Discrete Levels Research Articles

Initialisation from lattice Boltzmann to multi-step Finite Difference methods: Modified equations and discrete observability

Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical schemes. We propose a modified equation analysis of the initialisation schemes for lattice Boltzmann methods, determined by the choice of initial data. These modified equations provide guidelines to devise and analyze the initialisation in terms of order of consistency with respect to the target Cauchy problem and time smoothness of the numerical solution. In detail, the larger the number of matched terms between modified equations for initialisation and bulk methods, the smoother the obtained numerical solution. This is particularly manifest for numerical dissipation. Starting from the constraints to achieve time smoothness, which can quickly become prohibitive for they have to take the parasitic modes into consideration, we explain how the distinct lack of observability for certain lattice Boltzmann schemes—seen as dynamical systems on a commutative ring—can yield rather simple conditions and be easily studied as far as their initialisation is concerned. This comes from the reduced number of initialisation schemes at the fully discrete level. These theoretical results are successfully assessed on several lattice Boltzmann methods.

Relaxation kinetics of interface states and bulk traps in atomic layer deposited ZrO2/β-Ga2O3 metal-oxide-semiconductor capacitors

The study of interface states and bulk traps and their connection to device instability is highly demanded to achieve reliable β-Ga2O3 metal-oxide-semiconductor (MOS) devices. However, a comprehensive analysis of the capture/emission behavior of interface states and bulk traps can be challenging due to widespread time constant distribution. In this study, using capacitance transient measurement tools, trap states of the ZrO2/β-Ga2O3 MOS gate stack were explicitly investigated, particularly its bias- and temperature-dependent relaxation kinetics. As forward bias is enlarged, it is observed that the interface state density (Dit) increases by 12.6%. Two bulk traps with discrete levels identified as 0.43 eV (E1) and 0.74 eV (E2) below the conduction band minimum were extracted by deep-level transient spectroscopy. It is further revealed that the emission processes of E1 and E2 are thermally enhanced, while the capture processes remain insensitive to temperature. The electric-field dependence of E1 indicates that the dominant mechanism follows the rule of Poole–Frenkel emission. The capacitance–voltage (C–V) hysteresis deteriorated at a higher forward bias due to the higher trap density and increased population of trapped charges. These findings provide an important framework for future device optimization to improve the reliability and performance of β-Ga2O3 MOS devices.

The impact of feedback on consumer’s emotional state in post purchase context: exploring moderating factors

PurposeEmphasizing the increasing need for social presence in interpersonal interactions and the irreplaceable aspects of face-to-face communications, this study aims to explore the emotional impact of interpersonal influence on consumers after purchase. As individuals respond differently to others’ feedback (positive and negative/verbal and nonverbal), the author investigates potential moderating factors of the impact of feedback on consumer’s emotions in a postpurchase context.Design/methodology/approachA qualitative study was conducted using the method of semistructured individual interviews to collect data. The author selected a heterogeneous group of 30 consumers belonging to two categories: 13 adults (including seven women and six men) and 17 adolescents (including eight girls and nine boys). The author took into account this type of sampling in the selection of respondents, as investigating the influence of the respondent’s gender is one of the research objectives.FindingsThe thematic content analysis method released a set of propositions the author suggests for future validation: five moderating factors the author established from the literature review (strength of social ties, level of expertise, type of the product and consumer’s age and gender), while four factors sprang from the collected data (consumer’s level of conviction, repetition of the feedback, the feedback’s argumentation and its level of discretion).Research limitations/implicationsThe subjectivity of the interviewees’ personal descriptions of their felt internal states affects the accuracy of their responses. In addition, the psychological aspect of the study provoked reluctance and discretion from some respondents. Further research studies could target these limitations to study each identified moderating factor separately and search for the secondary variables that tend to be linked to these factors (e.g. the expertise level is linked to personality variables, such as the perceived level of self-confidence). Furthermore, subsequent studies can go beyond the affective impact of feedback and investigate the behavioral aspect (repurchase intentions).Practical implicationsThis study is of great importance in providing more explanations for the reasons why consumers repurchase or abandon a product. The importance of the emotional power of others’ feedback suggests that, when positioning their offers, marketers must ensure that their product has a strong chance of acceptance by consumer’s significant other. In addition, companies must argue their offers, allowing consumers to increase their knowledge about the product. Moreover, interpersonal cues and expertise level are more important competences to find in employees. Who is more than a vendor, for example, to be perceived as having a high level of expertise in his field?Social implicationsThis study stresses the importance of face-to-face interpersonal interaction in a time when social lives are submerged by social media and virtual communications. The findings suggest that offline social power still matters, and its impact is relative to multiple factors that count for consumers. Face-to-face interaction has been viewed as the most efficient way to satisfy individuals’ social needs for connectedness.Originality/valueThis paper provides new insights into the impact of offline interpersonal verbal and nonverbal feedbacks. The feedback-affect process within consumers was explored, and the postpurchase context was precisely emphasized.

