Symmetric Splitting Research Articles

An 8-MS/s 16-bit SAR ADC With Symmetric Complementary Switching and Split Passive Reference Segmentation in 180-nm Process

An 8-MS/s 16-bit SAR ADC With Symmetric Complementary Switching and Split Passive Reference Segmentation in 180-nm Process

High-throughput generation of monodisperse double emulsions via controllable symmetric splitting in Y-shaped microchannels

To achieve high-throughput generation of monodisperse double emulsions via controllable symmetric splitting, the splitting dynamics of double emulsions in Y-shaped microchannels are systematically investigated by the combination of experimental study and numerical simulation. Four distinct breakup flow patterns of double emulsions splitting are initially identified, namely non-breakup, once uneven breakup, twice uneven breakup and twice even breakup, and the underlying hydrodynamic mechanisms of each flow pattern are further elucidated through the flow field structures and pressure distributions. The results show that the upstream pressure created by the flow obstruction of continuous phase governs the stable and symmetric splitting of double emulsions in Y-shaped microchannels. Effects of the flowrates of continuous phase, the outer and inner diameters of double emulsions, the physical properties of all the inner, middle and outer fluids as well as the angle of Y-shaped microchannel on the flow pattern transition laws are systematically clarified, and the corresponding universal flow pattern diagrams for predicting the critical boundary for the transition of flow patterns are established. Based on controllable symmetric splitting of double emulsions, three-level splitting microfluidic networks are rationally designed to achieve high-throughput generation of monodisperse double emulsions as well as monodisperse microcapsules via template synthesis. The results in this study not only advance the deep understanding of the breakup dynamics of double emulsions in Y-shaped microchannels, but also offer valuable guidance for the rational design of microfluidic devices for mass production of monodisperse double emulsions, thus providing a significant contribution to the fields of micro-chemical engineering and droplet microfluidics.

PLOT AND STRUCTURE IN A CRITICAL EXAMINATION OF "KING LEAR" BY WILLIAM SHAKESPEARE

Known for its complicated character interactions and complex narrative, William Shakespeare's tragedy King Lear is the subject of this paper's critical analysis of the play's structure and plot. The analysis centers on the ways in which Shakespeare enhances the play's thematic resonance through the utilization of structural components, subplots, and parallel narratives. Shakespeare explores themes of power, insanity, familial devotion, and human suffering by intertwining King Lear and Gloucester's narratives. The symmetrical split of the play into acts and scenes reflects the fall into anarchy that occurs when Lear's power crumbles. The structural elements are also considered in this analysis, as they add to the dramatic tension by emphasizing the inevitable disaster through the pace of events. Dramatic irony and foreshadowing are also examined in the article; these devices are fundamental to the structural intricacy of the play and help the audience become more invested in the tragedy as it unfolds. Based on what we know now, King Lear's structural aspects are more than just plot devices; they are fundamental to the play's thematic development and provide light on the human condition via Shakespeare's expert use of the plot.

PhoenixMR: A GPU-based MRI simulation framework with runtime-dynamic code execution.

Simulations of physical processes and behavior can provide unique insights and understanding of real-world problems. Magnetic Resonance Imaging (MRI) is an imaging technique with several components of complexity. Several of these components have been characterized and simulated in the past. However, several computational challenges prevent simulations from being simultaneously fast, flexible, and accurate. The simulation of MRI experiments is underutilized by medical physicists and researchers using currently available simulators due to reasons including speed, accuracy, and extensibility constraints. This paper introduces an innovative MRI simulation engine and framework that aims to overcome these issues making available realistic and fast MRIsimulation. Using the CUDA C/C++ programing language, an MRI simulation engine (PhoenixMR), incorporating a Turing-complete virtual machine (VM) to simulate abstract spatiotemporal complexities, was developed. This engine solves a set of time-discrete Bloch equationsusing the symmetric operator splitting technique. An extensible front-end framework package (written in Python) aids the use of PhoenixMR to simplify simulationdevelopment. The PhoenixMR library and front-end codes have been developed and tested. A set of example simulations were performed to demonstrate the ease of use and flexibility of simulation components such as geometrical setup, pulse sequence design, phantom design, and so forth. Initial validation of PhoenixMR is performed by comparing its accuracy and performance against a widely used MRI simulator using identical simulation parameters. Validation results show PhoenixMR simulations are three orders of magnitude faster. There is also strong agreement betweenmodels. A novel MRI simulation platform called PhoenixMR has been introduced. This research tool is designed to be usable by physicists and engineers interested in performing MRI simulations. Examples are shown demonstrating the accuracy, flexibility, and usability of PhoenixMR in several key areas of MRIsimulation.

