A Simplified Tantalum Oxide Memristor Model, Parameters Estimation and Application in Memory Crossbars

In this paper, an improved and simplified modification of a tantalum oxide memristor model is presented. The proposed model is applied and analyzed in hybrid and passive memory crossbars in LTSPICE environment and is based on the standard Ta2O5 memristor model proposed by Hewlett–Packard. The discussed modified model has several main enhancements—inclusion of a simplified window function, improvement of its effectiveness by the use of a simple expression for the i–v relationship, and replacement of the classical Heaviside step function with a differentiable and flat step-like function. The optimal values of coefficients of the tantalum oxide memristor model are derived by comparison of experimental current–voltage relationships and by using a procedure for parameter estimation. A simplified LTSPICE library model, correspondent to the analyzed tantalum oxide memristor, is created in accordance with the considered mathematical model. The improved and altered Ta2O5 memristor model is tested and simulated in hybrid and passive memory crossbars for a state near to a hard-switching operation. After a comparison of several of the best existing memristor models, the main pros of the proposed memristor model are highlighted—its improved implementation, better operating rate, and good switching properties.

XFEM Analyses Using Two-Dimensional Quadrilateral Elements Enriched with Only the Heaviside Step Function

In the framework of the extended finite element method, a two-dimensional four-node quadrilateral element enriched with only the Heaviside step function is formulated for stationary and propagating crack analyses. In the proposed method, two types of signed distance functions are used to implicitly express crack geometry, and finite elements, which interact with the crack, are appropriately partitioned according to the level set values and are then integrated numerically for derivation of the stiffness matrix and internal force vectors. The proposed method was verified by evaluating stress intensity factors, performing crack propagation analyses and comparing the obtained results with reference solutions.

Applying the Heaviside step function to simulate the changes of temperature in automotive batteries

Discharged batteries do not provide the specified voltage in the car’s power supply system during parking, which can cause malfunctions of electrical equipment and an increase in the quiescent current in the on-board network, due to incorrect operation of electronic control units responsible for the operation of self-diagnosis systems, anti-theft alarm, multi-media, maintaining a thermal state, etc. Therefore, to ensure a reliable start of the ICE and the proper operation of the electrical equipment of a car at low temperatures, it is required to maintain the battery in a charged state. Vehicle generator is selected taking into account the nominal capacity of the battery, power and operating modes of electrical consumers, which excludes the battery operation with a low level of charge. However, when operating cars in large cities in winter, the battery charge level decreases. Deterioration of the battery charging characteristics, increased power consumption of additional equipment and low speed of movement of cars in the city with frequent stops at intersections are the reasons for the decrease in the efficiency of the battery charge. In such conditions, the battery can be discharged not only by starting the ICE and turning on consumers in the parking lot, but also when the ICE is idling and at low crankshaft speeds while driving on city routes and during rush hours. Considering that the operational characteristics of the battery change significantly with decreasing temperature, studies aimed at establishing and predicting the battery temperature during operation are relevant.

Multi-material topology optimization of permanent magnet synchronous motors

This paper presents a multi-material topology optimization for the design of permanent magnet synchronous motors (PMSMs). Specifically, structural shapes of permanent magnet (PM) and iron core in a PMSM rotor are simultaneously designed together with the orientation of PM magnetization. For a co-design of PM and iron core, relative permeability and residual magnetic flux density are interpolated by the three-field density approach based on the Helmholtz filtering and regularized Heaviside step function. Here, the Helmholtz filtering aims to attain smooth border in design results, and the Heaviside function enables us to acquire a clear border (i.e. zero-one design) without intermediate densities. The optimization goal is set as maximizing the average torque of PMSMs. The average torque is calculated by Maxwell stress tensor (MST) method considering a maximum torque per ampere (MTPA) control. To validate the effectiveness of the proposed multi-material topology optimization approach, a PMSM rotor with 4 poles and 12 slots is designed. In addition, design results at various settings of input current amplitude and PM strength are compared and discussed. When the input current is stronger than the PM strength, rotor PM and iron core are designed for utilizing both PM and reluctance torque components like V-shape interior PMSMs. On the other hand, in the case of stronger PM strength, PM is designed near the air-gap, which utilizes only PM torque component like surface PMSMs.