Aptamer-Functionalized Interface Nanopores Enable Amino Acid-Specific Peptide Detection.

Single-molecule proteomics based on nanopore technology has made significant advances in recent years. However, to achieve nanopore sensing with single amino acid resolution, several bottlenecks must be tackled: controlling nanopore sizes with nanoscale precision and slowing molecular translocation events. Herein, we address these challenges by integrating amino acid-specific DNA aptamers into interface nanopores with dynamically tunable pore sizes. A phenylalanine aptamer was used as a proof-of-concept: aptamer recognition of phenylalanine moieties led to the retention of specific peptides, slowing translocation speeds. Importantly, while phenylalanine aptamers were isolated against the free amino acid, the aptamers were determined to recognize the combination of the benzyl or phenyl and the carbonyl group in the peptide backbone, enabling binding to specific phenylalanine-containing peptides. We decoupled specific binding between aptamers and phenylalanine-containing peptides from nonspecific interactions (e.g., electrostatics and hydrophobic interactions) using optical waveguide lightmode spectroscopy. Aptamer-modified interface nanopores differentiated peptides containing phenylalanine vs. control peptides with structurally similar amino acids (i.e., tyrosine and tryptophan). When the duration of aptamer-target interactions inside the nanopore were prolonged by lowering the applied voltage, discrete ionic current levels with repetitive motifs were observed. Such reoccurring signatures in the measured signal suggest that the proposed method has the possibility to resolve amino acid-specific aptamer recognition, a step toward single-molecule proteomics.

Convergence of Adaptive Crouzeix–Raviart and Morley FEM for Distributed Optimal Control Problems

Abstract This article discusses the quasi-optimality of adaptive nonconforming finite element methods for distributed optimal control problems governed by 𝑚-harmonic operators for m = 1 , 2 m=1,2 . A variational discretization approach is employed and the state and adjoint variables are discretized using nonconforming finite elements. Error equivalence results at the continuous and discrete levels lead to a priori and a posteriori error estimates for the optimal control problem. The general axiomatic framework that includes stability, reduction, discrete reliability, and quasi-orthogonality establishes the quasi-optimality. Numerical results demonstrate the theoretically predicted orders of convergence and the efficiency of the adaptive estimator.

When MNEs bribe more? The role of managerial discretion

PurposeThis paper builds upon managerial discretion literature to study the relationship between foreign ownership and bribery intensity.Design/methodology/approachBuilding on World Bank’s data of 9,386 firms from 125 countries over the period 2006–2018, this paper uses Tobit regression, ordered probit and logit models to empirically test the hypotheses.FindingsThis paper finds that firms have higher bribery intensity when executives have a higher level of managerial discretion. Smaller firms with slack financial resources tend to bribe more when they face more government intervention, munificent and uncertain industrial environment.Originality/valueExtant corruption literature has addressed the effects of external institutional settings and internal corporate governance on bribery offering among multinational enterprises (MNEs). How much, and under what condition do top executives matter in bribery activities are yet to be answered. This paper integrates the concept of managerial discretion with corruption and bribery literature and offers a potential answer to the above question. In addition, prior corruption and bribery literature have primarily studied bribery through either micro- or macro-level analysis. This paper adopts multiple-level of analyses and elucidates the foreign ownership and bribery relationship from the organizational and industrial levels.

On the State of Usability for Lithium–Ion Batteries

Lithium–ion batteries are well established as traction batteries for electric vehicles. This has led to a growing market for second-life batteries that can be used in applications like home energy storage systems. Moreover, the recyclability and safe handling of aged or damaged cells and packs has become more important. While there are several indicators, like state of health (SOH), state of power (SOP), or state of safety (SOS), which describe the state of a battery before its defined end of life (EOL), there is no consistent classification methodology by which to describe the usability of a cell or pack after its EOL is reached. The proposed state of usability (SOU) provides a new indicator that accounts for the usability for second life, recyclability, and possible required safety handling of a lithium–ion battery after its first intended life cycle. This work presents a decision tree method, which in turn leads to five discrete usability levels enabling a fast and rough determination of the SOU for practical use. Further, a calculation methodology for reasonable continuous regions of the SOU is proposed. Both methods are based on a literature-based rating of all of the relevant defect and aging mechanisms displayed in a risk matrix. Finally, some experimental methods that can be used for SOU determination are proposed. The developed methodology and the hands-on approach using a decision tree are well-suited for real world application in recycling companies and battery test laboratories.