Splitting behavior and breakup mechanism of bubbles in the split‐and‐recombine microchannel

AbstractSplit‐and‐recombine (SAR) microreactor is an advanced reactor for chemical process intensification. Bubble flow in the SAR microchannel is an important phenomenon that affects reaction efficiency, however drew little attention before. This study aims to explore the underlying mechanisms of bubble splitting, retraction, and breakup behaviors in a compact SAR microchannel. Two breakup flow patterns, unilateral flow and unilateral alternate flow were identified with symmetric or asymmetric splitting, respectively. Mechanism analysis indicates that the splitting symmetry issue is related to liquid slug size, viscous effect and novel retraction behavior of a splitting filament. The retraction is induced by the interconnection and unequal pressures between the splitting filaments. The correlation between normalized breakup time and Ca number confirms the Capillary‐pressure breakup mechanism for the splitting gas filaments. Two empirical correlations for the two breakup flow patterns were proposed, which illustrate the significant contribution of bubble retraction to the breakup degree.

Effect of external fields and currents on electronic nematic ordering with quadrupole moments

We theoretically investigate the effect of external fields and currents on electronic nematic orderings based on the concept of augmented multipoles consisting of electric, magnetic, magnetic toroidal, and electric toroidal multipoles. We show the relation between rank-2 electric quadrupoles and the other multipoles, the former of which corresponds to the microscopic order parameter for the nematic phases. The electric (magnetic) field induces the rank-1 and rank-3 electric (magnetic) multipoles and rank-2 electric toroidal (magnetic toroidal) quadrupoles, while the electric current induces the rank-1 and rank-3 magnetic toroidal multipoles and rank-2 magnetic quadrupoles. We classify the active multipoles under magnetic point groups, which will be a reference to explore cross-correlation and transport phenomena in nematic phases. As a demonstration, we show that unconventional symmetric and antisymmetric spin splittings are brought about by field-induced toroidal multipoles.

Robust dual-angle measurement in magnetization transfer spectroscopy by time-optimal control.

Magnetization transfer spectroscopy relies heavily on the robust determination of relaxation times of nuclei participating in metabolic exchange. Challenges arise due to the use of surface RF coils for transmission (high variation) and the broad resonance band of most X nuclei. These challenges are particularly pronounced when fast mapping methods, such as the dual-angle method, are employed. Consequently, in this work, we develop resonance offset and robust excitation RF pulses for 31P magnetization transfer spectroscopy at 7T through ensemble-based time-optimal control. In our approach, we introduce a cost functional for designing robust pulses, incorporating the full Bloch equations as constraints, which are solved using symmetric operator splitting techniques. The optimal control design of the RF pulses developed demonstrates improved accuracy, desired phase properties, and reduced RF power when applied to dual-angle mapping, thereby improving the precision of exchange-rate measurements, as demonstrated in a preclinical in vivo study quantifying brain creatine kinase activity.

Fast nonlinear Fourier transform algorithms for optical data processing.

The nonlinear Fourier transform (NFT) is an approach that is similar to a conventional Fourier transform. In particular, NFT allows to analyze the structure of a signal governed by the nonlinear Schrödinger equation (NLSE). Recently, NFT applied to NLSE has attracted special attention in applications of fiber-optic communication. Improving the speed and accuracy of the NFT algorithms remains an urgent problem in optics. We present an approach that allows to find all variants of symmetric exponential splitting schemes suitable for the fast NFT (FNFT) algorithms with low complexity. One of the obtained schemes showed good numerical results in computing the continuous spectrum compared with other fast fourth-order NFT schemes.

