a suboptimal strategy of the first (resp. second) player and evaluate the approximation accuracy using the modulus of continuity of the reward function and the distance between the original and model games. This gives the approximations of the value function of the mean field type differential game by values of the finite-dimensional differential games. Furthermore, we present the way to build a finite-dimensional differential game that approximates the original game with a given accuracy.

Effect of pressure on thermalization of one-dimensional nonlinear chains.

Pressure plays a vital role in changing the transport properties of matter. To understand this phenomenon at a microscopic level, we here focus on a more fundamental problem, i.e., how pressure affects the thermalization properties of solids. As illustrating examples, we study the thermalization behavior of the monatomic chain and the mass-disordered chain of Fermi-Pasta-Ulam-Tsingou-β under different strains in the thermodynamic limit. It is found that the pressure-induced change in integrability results in qualitatively different thermalization processes for the two kinds of chains. However, for both cases, the thermalization time follows the same law-it is inversely proportional to the square of the nonintegrability strength. This result suggests that pressure can significantly change the integrability of a system, which provides a new perspective for understanding the pressure-dependent thermal transport behavior.

Multi-Product Multi Echelon Measurements of Perishable Supply Chain: Fuzzy Non-Linear Programming Approach

The perishable milk products industry has to deal with multiple pressures such as demand forecasting, price fluctuations, lead time, order batching, and inflated orders along with difficulties of climatic and traffic conditions, storage areas and shipment in unfavorable circumstances. The Indian dairy industry faces immense wattage issue due to improper infrastructure for the cold chain storage facilities, resulting in unsatisfied customers. A study is undertaken to comprehend the supply chain framework that handles perishability issues in production and distribution. Researchers propose a multi-objective mixed-integer non-linear supply chain coordination model under uncertain environments to minimize the cost of transportation, offset wastage of products and neutralize the losses due to insufficiencies of transit and storage amenities. The proposed model is meant for managing the delivery with lesser deterioration losses for producers, warehouses, and retailers. The model considers various costs for holding, halting, discounts on purchased cost, transportation cost for truckload policy under regular and unforeseen circumstances of curfew, and identify the rate of deterioration to know the impact on the cost for all players involved in the SCM framework. To handle uncertainty of objective functions, fuzzy set concepts and the defuzzification method are imposed, and fuzzy non-linear programming algorithms are used to get the single objective function from the defuzzified multi-objective functions. Data analysis is done on Lingo 18.0 software. Rate of deterioration is highest for the warehouse, which indicates that efforts should be made to augment warehouse facilities for less spoilage to reduce losses in cost. Finally, the study ends with main findings, conclusions, limitations and future scopes.

Upper mantle radial anisotropy under the Indian Ocean from higher mode surface waves and a hierarchical transdismensional approach

SUMMARYWe investigated the likelihood of radial anisotropy in the shallow and deep upper mantle, including the mantle transition zone (MTZ) under the Indian Ocean. Seismic anisotropy can be an indicator of mantle deformation through lattice preferred orientation of anisotropic crystals in the mantle. It has thus the potential to illuminate Earth’s dynamic interior, but previous seismic tomography studies have not achieved consensus on the existence of radial anisotropy below ∼250 km depth. We developed a fully nonlinear transdimensional hierarchical Bayesian Markov Chain Monte Carlo approach to invert fundamental and higher mode surface wave dispersion data and applied it to a subset of a global Love and Rayleigh wave data set. We obtained posterior model parameter distributions for shear wave velocity (VS) and radial anisotropy ξ under the Indian Ocean. These posterior model distributions were used to calculate the probability of having radial anisotropy at different depths. We demonstrated that separate inversions of Love and Rayleigh waves yield models compatible with the results of joint inversions within uncertainties. The obtained pattern of VS anomalies agrees with most previous studies. They display negative anomalies along ridges in the uppermost mantle, but those are stronger than for regularized inversions. The Central Indian Ridge and the Southeastern Indian Ridge present velocity anomalies that extend to ∼200 km depth, whereas the Southwestern Indian Ridge seems to have a shallower origin. Weaker, laterally variable velocity perturbations were found at larger depths. The anisotropy models differ more strongly from regularized inversion results and their uncertainties were rather large. We found that anisotropy models from regularized inversions also depend on the chosen parametrization, which is consistent with the existence of a large model null-space. Apart from a fast horizontally polarized shear wave signal in the top 100 km, likely reflecting the horizontal plate motion due to asthenospheric deformation, no clear relation to surface geology was detected in the anisotropy models. We found that, although the anisotropy model uncertainties are rather large, and lateral variations are present, the data generally prefer at least 1 per cent anisotropy in the MTZ with fast vertically polarized shear waves, within errors. Incorporating group velocity data did not help better constrain deep structure by reducing parameter trade-offs. We also tested the effect of prior constraints on the 410- and 660-km topography and found that the undulations of these discontinuities had little effect on the resulting models in our study region.

Symmetries of a Certain Periodic Chain

We consider a periodic closure of a nonlinear integrable two-dimensional three-point chain. Integrability is understood in the sense that the chain admits a wide class of reductions, which are nonlinear hyperbolic Darboux integrable systems with two independent variables.We consider a system obtained as a period-2 periodic closure of one of two-dimensional three-point chains found within this framework. For this system, a second-order higher symmetry depending on two arbitrary functions is constructed.