Circulating current suppression and natural voltage balancing using phase-shifted modulation for modular multilevel converter

The challenge of achieving a balanced capacitor voltage is one of the factors affecting the efficient operation of modular multilevel converters (MMC). This paper investigates this challenge through a proposed method that utilizes a high carrier frequency phase-shifted pulse width modulation (PS-PWM) scheme. This method aims to achieve natural balancing without the need for any additional control mechanisms. Moreover, the number of output voltage levels is affected by the phase shift between the carriers of the upper and lower arms. When there is no phase shift, N<sup>+1</sup> discrete levels are achieved, but when there is a phase shift, the number of discrete levels increases to 2<sup>N+1</sup>. The proportional-resonant (PR) controller and moving average filter (MAF) are employed to decrease the capacitor voltage ripples by suppressing the fourth and second harmonics in the circulating currents. The MMC inverter structure is modeled and simulated in the PLECS and MATLAB/Simulink environments to evaluate the impact of this control scheme on the converter’s performance.

A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limiting

We present a novel semi-implicit hybrid finite volume/finite element (FV/FE) method for the equations of viscous and resistive incompressible magnetohydrodynamics (MHD). The scheme preserves the divergence-free property of the magnetic field exactly on the discrete level, is second order accurate in space, and is stable in the limit of vanishing viscosity and resistivity. In particular, the MHD system is first split into a fluid and a magnetic subsystem. The former is then addressed via a semi-implicit hybrid FV/FE method. The latter belongs to a class of generalized advection-diffusion problems, for which we propose a novel semi-implicit scheme based on compatible finite element spaces and interpolation-contraction operators. In the case of vanishing resistivity, the new algorithm avoids the solution of a linear system at each time step, thanks to the framework of physical degrees of freedom, which allow to express the exterior derivative as the incidence matrix of an appropriate refinement of the original mesh. Regarding the timestepping, a local fully-discrete Lax-Wendroff-type evolution is proposed as an alternative to the classical semi-discrete method of lines. In order to suppress spurious oscillations in the presence of discontinuities or steep gradients in the magnetic field, a new simple but efficient a posteriori limiting procedure based on a nonlinear artificial resistivity is introduced. The novel methodology is validated with several test cases in two and three space dimensions using unstructured simplex meshes.

A step-by-step simulation code for estimating yields of water radiolysis species based on electron track-structure mode in the PHITS code

Objective. Time-dependent yields of chemical products resulting from water radiolysis play a great role in evaluating DNA damage response after exposure to ionizing radiation. Particle and Heavy Ion Transport code System (PHITS) is a general-purpose Monte Carlo simulation code for radiation transport, which simulates atomic interactions originating from discrete energy levels of ionizations and electronic excitations as well as molecular excitations as physical stages. However, no chemical code for simulating water radiolysis products exists in the PHITS package. Approach. Here, we developed a chemical simulation code dedicated to the PHITS code, hereafter called PHITS-Chem code, which enables the calculation of the G values of water radiolysis species (•OH, eaq −, H2, H2O2 etc) by electron beams. Main results. The estimated G values during 1 μs are in agreement with the experimental ones and other simulations. This PHITS-Chem code also simulates the radiolysis in the presence of OH radical scavengers, such as tris(hydroxymethyl)aminomethane and dimethyl sulfoxide. Thank to this feature, the contributions of direct and indirect effects on DNA damage induction under various scavenging capacities can be analyzed. Significance. This chemical code coupled with PHITS could contribute to elucidating the mechanism of radiation effects by connecting physical, physicochemical, and chemical processes.

A Conservative Finite Element Scheme for the Kirchhoff Equation

This article presents an implicit two-layer finite element scheme for solving the Kirchhoff equation, a nonlinear nonlocal equation of hyperbolic type with the Dirichlet integral. The discrete scheme was designed considering the solution of the problem and its derivative for the time variable. It ensures total energy conservation at a discrete level. The use of the Newton method was proven to be effective for solving the scheme on the time layer despite the nonlocality of the equation. The test problems with smooth solutions showed that the scheme can define both the solution of the problem and its time derivative with an error of O(h2+τ2) in the root-mean-square norm, where τ and h are the grid steps in time and space, respectively.