Characterization and Mitigation of Model Bias in Parametric Mapping of Dopamine Response to Behavioral Challenge

Compartmental modeling of 11C-raclopride (RAC) is commonly used to measure dopamine response to intra-scan behavioral tasks. Bias in estimates of binding potential (BPND) and its dynamic changes (ΔBPND) can arise when the selected compartmental model deviates from the underlying biology. In this work, we characterize the bias associated with assuming a single target compartment and propose a model for reducing this bias by selectively discounting the contribution of the initial uptake period. Methods: 69 healthy young adult participants were scanned using RAC PET/MR while simultaneously performing a rewarded behavioral task. BPND and ΔBPND were estimated using an extension of the Multilinear Reference Tissue Model (MRTM2) with the task challenge encoded as a Heaviside step function. Bias was estimated using simulations designed to match the acquired data and was reduced by introducing a new model (DE-MRTM2) that reduces the biasing influence of the initial uptake period in the modeled estimation of BPND for both simulations and participant data. Results: Bias in ΔBPND was observed to vary both spatially with BPND and with the assumed value of k4. At the most likely value of k4 (0.13 min-1), the average bias and the maximum voxel bias magnitude in the nucleus accumbens were estimated to be 1.2% and 3.9% respectively. Simulations estimated that debiasing the contribution of the first 27 minutes of acquired data reduced average bias and maximum voxel bias in the nucleus accumbens ΔBPND to -0.3% and 2.4% respectively. In the acquired participant data, DE-MRTM2 produced modest changes in the experimental estimates of striatal ΔBPND, while extrastriatal bias patterns were greatly reduced. DE-MRTM2 also considerably reduced the dependence of ΔBPND upon the first-pass selection of k2'. Conclusion: Selectively discounting the contribution of the initial uptake period can help mitigate BPND- and k4-dependent bias in single compartment models of ΔBPND, while also reducing the dependence of ΔBPND on the first-pass estimation of k2'.

An Explicit Form of Heaviside Step Function

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

On the Pseudo-Spectral Method and Spectral Accuracy

There are numerical accuracy problems related to the implementation of sharp internal interfaces in pseudo-spectral and finite-difference schemes. It is common practice to classify numerical errors due to the implementation of interfaces as being to some order in a Taylor expansion. An alternative approach is to classify these errors as being to some order in a Fourier expansion.The pseudo-spectral method does not provide spectral accuracy in inhomogeneous media. The numerical errorsfor the upper half of the frequency/wavenumber spectra of the propagating fields are not related to theimplementation of the derivative operators but to aliasing effects coming from the multiplicationof static material-parameter fields with the dynamic, propagating, fields. The pseudo-spectral methodcan only provide half-spectral accuracy. The same type of spatial aliasing errors are present also forfinite-difference schemes. High-order finite differences can provide the same accuracy as the pseudo-spectral method if the staggered finite-difference derivative operators have a negligible errorat four grid points per shortest wavelength and above. Smoothing of the material-parameter field leads to additional reduction in the error-free bandwidthof the propagating fields. Assuming that there is a maximum wavenumber up to which the spectrumof the smoothed model coincide with the implementation using a properly bandlimited Heaviside step function, then there exists a local critical wavenumber for the propagating field equal toone half of the maximum wavenumber for the smoothed model. Harmonic averaging of material-parameter fields also results in wavenumber spectra where there is a maximum wavenumber above whichthe wavenumber spectrum deviates from an implementation with a bandlimited Heaviside step function.The same one-half rule is applicable also in this case.

D Minus 1 Production Scenario: Production Model for Produced Hospital Furniture

Many kinds of production systems are used in medical equipment industries, one of which is through the work-in-process (WIP) buffer control system and feeding material scenarios to assure ability of the process to produce the expected throughput. The production model, known as the D minus 1 production scenario, is used to control production activities at the factory to be carried out using the day minus 1 rule. This rule is a time-based buffer production scenario in 1 day, ending at the finished goods assembly station used as the zero point (D0), from each workstation, pushed for one consecutive day to the beginning of the buffer. With the success of providing WIP buffers on D-1 and D-2 days, the product is certain to be ready on time. Production activities are modeled as Heaviside step function of the various processes involved therein. Production schedule, also production simulation, can be planned through a production dashboard provided for this purpose. Customers demand transformed to an integrated production schedule throughout the production flow, followed by production dispatching and execution. The integrated production schedule includes the supply of raw components, welding, paint, and product assembly to meet on time deliveries.