Electrochemical aptasensor based on proximity binding-induced DNA networked for enzyme-free and ultrasensitive detection of thrombin

The abnormal change of thrombin concentration is closely related with various diseases. By using proximity binding-induced DNA network assembled by nonlinear hybridization chain reaction (HCR), we here developed an enzyme-free and ultrasensitive electrochemical strategy for analyzing thrombin in human serums. The binding of the two different aptamers to a thrombin enhanced the local concentration of the aptamers and facilitates the formation of an intact strand. Subsequently, the formed strand caused nonlinear HCR, forming DNA network. The DNA network bound to the capture probes (CP)-modified electrode, producing electrochemical signal of MB. Benefiting from the proximity binding-induced DNA network, the proposed biosensor exhibited a wide linear range from 1.0 pM to 1.0 nM with a low detection limit of 0.56 pM and high specificity. More importantly, the developed enzyme-free electrochemical biosensor has been used to detect thrombin in serum samples with good performance. This makes such a strategy possess potential promise in the application of clinical diagnosis.

Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Analytic solutions of fractional order physical equations are very significant to explain the behavior of mathematical models expressing complex phenomena in engineering and natural sciences. The modified extended tanh-function (METHF) method is an especially capable and highly effective mathematical technique to attain analytic traveling wave solutions. This research proposes to examine the analytic solutions of the time-fractional (2+1)-dimensional non-linear Heisenberg ferromagnetic spin chain (HFSC) equation that describes electromagnetic waves in modern magnet theory by using the suggested method and the definition of conformable fractional derivative. We obtain some new analytic solutions of the proposed equation in terms of hyperbolic, trigonometric, and rational functions. The validity and precision of these solutions are also examined. The 2D, 3D, and contour graphs of solutions are given to manifest the physical behavior of the waves with the aid of the Mathematica package program.

Wavenumber-space band clipping in nonlinear periodic structures

In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as an initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

Mechanisms for transient localization in a diatomic nonlinear chain

We investigate transient nonlinear localization, namely the self-excitation of energy bursts in an atomic lattice at finite temperature. As a basic model we consider the diatomic Lennard-Jones chain. Numerical simulations suggest that the effect originates from two different mechanisms. One is the thermal excitation of genuine discrete breathers with frequency in the phonon gap. The second is an effect of nonlinear coupling of fast, lighter particles with slow vibrations of the heavier ones. The quadratic term of the force generate an effective potential that can lead to transient grow of local energy on time scales the can be relatively long for small mass ratios. This heuristics is supported by a multiple-scale approximation based on the natural time-scale separation. For illustration, we consider a simplified single-particle model that allows for some insight of the localization dynamics.

Response enhancement and energy localization in autoresonant nonlinear chains

The response enhancement (autoresonance) in a weakly dissipative nonlinear chain subjected to harmonic forcing with a slowly-varying frequency may be of interest for both a fundamental standpoint as well as practical applications. However, the cumulative effect of dissipation and forcing parameters on the emergence and stability of autoresonance in an anharmonic array has not been discussed thus far in the literature. Recent theoretical and numerical developments were focused on the study of unbounded autoresonance in a non-dissipative strongly nonlinear chain. In this work, the asymptotic methods are employed to construct the evolutionary equations, which describe the long-term behavior of a weakly dissipative strongly nonlinear chain under the condition of 1:1 resonance. Analytical approximations and numerical examples demonstrate that weak dissipation permits the emergence of autoresonance on a bounded time interval but an increase of dissipation leads to escape from resonance of either the entire chain or a part of the chain distant from the source of energy. Numerical simulations for a series of examples confirm close proximity of the exact (numerical) results to their analytical approximations, together with the dependence of the duration of autoresonance, its localization length, and the amplitudes attainable on dissipation and detuning parameters.

Projective surjectivity of quadratic stochastic operators on L1 and its application

A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over a infinite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex). In the present paper, we consider a continuous analogue of the mentioned mapping acting on $L^1$-spaces. Main aim of the current paper is to investigate projective surjectivity of quadratic stochastic operators (QSO) acting on the set of all probability measures. To prove the main result, we study the surjectivity of infinite dimensional nonlinear Markov operators and apply them to the projective surjectivity of a QSO. Furthermore, the obtained result has been applied for the existence of positive solution of some Hammerstein integral equations.

Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices.

The study of nonlinear oscillator chains in classical many-body dynamics has a storied history going back to the seminal work of Fermi etal. [Los Alamos Scientific Laboratory Report No. LA-1940, 1955 (unpublished)]. We introduce a family of such systems which consist of chains of N harmonically coupled particles with the nonlinearity introduced by confining the motion of each individual particle to a box or stadium with hard walls. The stadia are arranged on a one-dimensional lattice but they individually do not have to be one dimensional, thus permitting the introduction of chaos already at the lattice scale. For the most part we study the case where the motion is entirely one dimensional. We find that the system exhibits a mixed phase space for any finite value of N. Computations of Lyapunov spectra at randomly picked phase space locations and a direct comparison between Hamiltonian evolution and phase space averages indicate that the regular regions of phase space are not significant at large system sizes. While the continuum limit of our model is itself a singular limit of the integrable sinh Gordon theory, we do not see any evidence for the kind of nonergodicity famously seen in the work of Fermi etal. Finally, we examine the chain with particles confined to two-dimensional stadia where the individual stadium is already chaotic and find a much more chaotic phase space at small system sizes.