Discrete Effects Research Articles

A strategy for scaling the hardening behavior in finite element modelling of geometrically exact beams

AbstractA yield function in the stress resultant space of geometrically exact beams based on the elastoplastic cross-sectional warping problem has been proposed by Herrnböck et al. (Comput Mech, 67(3):723–742, 2021). This plasticity framework has been extended with a hardening tensor to model the kinematic hardening effects in Herrnböck et al. (Comput Mech, 71(1):1–24, 2022). While this framework provides scaling for the yield surface in ideal plasticity, scaling in hardening plasticity has not yet been explored. This paper focuses on the numeric modelling of hardening beams and beam assemblies at different geometric scales. Discretization effects from the introduction of plasticity into the geometrically exact beam model are demonstrated. Furthermore, the effects of scaling are explored, and a method to mitigate undesirable effects in order to achieve a size-agnostic formulation is proposed. Consistent geometric scaling is demonstrated for two alternative scaling approaches of the yield function.

A Meshless Radial Point Interpolation Method for Solving Fractional Navier–Stokes Equations

This paper aims to develop a meshless radial point interpolation (RPI) method for obtaining the numerical solution of fractional Navier–Stokes equations. The proposed RPI method discretizes differential equations into highly nonlinear algebraic equations, which are subsequently solved using a fixed-point method. Furthermore, a comprehensive analysis regarding the effects of spatial and temporal discretization, polynomial order, and fractional order is conducted. These factors’ impacts on the accuracy and efficiency of the solutions are discussed in detail. It can be shown that the meshless RPI method works quite well for solving some benchmark problems accurately.

It's about (taking up) space: Discreteness of individuals and the strength of spatial coexistence mechanisms.

One strand of modern coexistence theory (MCT) partitions invader growth rates (IGR) to quantify how different mechanisms contribute to species coexistence, highlighting fluctuation-dependent mechanisms. A general conclusion from the classical analytic MCT theory is that coexistence mechanisms relying on temporal variation (such as the temporal storage effect) are generally less effective at promoting coexistence than mechanisms relying on spatial or spatiotemporal variation (primarily growth-density covariance). However, the analytic theory assumes continuous population density, and IGRs are calculated for infinitesimally rare invaders that have infinite time to find their preferred habitat and regrow, without ever experiencing intraspecific competition. Here we ask if the disparity between spatial and temporal mechanisms persists when individuals are, instead, discrete and occupy finite amounts of space. We present a simulation-based approach to quantifying IGRs in this situation, building on our previous approach for spatially non-varying habitats. As expected, we found that spatial mechanisms are weakened; unexpectedly, the contribution to IGR from growth-density covariance could even become negative, opposing coexistence. We also found shifts in which demographic parameters had the largest effect on the strength of spatial coexistence mechanisms. Our substantive conclusions are statements about one model, across parameter ranges that we subjectively considered realistic. Using the methods developed here, effects of individual discreteness should be explored theoretically across a broader range of conditions, and in models parameterized from empirical data on real communities.

Effect of discretization on off-axis listeners in binaural synthesis based on the optimal source distribution

3D sound reproduction based on binaural synthesis over loudspeakers is one of the most important techniques in immersive spatial audio. The system inversion involved in the binaural synthesis gives rise to several problems such as dynamic range loss, distortion of the reproduction transfer function, and a lack of robustness to room reflections. The principle of Optimal Source Distribution was proposed to overcome these problems. This utilizes a pair of conceptual monopole transducers whose azimuthal location varies continuously as a function of frequency. Another potential of the principle is that it can provide listening positions for multiple off-axis listeners, in addition to the on-axis listener whose inverse matrix is given, since the phase interference state is aligned at all frequencies. However, these continuously varying transducers are too conceptual to realize in practice. It is necessary to provide discretized sound sources with appropriate frequency ranges according to the principle. In this paper, the effect of discretization of the principle on off-axis listeners' performance is numerically investigated to reveal how those off-axis sweet spots are formed as the discretization becomes finer. An experiment is also carried out using an actual discretized system and the effect of the head-related transfer functions is considered.

Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network

Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser lattices, thereby allowing one to circumvent problems with critical slowing down and topological freezing toward the continuum limit. A crucial ingredient for practical applications is to find an accurate and compact parametrization of a fixed point action, since many of its properties are only implicitly defined. Here we use machine learning methods to revisit the question of how to parametrize fixed point actions. In particular, we obtain a fixed point action for four-dimensional SU(3) gauge theory using convolutional neural networks with exact gauge invariance. The large operator space allows us to find superior parametrizations compared to previous studies, a necessary first step for future Monte Carlo simulations and scaling studies. Published by the American Physical Society 2024

Spectrum of global string networks and the axion dark matter mass

Cold dark matter axions produced in the post-inflationary Peccei-Quinn symmetry breaking scenario serve as clear targets for their experimental detection, since it is in principle possible to give a sharp prediction for their mass once we understand precisely how they are produced from the decay of global cosmic strings in the early Universe. In this paper, we perform a dedicated analysis of the spectrum of axions radiated from strings based on large scale numerical simulations of the cosmological evolution of the Peccei-Quinn field on a static lattice. Making full use of the massively parallel code and computing resources, we executed the simulations with up to 112643 lattice sites, which allows us to improve our understanding of the dependence on the parameter controlling the string tension and thus give a more accurate extrapolation of the numerical results. We found that there are several systematic effects that have been overlooked in previous works, such as the dependence on the initial conditions, contaminations due to oscillations in the spectrum, and discretisation effects, some of which could explain the discrepancy in the literature. We confirmed the trend that the spectral index of the axion emission spectrum increases with the string tension, but did not find a clear evidence of whether it continues to increase or saturates to a constant at larger values of the string tension due to the severe discretisation effects. Taking this uncertainty into account and performing the extrapolation with a simple power law assumption on the spectrum, we find that the dark matter mass is predicted in the range of m a ≈ 95–450 μeV.

Discrete time stability of augmented Lagrangian formalism based underactuated inverse dynamics control method

Stability problems of robotic systems arise sometimes suddenly, seemingly for no reason. The digital time sampling is often the main cause of these instabilities. Discrete models, which are capable of the prediction of stability, are available for low-degree-of-freedom template models of linear position and force control. However, for the inverse dynamics control of underactuated systems, the literature has a lack of generally applicable results related to the effect of time discretization. Several control approaches are available in the literature out of which a widely used one, the augmented Lagrangian formalism and its stability properties are analysed in this work. Theoretical stability properties are obtained for a generally usable, linear, underactuated, two-degree-of-freedom constrained template model. The actuator dynamics, the finite difference approximation of the feedback velocity and the filtering of the feedback data are considered in the model. These phenomena strongly affects the stability properties. The theoretically obtained stability maps are experimentally validated on an underactuated crane-like indoor robot. The position and orientation accuracy of the robot were assessed: the absolute position error was below 30 mm and the orientation error was below 3°.

Absorbing discretization effects with a massive renormalization scheme: The charm-quark mass

We present the first numerical implementation of the massive symmetric-momentum-subtraction (mSMOM) renormalization scheme and use it to calculate the charm-quark mass. Based on ensembles with three flavors of dynamical domain-wall fermions with lattice spacings in the range 0.11–0.08 fm, we demonstrate that the mass scale which defines the mSMOM scheme can be chosen such that the extrapolation has significantly smaller discretization effects than the SMOM scheme. Converting our results to the MS¯ scheme we obtain m¯c(3 GeV)=1.008(13) GeV and m¯c(m¯c)=1.292(12) GeV. Published by the American Physical Society 2024

Global spectrum model of discrete dislocation equation

The fully discrete dislocation equation can be rationally derived from the spectrum model. In this paper, the previous spectrum model is reinterpreted to cover the global feature of the spectrum. Instead of the local behavior around the origin of the Brilouin zone, the global spectrum model focuses the maximum at the boundary of the Brillouin as well as the slope at the origin of the Brilouin zone. The strength of the point-contact interaction that effectively describes the discreteness effect becomes larger because the whole lattice effect is included in the global spectrum model. The validness and signification of the new model are illustrated by a solvable lattice dynamical model of the cubic lattice.