A social inference model of idealization and devaluation.

People often form polarized beliefs, imbuing objects (e.g., themselves or others) with unambiguously positive or negative qualities. In clinical settings, this is referred to as dichotomous thinking or "splitting" and is a feature of several psychiatric disorders. Here, we introduce a Bayesian model of splitting that parameterizes a tendency to rigidly categorize objects as either entirely "Bad" or "Good," rather than to flexibly learn dispositions along a continuous scale. Distinct from the previous descriptive theories, the model makes quantitative predictions about how dichotomous beliefs emerge and are updated in light of new information. Specifically, the model addresses how splitting is context-dependent, yet exhibits stability across time. A key model feature is that phases of devaluation and/or idealization are consolidated by rationally attributing counter-evidence to external factors. For example, when another person is idealized, their less-than-perfect behavior is attributed to unfavorable external circumstances. However, sufficient counter-evidence can trigger switches of polarity, producing bistable dynamics. We show that the model can be fitted to empirical data, to measure individual susceptibility to relational instability. For example, we find that a latent categorical belief that others are "Good" accounts for less changeable, and more certain, character impressions of benevolent as opposed to malevolent others among healthy participants. By comparison, character impressions made by participants with borderline personality disorder reveal significantly higher and more symmetric splitting. The generative framework proposed invites applications for modeling oscillatory relational and affective dynamics in psychotherapeutic contexts. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Abrupt focus and bright spot formation in fractional system with PT-symmetric nonlocal nonlinearity

Abstract We study the dynamics of Gaussian beams in fractional system with PT-symmetric nonlocal nonlinearity. It is found that the Gaussian beam with transverse displacement can abruptly focus to form bright spot in one sub-branch after experiencing a symmetric split, depending on the nonlinear intensity, initial launched amplitude, angle and chirp of the beam, and the initial chirp can shift the time of abrupt focus and bright spot formation. Furthermore, the Talbot-like effect and breather train are explored by setting the initial amplitude parameter of every component of an initial Gaussian beam train. Moreover, for longitudinally periodically modulated nonlinearity, the bright spots can be formed periodically and asymmetrically in two sub-branches for a single Gaussian beam, and Moiré-like lattices can be generated for a Gaussian beam train. Finally, the conical diffraction and crescent-like evolution in the two-dimensional system are investigated in detail. It is found that the direction of crescent-like evolution is determined by the initial launched angles, which may be an inspiration to design channel path through choosing suitable initial launched angles at will.

Deterministic relation between thermal-phonon dressings and a non-Hermitian multi-Fano interferences router in ion-doped microcrystals

We report the multi-Fano interference obtained through the simultaneous acquisition of bright and dark states in different phase transitions of Eu3+: BiPO4 (7:1, 6:1, 1:1, and 0.5:1) and Eu3+: NaYF4 (1:1/4) crystals. We employ multi-dressed spontaneous four-wave mixing and multi-dressed fluorescence (multi-order) to optimize the strong photon-phonon nested dressing effect resulting in more obvious multi-Fano interference. Firstly, the multi-Fano is produced through interference in continuous and multi-bound states. Secondly, five multi-Fano dips originate from nested five dressings (one photon and four phonons) under symmetrical splitting of 7F1 energy level. We depict that the pure H-phase (0.5:1) sample exhibits the strongest photon-phonon dressed effect (five Fano dips). Further, we investigate high-order non-Hermitian exceptional points in multi-Fano interference by adjusting the ratio of Rabi-frequency to de-phase rate through nested photon and phonon dressing. Our experimental results are validated by theoretical simulations, which may be applied to designing optoelectronic devices such as non-Hermitian multi-Fano interferences (multi-channel) router.