A Quantum Oscillator Model of Stock Markets

Classical oscillators have long been used to model financial time series, but suffer from the drawback that the underlying system does not behave like a mechanical spring: there are no regular oscillations, and price is not a well-defined mechanical quantity but always has a degree of uncertainty. In recent years a number of authors have attempted to address these problems by basing their models on quantum harmonic oscillators, which always have a non-zero volatility, however the role of other features that are characteristic of quantum systems, such as discrete energy levels, has not been clear. This paper develops a quantum model in which the energy level corresponds to an integer number of transactions. The model is derived by quantizing entropic forces which represent the intentions of buyers and sellers to transact as a function of price. It is shown that the model captures the non-Gaussian nature of financial statistics, and correctly predicts empirical phenomena including the square-root law of price impact, along with its associated variance.

STICAP : Spatio-temporal Interactive Attention for Citywide Crowd Activity Prediction

Accurate citywide crowd activity prediction (CAP) can enable proactive crowd mobility management and timely responses to urban events, which has become increasingly important for a myriad of smart city planning and management purposes. However, complex correlations across the crowd activities, spatial and temporal urban environment features and their interactive dependencies, and relevant external factors (e.g., weather conditions) make it highly challenging to predict crowd activities accurately in terms of different venue categories (for instance, venues related to dining, services, and residence) and varying degrees (e.g., daytime and nighttime). To address the above concerns, we propose STICAP , a citywide spatio-temporal interactive crowd activity prediction approach. In particular, STICAP takes in the location-based social network check-in data (e.g., from Foursquare/Gowalla) as the model inputs and forecasts the crowd activity within each time step for each venue category. Furthermore, we have integrated multiple levels of temporal discretization to interactively capture the relations with historical data. Then, three parallel Residual Spatial Attention Networks ( RSAN ) in the Spatial Attention Component exploit the hourly, daily, and weekly spatial features of crowd activities, which are further fused and processed by the Temporal Attention Component for interactive CAP . Along with other external factors such as weather conditions and holidays, STICAP adaptively and accurately forecasts the final crowd activities per venue category, enabling potential activity recommendation and other smart city applications. Extensive experimental studies based on three different real-world crowd activity datasets have demonstrated that our proposed STICAP outperforms the baseline and state-of-the-art algorithms in CAP accuracy, with an average error reduction of 35.02%.

Evaluation of OFDM system in terms of PAPR and BER using PAPR Reduction Techniques : Windowing and Clipping

The issue of transferring signals in a non-intrusive and efficient manner is highly intriguing. Consequently, the utilisation of the Orthogonal Frequency Division Multiplexing (OFDM) transmission technology is employed due to its enhanced resilience against multipath fading and its ability to achieve better efficiency compared to alternative wireless communication methods. Although the PAPR issue offers certain benefits, it poses undesirable consequences for OFDM, leading to a significant decrease in data transmission rate. Consequently, the mitigation of peak-to-average power ratio (PAPR) issues leads to an improvement in the quality of service. The reduction of PAPR can be achieved by the implementation of clipping and windowing techniques. These approaches arrange the signal into discrete levels of similar magnitude and apply clipping to minimise the bit error rate (BER), resulting in a drop in PAPR. The proposed approach is implemented using the MATLAB software.

Error analysis of the linearized Crank-Nicolson FEM for the incompressible vector potential magnetohydrodynamic system

A linearized fully discrete Crank-Nicolson finite element scheme is proposed for solving the three-dimensional incompressible magnetohydrodynamic equations based on a magnetic vector potential formulation, where the magnetic induction is written to a rotation of magnetic vector potential. By using the MINI element and lowest order Nédélec edge element to approximate the velocity field and pressure of fluid and magnetic vector potential, respectively, the numerical solution of magnetic induction can preserve the exactly divergence-free condition in fully discrete level. Error estimates for the velocity field and magnetic vector potential are rigorously analyzed under some reasonable regularity assumptions of exact solution. Finally, numerical results are given to support the theoretical analysis.

Nonlinear energy harvesting based alternate cooperative nonorthogonal multiple access with adaptive interference cancellation

We consider an energy-limited network, where a source node intends to communicate with two energy harvesting (EH) near-users and one far-user. We design a nonlinear EH-based alternate cooperative nonorthogonal multiple access (CNOMA) scheme, where the source node alternately superimposes the data of each near-user and the far-user and broadcasts the composite signal. When one near-user decodes the data of both the far-user and itself by using the adaptive interference cancellation technique, the other near-user can harvest energy from the received signal. The two near-users alternately and adaptively forward data to the far-user. We properly model the energy statuses of both the two near-users by defining a group of unequally-spaced discrete energy levels. We analyze the average success probability and throughput of each user, and use the differential evolution (DE) algorithm to efficiently achieve the maximum system throughput by jointly optimizing both the time and power allocation factors. We also present two benchmark EH-based transmission schemes for comparison. Extensive simulations are conducted to validate our theoretical analysis and reveal the impacts of various parameters.