Evaluating the effects of nonlocality and numerical discretization in peridynamic solutions for quasi-static elasticity and fracture

The difference between the computational peridynamic results and the corresponding exact classical solutions is contributed by the error induced by numerical discretization and the nonlocality-induced difference. To evaluate and compare these contributions and investigate their dependence on the peridynamic influence functions, in this paper, we apply different peridynamic influence functions and different horizon factors (m, the ratio between the horizon size and the grid spacing) to conduct static (or quasi-static) tensile numerical tests. We calculate the difference between the peridynamic solutions and the corresponding classical solutions for static uniaxial tension of thin plates with or without hole, the J-integral of a single crack under Mode I loading condition, and the quasi-static fracture in a perforated thin plate. For the case of uniaxial tension in a thin, homogeneous plate, we separate the effects of nonlocality and numerical discretization by implementing the boundary conditions in different ways. The numerical results show that both the effects of nonlocality and numerical discretization correspond to the nonlocal constants of the influence functions (with few exceptions). For problems with the presence of the peridynamic surface effect, such as holes, influence function with weaker nonlocality is a better choice to obtain more accurate results.

Charge regulation of nanoparticles in the presence of multivalent electrolytes.

We explore the charge regulation (CR) of spherical nanoparticles immersed in an asymmetric electrolyte of a specified pH. Using a recently developed reactive canonical Monte Carlo (MC) simulation method, titration isotherms are obtained for suspensions containing monovalent, divalent, and trivalent coions. A theory based on the modified Poisson-Boltzmann approximation, which incorporates the electrostatic ion solvation free energy and discrete surface charge effects, is used to compare with the simulation results. A remarkably good agreement is found without any fitting parameters, both for the ion distributions and titration curves, suggesting that ionic correlations between coions and hydronium ions at the nanoparticle surface play only a minor role in determining the association equilibrium between hydroniums and the functional sites on the nanoparticle surface. On the other hand, if suspension contains multivalent counterions, we observe a large deviation between theory and simulations, showing that the electrostatic correlations between counterions and hydronium ions at the nanoparticle surface are very significant and must be properly taken into account to correctly describe CR for such solutions.

A Variational Model of Charged Drops in Dielectrically Matched Binary Fluids: The Effect of Charge Discreteness

This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. Introducing the model that describes two immiscible fluids with the same dielectric constant, with a drop of one fluid containing a fixed number of elementary charges together with their solvation spheres, we interpret the equilibrium shape of the drop as a global minimizer of the sum of its surface energy and the electrostatic repulsive energy between the charges under fixed drop volume. For all model parameters, we establish the existence of generalized minimizers that consist of at most a finite number of components “at infinity”. We also give several existence and non-existence results for classical minimizers consisting of only a single component. In particular, we identify an asymptotically sharp threshold for the number of charges to yield existence of minimizers in a regime corresponding to macroscopically large drops containing a large number of charges. The obtained non-trivial threshold is significantly below the corresponding threshold for the Rayleigh model, consistently with the ill-posedness of the latter and demonstrating a particular regularizing effect of the charge discreteness. However, when a minimizer does exist in this regime, it approaches a ball with the charge uniformly distributed on the surface as the number of charges goes to infinity, just as in the Rayleigh model. Finally, we provide an explicit solution for the problem with two charges and a macroscopically large drop.

A novel 4-DOF marine stern bearing support model considering discrete distribution effects