Matrix splitting preconditioning based on sine transform for solving two-dimensional space-fractional diffusion equations

Finite difference discretization of the two-dimensional space-fractional diffusion equations derives a complicated linear system consisting of identity matrix and four scaled block-Toeplitz with Toeplitz block (BTTB) matrices resulted from the left and right Riemann–Liouville fractional derivatives in different directions. Incorporating with the diffusion coefficients and the symmetric parts of the BTTB matrices, we construct a diagonal and symmetric splitting (DSS) iteration method, which is demonstrated to be convergent conditionally when the considered space-fractional diffusion equations have sufficiently close diffusion coefficients. By further replacing the symmetric Toeplitz matrices involved in the BTTB matrices with τ matrices, an approximated DSS (ADSS) preconditioner based on two-dimensional fast sine transform is designed to accelerate the convergence rates of the Krylov subspace iteration methods. In this way, the total computational complexity of the ADSS-preconditioned GMRES method will be of O(n2logn), where n2 represents the dimension of the corresponding discrete linear system. In addition, theoretical analysis demonstrates that the eigenvalues of the ADSS-preconditioned matrix are weakly clustered around a complex disk centered at 1 with the radius less than 1. Numerical experiments show that the ADSS-preconditioned GMRES method is much more efficient than the other existing methods, and can show h-independent convergence behavior.

How Important Is Budding Speciation for Comparative Studies?

The acknowledgment of evolutionary dependence among species has fundamentally changed how we ask biological questions. Phylogenetic models became the standard approach for studies with 3 or more lineages, in particular those using extant species. Most phylogenetic comparative methods (PCMs) translate relatedness into covariance, meaning that evolutionary changes before lineages split should be interpreted together whereas after the split lineages are expected to change independently. This clever realization has shaped decades of research. Here, we discuss one element of the comparative method often ignored or assumed as unimportant: if nodes of a phylogeny represent the dissolution of the ancestral lineage into two new ones or if the ancestral lineage can survive speciation events (i.e., budding). Budding speciation is often reported in paleontological studies, due to the nature of the evidence for budding in the fossil record, but it is surprisingly absent in comparative methods. Here, we show that many PCMs assume that divergence happens as a symmetric split, even if these methods do not explicitly mention this assumption. We discuss the properties of trait evolution models for continuous and discrete traits and their adequacy under a scenario of budding speciation. We discuss the effects of budding speciation under a series of plausible evolutionary scenarios and show when and how these can influence our estimates. We also propose that long-lived lineages that have survived through a series of budding speciation events and given birth to multiple new lineages can produce evolutionary patterns that challenge our intuition about the most parsimonious history of trait changes in a clade. We hope our discussion can help bridge comparative approaches in paleontology and neontology as well as foster awareness about the assumptions we make when we use phylogenetic trees.

Charge distribution of light mass fission products in the thermal neutron induced fission of 233U, 235U and 239Pu

Fractional cumulative yields (FCY) of various light mass fission products in the 233U(nth, f), 235U(nth, f) and 239Pu(nth, f) reactions were measured by using an off-line γ-ray spectrometric technique. The values of most probable charge (ZP) were obtained by using the width of isobaric charge distribution (σZ) of nearby fissioning systems with proper apportion. From the ZP values, the experimental charge polarization (ΔΖEXPT) as a function of fragment mass were also deduced. The ΔΖEXPT values for the light mass chains from the present work and for the heavy mass chains from earlier work show an oscillating nature in the interval of five mass units due to even-odd staggering. A local effect around the shell region and a systematic decreasing trend with the approach of symmetric split was also observed. The ΔΖMPE values based on minimum potential energy surface were theoretically calculated, which shows no oscillation but only a systematic decreasing trend with the approach of symmetric split due to the assumption of liquid drop behaviour of the fissioning nucleus.

Electronic Born-Oppenheimer approximation in nuclear-electronic orbital dynamics.

Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born-Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density is quenched to the ground state at each time step, and the real-time nuclear quantum dynamics is propagated on an instantaneous electronic ground state defined by both the classical nuclear geometry and the nonequilibrium quantum nuclear density. Because the electronic dynamics is no longer propagated, this approximation enables the use of an order-of-magnitude larger time step, thus greatly reducing the computational cost. Moreover, invoking the electronic BO approximation also fixes the unphysical asymmetric Rabi splitting observed in previous semiclassical RT-NEO-TDDFT simulations of vibrational polaritons even for small Rabi splitting, instead yielding a stable, symmetric Rabi splitting. For the intramolecular proton transfer in malonaldehyde, both RT-NEO-Ehrenfest dynamics and its BO counterpart can describe proton delocalization during the real-time nuclear quantum dynamics. Thus, the BO RT-NEO approach provides the foundation for a wide range of chemical and biological applications.

