A phenomenological memristor model for synaptic memory and learning behaviors

Properties that are similar to the memory and learning functions in biological systems have been observed and reported in the experimental studies of memristors fabricated by different materials. These properties include the forgetting effect, the transition from short-term memory（STM） to long-term memory（LTM）, learning-experience behavior, etc. The mathematical model of this kind of memristor would be very important for its theoretical analysis and application design.In our analysis of the existing memristor model with these properties, we find that some behaviors of the model are inconsistent with the reported experimental observations. A phenomenological memristor model is proposed for this kind of memristor. The model design is based on the forgetting effect and STM-to-LTM transition since these behaviors are two typical properties of these memristors. Further analyses of this model show that this model can also be used directly or modified to describe other experimentally observed behaviors. Simulations show that the proposed model can give a better description of the reported memory and learning behaviors of this kind of memristor than the existing model.

The Importance of Mathematical Models to Explore the Effects of Marijuana and Other Plant Based Products on Learning and Memory

This article describes the use of the first order system transfer function for learning and memory studies involving consumption of marijuana and other plant based products. We provide detailed instructions on how the model can be used to analyze the performance of individual participants using a memory test developed by the senior authors. The importance of identifying possible learning and memory deficits of marijuana is paramount due to the growing number of states in the U.S. legalizing marijuana use for medicinal and recreational purposes. The model can also be extended to other plant based products purported to improve memory. While this article does not study the effect of marijuana, we provide details on how it can be used by illustrating its application on individuals consuming an amphetamine-like psychostimulant drug using our own memory test.

Three-Dimensional Simulations of RESET Operation in Phase-Change Random Access Memory with Blade-Type Like Phase Change Layer by Finite Element Modeling

An optimized device structure for reducing the RESET current of phase-change random access memory （PCRAM） with blade-type like （BTL） phase change layer is proposed. The electrical thermal analysis of the BTL cell and the blade heater contactor structure by three-dimensional finite element modeling are compared with each other during RESET operation. The simulation results show that the programming region of the phase change layer in the BTL cell is much smaller, and thermal electrical distributions of the BTL cell are more concentrated on the TiN/GST interface. The results indicate that the BTL cell has the superiorities of increasing the heating efficiency, decreasing the power consumption and reducing the RESET current from 0.67mA to 0.32mA. Therefore, the BTL cell will be appropriate for high performance PCRAM device with lower power consumption and lower RESET current.

Understanding long-term memory in global mean temperature:An attribution study based on model simulations

Long-term memory(LTM)in the climate system has been well recognized and applied in different research fields,but the origins of this property are still not clear.In this work,the authors contribute to this issue by studying model simulations under different scenarios.The global mean temperatures from pre-industrial control runs(pi Control),historical(all forcings)simulations,natural forcing only simulations(Historical Nat),greenhouse gas forcing only simulations(Historical GHG),etc.,are analyzed using the detrended fluctuation analysis.The authors find that the LTM already exists in the pi Control simulations,indicating the important roles of internal natural variability in producing the LTM.By comparing the results among different scenarios,the LTM from the piControl runs is further found to be strengthened by adding natural forcings such as the volcanic forcing and the solar forcing.Accordingly,the observed LTM in the climate system is suggested to be mainly controlled by both the‘internal’natural variability and the‘external’natural forcings.The anthropogenic forcings,however,may weaken the LTM.In the projections from RCP2.6 to RCP8.5,a weakening trend of the LTM strength is found.In view of the close relations between the climate memory and the climate predictability,a reduced predictability may be expected in a warming climate.

Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation

The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.

Using Pipeline Instructions by Parallel Simulation of Mathematical Models

Simulation is an important and useful technique helping users understand and model real life systems. Once built, the models can run proving realistic results. This supports making decisions on a more logical and scientific basis. The paper introduces method of simulation, and describes various types of its application. The authors used the method of analysis of the creation and implementation of the programme code. The authors compared parallel instruction of computing defined to pipelined instructions. The power of simulation is that a common model can be used to design a large variety of systems. An important aspect of the simulation method is that a simulation model is designed to be repeated in actual computer systems, especially in multicore processors. For this reason, it is important to minimize average waiting time for fetch and decode stage instructions. The objective of the research is to prove that the parallel operation of programme code is faster than sequential operation code on the multi processor architecture. The system modeling uses methods and simulation on the parallel computer systems is very precise. The time benefit gained in simulation of mathematical model on the pipeline processor is higher than the one in simulation of mathematical model on the multi processors computer system.