To address the issue of the traditional support model's inability to accurately describe the non-uniform dynamics behavior inside the bearing, this study proposes a novel 4-degree-of-freedom (DOF) bearing support model that incorporates the discrete distribution effects induced by the bi-directional misalignment and bending deformation of the journal. Additionally, a coupling algorithm is designed to study the interaction behaviors between the marine stern bearing lubrication performance and the shaft dynamics. Moreover, a full-size marine shaft alignment test rig for measuring dynamic bearing loads is designed to verify the validity of the present model. On this basis, the effects of different bearing models, rotational speeds, external loads, and bush elastic modulus on the shaft dynamic alignment and the static and dynamic characteristics of the stern bearing are investigated. The experimental results indicate that the 4-DOF model, which takes into account discrete distribution, exhibits a more precise prediction of the alignment characteristics of the shaft system, with a forecast error for the stern bearing load of 1.32%. Heavy loads or low rotational speeds significantly deteriorate the edge-loading effect and increase the stiffness and damping coefficient of the bearings. The bearing lubrication performance directly affects the alignment performance of the shaft system, particularly in low-speed conditions. A softer bush material can increase the minimum oil film thickness, carrying region, and damping coefficient, mitigate the phenomenon of edge-loading, and facilitate the vibration control of the shaft. Research results have made a great contribution to marine shaft alignment optimization and structure design.

Therapeutic Targets in Innate Immunity to Tackle Alzheimer's Disease.

There is an urgent need for effective disease-modifying therapeutic interventions for Alzheimer's disease (AD)-the most prevalent cause of dementia with a profound socioeconomic burden. Most clinical trials targeting the classical hallmarks of this disease-β-amyloid plaques and neurofibrillary tangles-failed, showed discrete clinical effects, or were accompanied by concerning side effects. There has been an ongoing search for novel therapeutic targets. Neuroinflammation, now widely recognized as a hallmark of all neurodegenerative diseases, has been proven to be a major contributor to AD pathology. Here, we summarize the role of neuroinflammation in the pathogenesis and progression of AD and discuss potential targets such as microglia, TREM2, the complement system, inflammasomes, and cytosolic DNA sensors. We also present an overview of ongoing studies targeting specific innate immune system components, highlighting the progress in this field of drug research while bringing attention to the delicate nature of innate immune modulations in AD.

Effects of sentiment discreteness on MOOCs’ disconfirmation: text analytics in online reviews

ABSTRACT In Massive Open Online Courses (MOOCs), online reviews serve as a basis for teachers to improve their courses. The disconfirmation effect of online reviews, i.e. the inconsistency between the level of attention paid to a course factor and the actual weight of that factor’s influence on learner satisfaction, leads to erroneous judgments by teachers. Based on the two-factor theory of emotion, 4,070 courses and 165,705 online reviews are adopted as a corpus to identify the effect of learner sentiment on the disconfirmation effect. The empirical results show that there is a significant disconfirmation effect for negative reviews, but not for positive ones. A fine-grained analysis on negative sentiment finds that reviews containing more sadness and anger sentiments have a stronger disconfirmation effect. A comparison of course types reveals that the disconfirmation effect is stronger for instrument-based courses than that for knowledge-based and practice-based ones. In addition, negative word-of-mouth weakens the disconfirmation effect of sadness and anger reviews and enhances the disconfirmation effect of positive reviews. Further, learner’s reputation weakens the disconfirmation effect of sadness reviews and enhances the disconfirmation effect of positive and anger reviews.

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit (mu=md) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with Nf=2+1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass mπ∼139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a=0.11–0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS¯ scheme at 3 GeV are BK≡B1=0.5240(17)(54), B2=0.4794(25)(35), B3=0.746(13)(17), B4=0.897(02)(10) and B5=0.6882(78)(94), where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS¯. Published by the American Physical Society 2024

Recursive and batch Bayesian estimation of exponential non-viscous damping systems

Non-viscous damping systems include a convolutional integral and a kernel function in their equation of motion to incorporate time-hysteresis damping effects, which are present in dynamical behavior of most engineering materials yet are absent in commonly used viscous damping models. When an exponential kernel function is adopted by the non-viscous model, the unique damping characteristic is realized by an additional model parameter known as the relaxation parameter. The objective of this paper is to investigate various aspects of estimation problems on exponential non-viscous damping systems through recursive and batch Bayesian time-domain frameworks, with a focus on how the relaxation parameter introduces additional complexity in estimation problems compared to viscous damping systems. Two well-established algorithms are employed: the unscented Kalman filter (UKF) for recursive Bayesian estimation and the transitional Markov Chain Monte Carlo (TMCMC) for batch Bayesian estimation. We first analyze the complexity of estimation problems in SDOF viscous and non-viscous damping systems. The TMCMC algorithm offers a quantitative analysis that reveals greater uncertainty and stronger parameter correlation in non-viscous damping systems compared to viscous damping systems. Subsequently, the same SDOF systems are utilized to study recursive Bayesian estimation via UKF such as the effects of measurement data type, discretization, and initial conditions. Based on the results of the TMCMC algorithm, we study the dependence of UKF performance on the initial condition for various SDOF non-viscous damping systems with different levels of non-viscosity. In the end, a laboratory experiment compares the estimation results between viscous and non-viscous damping systems using both TMCMC and UKF.