An unconditionally energy stable linear scheme for Poisson–Nernst–Planck equations

This paper proposes a linear, unconditionally energy-stable scheme for the Poisson–Nernst–Planck (PNP) equations. Based on a gradient-flow formulation of the PNP equations, the energy factorization approach is applied to linearize the logarithm function at the previous time step, resulting in a linear semi-implicit scheme. Numerical analysis is conducted to illustrate that the proposed fully discrete scheme has desired properties at a discrete level, such as unconditional unique solvability, mass conservation, and energy dissipation. Numerical simulations verify that the proposed scheme, as expected, is first-order accurate in time and second-order accurate in space. Further numerical tests confirm that the proposed scheme can indeed preserve the desired properties. Applications of our numerical scheme to the simulations of electrolyte solutions demonstrate that, as a linear energy stable scheme of efficiency, it will be promising in simulating complicated transport phenomena of charged systems.

Numerical schemes for mixture theory models with filling constraint: application to biofilm ecosystems

The mixture theory framework is a powerful way to describe multi-phasic systems at an intermediary scale between microscopic and macroscopic scales. In particular, mixture theory reveals a powerful approach to represent microbial biofilms where a consortium of cells is embedded in a polymeric structure. To simulate a model of microalgal biofilm, we propose an upgraded numerical scheme, consolidating the one proposed by Berthelin et al. (2016) to enforce the volume-filling constraint in mixture models including mass exchanges. The strategy consists in deducing the discrete version of the incompressibility constraint from the discretized mass balance equations. Numerical simulations show that this method constrains the total volume filling constraint, even at the discrete level. Moreover, we add viscous terms in the biofilm model to properly represent biofilms interactions with its fluidic environment. It turns out that a well-balanced numerical scheme becomes of outmost importance to capture the biofilm dynamic when including the viscosity. This modelling upgrade also involves recalibrating model parameters. In particular, the elastic tensors to recover realistic front features. With the new parameters, the numerical set-up becomes more demanding to reach convergence.

Extension of an all-Mach Roe scheme able to deal with low Mach acoustics to full Euler system

We propose to extend the fix of Roe’s approximate Riemann solver developed for the Barotropic Euler equations in [2] to the full Euler equations. This scheme is built mainly to handle low Mach acousticwaves. Moreover, compared to pressure-centered type schemes, this numerical fix has the advantage of improving the numerical solution in the sense that the oscillating modes are reduced. The theoretical study is based on a two-time scales asymptotic analysis. It is proved that the Euler system equipped with a general equation of state is consistent with a first-order wave system in a low Mach number regime. Similar analysis is performed at the discrete level on the Roe scheme to derive the new fix. Numerical tests confirm the results obtained for the Barotropic case about the ability of this fix to deal with both steady and low Mach acoustic computations also in the case of full Euler equations.

Two arbitrary-order constraint-preserving schemes for the Yang–Mills equations on polyhedral meshes

<abstract><p>Two numerical schemes are proposed and investigated for the Yang–Mills equations, which can be seen as a nonlinear generalisation of the Maxwell equations set on Lie algebra-valued functions, with similarities to certain formulations of General Relativity. Both schemes are built on the Discrete de Rham (DDR) method, and inherit from its main features: an arbitrary order of accuracy, and applicability to generic polyhedral meshes. They make use of the complex property of the DDR, together with a Lagrange-multiplier approach, to preserve, at the discrete level, a nonlinear constraint associated with the Yang–Mills equations. We also show that the schemes satisfy a discrete energy dissipation (the dissipation coming solely from the implicit time stepping). Issues around the practical implementations of the schemes are discussed; in particular, the assembly of the local contributions in a way that minimises the price we pay in dealing with nonlinear terms, in conjunction with the tensorisation coming from the Lie algebra. Numerical tests are provided using a manufactured solution, and show that both schemes display a convergence in $ L^2 $-norm of the potential and electrical fields in $ \mathcal O(h^{k+1}) $ (provided that the time step is of that order), where $ k $ is the polynomial degree chosen for the DDR complex. We also numerically demonstrate the preservation of the constraint.</p></abstract>