A Study on the Nonlinear Caputo-Type Snakebite Envenoming Model with Memory

In this article,we introduce a nonlinear Caputo-type snakebite envenoming model with memory.The well-known Caputo fractional derivative is used to generalize the previously presented integer-order model into a fractionalorder sense.The numerical solution of the model is derived from a novel implementation of a finite-difference predictor-corrector(L1-PC)scheme with error estimation and stability analysis.The proof of the existence and positivity of the solution is given by using the fixed point theory.From the necessary simulations,we justify that the first-time implementation of the proposedmethod on an epidemicmodel shows that the scheme is fully suitable and time-efficient for solving epidemic models.This work aims to show the novel application of the given scheme as well as to check how the proposed snakebite envenoming model behaves in the presence of the Caputo fractional derivative,including memory effects.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, effiux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch （ABU） should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch （PBU） is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

Numerical Simulation of a Mathematical Model for Dry/Wet-Spun Nascent Hollow Fiber Membrane

In an effort to find the effect of mass transfer, surface tension and drag forces on the velocity distribution, the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method). The effect of mass transfer on velocity distribution based on the complicated function (G(Cs h)) was presented and the effects of a complicated function were studied in two cases: in the first case, G(Cs h) was constant; in the second, G(Cs h) was variable. The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region. One empirical equation was used to describe this change and the predicted values had a better agreement with the experimental values. To verify the model hypotheses, hollow fiber membranes were spun from 20∶80 polybenzimidazole/polyetherimide dopes with 25.6 wt% solid in N, N-dimethylacetamide (DMAc) using water as the external and internal coagulants. Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes, it is found that the model calculated values were in a good agreement with the experimental values.

Numerical Simulation Analysis of a Mathematical Model of Circadian Pacemaker Neurons

Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.

The mathematical model and simulation of the electrostatic suspension system in the vertical direction

In order to research the vibration law of electrostatic suspension systems in the vertical direction, the mathematical model as a nonlinear differential equation is established. A series of simulation is carried out. The results show that the solution of the differential equation is a periodic function. The amplitude becomes bigger with the original velocity increased. The period becomes smaller with the original velocity increasing. The numerical methods are presented to derive the amplitude and the frequency, and the results coincide with that of the simulation. The condition during which the simple harmonic vibration arises is pointed out. The expressions for the amplitude and the period of simple harmonic vibration are derived respectively, and the results are the same with that of the simulation. This study is helpful for researching the vibration characteristics of the electrostatic suspension system. The external disturb should be controlled to lower the amplitude and the frequency of the vibration.

Simulation of a Mathematical Model Minimizing Energy Consumption in SDN Type Networks

Several works by the authors have shown that energy consumption in communication networks does not only depend on the traffic load but on all connected equipment in the network. We have contributed a new mathematical model and a new energy saving strategy with Software Defined Network (SDN) technology [1]. Our Model solution is based on the Modified SPRING Protocol (MSP). In this paper, we simulated our work and compared it to that of the authors [2] and [3]. The OMNET++ simulator was used for our work. Thus, the results of the simulations gave a delay that tends to zero, a packet loss of the order of 10% and a constant jitter of 4% better than the previous authors.

Target morphology and cell memory:a model of regenerative pattern formation

Despite the growing body of work on molecular components required for regenerative repair,we still lack a deep understanding of the ability of some animal species to regenerate their appropriate complex anatomical structure following damage.A key question is how regenerating systems know when to stop growth and remodeling-what mechanisms implement recognition of correct morphology that signals a stop condition？In this work,we review two conceptual models of pattern regeneration that implement a kind of pattern memory.In the first one,all cells communicate with each other and keep the value of the total signal received from the other cells.If a part of the pattern is amputated,the signal distribution changes.The difference fromthe original signal distribution stimulates cell proliferation and leads to pattern regeneration,in effect implementing an error minimization process that uses signaling memory to achieve pattern correction.In the second model,we consider a more complex pattern organization with different cell types.Each tissue contains a central（coordinator）cell that controls the tissue and communicates with the other central cells.Each of them keeps memory about the signals received from other central cells.The values of these signals depend on the mutual cell location,and the memory allows regeneration of the structure when it is modified.The purpose of these models is to suggest possible mechanisms of pattern regeneration operating on the basis of cell memory which are compatible with diverse molecular implementation mechanisms within specific organisms.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.