Variations in the Antivirulence Effects of Fatty Acids and Virstatin against Vibrio cholerae Strains.

The expression of two major virulence factors of Vibrio cholerae, cholera toxin (CT) and toxin coregulated pilus (TCP), is induced by environmental stimuli through a cascade of interactions among regulatory proteins known as the ToxR regulon when the bacteria reach the human small intestine. ToxT is produced via the ToxR regulon and acts as the direct transcriptional activator of CT (ctxAB), TCP (tcp gene cluster), and other virulence genes. Unsaturated fatty acids (UFAs) and several smallmolecule inhibitors of ToxT have been developed as antivirulence agents against V. cholerae. This study reports the inhibitory effects of fatty acids and virstatin (a small-molecule inhibitor of ToxT) on the transcriptional activation functions of ToxT in isogenic derivatives of V. cholerae strains containing various toxT alleles. The fatty acids and virstatin had discrete effects depending on the ToxT allele (different by 2 amino acids), V. cholerae strain, and culture conditions, indicating that V. cholerae strains could overcome the effects of UFAs and small-molecule inhibitors by acquiring point mutations in toxT. Our results suggest that small-molecule inhibitors should be examined thoroughly against various V. cholerae strains and toxT alleles during development.

Discrete orbit effect lengthens merger times for inspiraling binary black holes

The inspiral merger time for two black holes captured into a nonrelativistic bound orbit by gravitational radiation emission has been often calculated by a formula of Peters that assumes the adiabatic approximation that the changes per orbit are small. However, initially this is not true for the semimajor axis and period of most of the initially highly eccentric orbits, which change significantly during closest approach and much less elsewhere along the orbit. This effect can make the merger time much longer (using other formulas from Peters that do not assume the adiabatic approximation) than that calculated by the adiabatic formula of Peters.

Effect of Corrosion Inhibitors on Bond Strength of Reinforced Concrete Structures

Corrosion of steel reinforcement is a major factor affecting the durability and strength of reinforced concrete structures. This study investigated the influence of plant-derived corrosion inhibitors, applied as coatings, on the bond strength between reinforcing steel and concrete. Thirty-six 150 mm concrete cubes with 12 mm diameter embedded steel bars were prepared and divided into uncoated, corrosion inhibitor coated, and control groups. The samples were immersed in 5% sodium chloride solution over 360 days to accelerate corrosion. Pull-out testing measured the bond strength and failure load. The corroded samples showed 31-26% lower bond strength and 82-87% higher maximum slip than controls, indicating corrosion damage at the steel-concrete interface. However, inhibitor-coated samples displayed 24-36% higher bond strength and 42-43% lower maximum slip versus corroded samples. Although the coatings did not fully restore original bond strength, this demonstrates their effectiveness at protecting bond properties. Microscopic analysis revealed non-uniform, localized corrosion preferentially initiated at steel defects. Statistical correlations confirmed the direct relationship between steel weight loss and reductions in post-corrosion rebar weight due to material loss. While nominal rebar diameters showed minimal differences between sample types, localized diameter reductions and cross-sectional area increases in corroded samples highlighted discrete corrosion effects. These were mitigated in coated samples. Together with direct weight loss measurements, this proves corrosion occurred in unprotected samples. Overall, the significant recovery of bond strength, slip resistance, diameter, area, and weight in coated samples validates the success of the natural corrosion inhibitors in reducing steel deterioration and interface degradation. The results provide new insights on optimizing inhibitor coatings to maximize corrosion protection for reinforced concrete structures.