Modeling of Pneumatic Muscle with Shape Memory Alloy and Braided Sleeve

Pneumatic muscle （PM） of flexible actuators used in bionic robot is an active area of recent research. A novel PM with shape memory alloy （SMA） braided sleeve is proposed in this paper, and SMA is used to improve PM working characteristics. Based on the principle of virtual work, output force model of PM and relationship with braided wire inner-stress are established, and analysis of PM deformation has shown that braided wire length is the key factor of output force characteristic. Based on the crystal structure transitions, the relationship of temperature with wire shrinkage is derived. Then, the synthetic dynamics of novel PM is established. A physical prototype of PM with SMA braided sleeve is developed, and test platform that is built for the experiment. Experiment and simulation test of static isometric-length, static isobaric-pressure, and dynamic characteristics are done. The experimental results are compared with the simulation of theoretical model. Moreover, based on experiment, model of output force was improved by adding a correction factor to deal with the elastic force of rubber tube. The results analysis demonstrates that the established models are correct, and SMA wires can reinforce PM and make PM working characteristics adjustable. PM proposed in this paper has greater output force and is beneficial to achieve more accurate control that is useful for manipulating fragile things.

SIMULATED MATHEMATICAL MODEL FOR HIGH PRESSURE CYLINDER WALL TEMPERATURE OF HOMEMADE TURBINE

In order to balance the contradiction between the demand of high precision and that of short time interval of model computing for the power plant simulator, a set of simulated mathematical models are constructed. The model describes the cylinder wall temperature located at four key positions of the high pressure cylinder. The simulated model is confirmed to be not only simple but also precise via comparison between the simulated results and the autoptic data of a power plant.

Experimental optimization and mathematical modeling of supercritical carbon dioxide extraction of essential oil from Pogostemon cablin

The supercritical carbon dioxide extraction was applied to obtain essential oil from Pogostemon cablin in this work.Effect of extraction parameters including temperature,pressure,extraction time and particle size on extraction yield was investigated,and the response surface methodology with a Box–Behnken Design was used to achieve the optimized extraction conditions.The maximum yield of essential oil was 2.4356%under the conditions of extraction temperature 47°C,pressure 24.5 MPa and extraction time 119 min.Moreover,based on the Brunauer–Emmett–Teller theory of adsorption,a mathematical modeling was performed to correlate the measured data.The model shows a function relationship between extraction yield and time by a simple equation with three significantly adjustable parameters.These model parameters have been optimized through simulated annealing algorithm.The predicted data from the mathematical model show a good agreement with the experimental data of the different extraction parameters.

A continuous and high-efficiency process to separate coal bed methane with porous ZIF-8 slurry:Experimental study and mathematical modelling

Coal bed methane has been considered as an important energy resource.One major difficulty of purifying coal bed methane comes from the similar physical properties of CH_4 and N_2.The ZIF-8/water-glycol slurry was used as a medium to separate coal bed methane by fluidifying the solid adsorbent material.The sorption equilibrium experiment of binary mixture(CH_4/N_2)and slurry was conducted.The selectivity of CH_4 to N_2 is within the range of 2-6,which proved the feasibility of the slurry separation method.The modified Langmuir equation was used to describe the gas-slurry phase equilibrium behavior,and the calculated results were in good agreement with the experimental data.A continuous absorption-adsorption and desorption process on the separation of CH_4/N_2 in slurry is proposed and its mathematical model is also developed.Sensitivity analysis is conducted to determine the operation conditions and the energy performance of the proposed process was also evaluated.Feed gas contains 30 mol%of methane and the methane concentration in product gas is 95.46 mol%with the methane recovery ratio of 90.74%.The total energy consumption for per unit volume of product gas is determined as 1.846 kWh Nm^(-3).Experimental results and process simulation provide basic data for the design and operation of pilot and industrial plant.

A Practical Approach of Developing Mathematical Model for All Speed Governors

The paper introduced a special approach for diesel’s all-speed-governor modeling, which, in some cases, could solve the knotty problem frequently met in computer simulation of diesel propulsion system or diesel generating set. Suppose that it is hard to get a control-oriented governor mathematical model when the general approaches, the analytical approach or the experimental approach, are applied, and that an open-loop step response of the diesel engine and its system is available by means of computer simulation, the critical three parameters of a governor mathematical model, the proportional gain K_p, integral time constant K_i, and derivative time constant K_d, can be determined by use of PID tuning method which are widely applied in industrial process control. This paper discussed the train of thought of the approach, precondition, procedure, several modifications of the classical PID model, and some points for attention. A couple of case studies were given to demonstrate the effectiveness of this approach.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.