Refraction, beam splitting and dispersion of GHz surface acoustic waves by a phononic crystal

We exploit a time-resolved ultrafast optical technique to study the propagation of point-excited surface acoustic waves on a microscopic two-dimensional phononic crystal in the form of a square lattice of holes in a silicon substrate. Constant-frequency images and the dispersion relation are extracted, and the latter measured in detail in the region around the phononic band gap. Mode conversion and refraction at the interface between the phononic crystal and surrounding non-structured silicon substrate is studied at constant frequencies. Symmetric phonon beam splitting, for example, is shown to lead to a striking Maltese-cross pattern when phonons exit a square region of phononic crystal excited near its center.

Human decision change in crowd evacuation: A virtual reality-based study

In complex building evacuations, continuous decision-making is unavoidable to make a sequence of route choices at intersections. Evacuees can change their initial decisions with the environmental context changes to deal with the uncertainties of the evacuation. However, this decision-changing phenomenon in evacuation wayfinding has not been well explained. Therefore, this study investigates the decision-changing behavior in crowd evacuation. The influence of two typical crowd flow modes (i.e., symmetric split and asymmetric split crowd flow) on human decision changes in evacuation wayfinding is explored. The results show that evacuees are likely to change their initial route choice decision under the influence of crowd flows, and asymmetric crowd flow significantly reinforces this trend. Moreover, crowd flow modes significantly affected participants' wayfinding performance, including evacuation time, distance, and speed. This study provides behavioral observations and empirical evidence of the persistent effects of crowd flows on evacuees' wayfinding decisions changing and performance during the evacuation.

Fast solution methods for Riesz space fractional diffusion equations with non-separable coefficients

In this paper, efficient preconditioned iterative methods for solving the Riesz space fractional diffusion equations with variable diffusion coefficients are considered. Crank–Nicolson and weighted and shifted Grünwald difference scheme are applied to discretize the problem. For one-dimensional problems, we transform the asymmetric discretized linear system into a symmetric one and solve the resulted linear system by preconditioned conjugate gradient method. The preconditioned conjugate gradient method with a symmetric Toeplitz preconditioner and a sine transform based preconditioner are employed to solve the resulting linear system. Theoretically, we respectively prove that the condition numbers of preconditioned matrices have uniform upper bounds, which is independent of discretization step-sizes and fractional order. For two-dimensional problems, we propose an optional and symmetric splitting iteration method, which can be embedded by conjugate gradient method although the diffusion coefficients are non-separable. We prove that the optional and symmetric splitting iteration method is unconditionally convergent. Numerical results are reported to illustrate the efficiency of the proposed methods.

Study of magnetoplasmons in graphene rings with two-dimensional finite element method

Graphene plasmons are important collective excitations in graphene, which play a key role in determining the optical properties of graphene. They have quite lots of unique features in comparison with classical plasmons in noble metals. Of them, the active tunability is the most attractive, which is realized by external gating (equivalently electric field). As is well known, graphene also has strong magnetic response (e.g. room temperature quantum Hall effect), so magnetic field can act as another degree of freedom for actively tuning graphene plasmons, with the new quasi particles being so-called graphene magneto-plasmons. Because of the two-dimensional nature of graphene, the numerical studies (or full wave simulations) of graphene magneto-plasmons are usually carried out through a three-dimensional approximation, e.g. treating two-dimensional graphene as a very thin three-dimensional film. Actually, this treatment takes quite some time and requires high memory consumption. Herein, starting from Coulomb law and charge conservation law, we propose an alternative numerical method, namely, two-dimensional finite element method, to solve this problem. All the calculations are now performed in two-dimensional graphene plane, and the usual three-dimensional approximation is not required. To characterize the excitations of graphene magneto-plasmons, the eigenvalue loss spectrum is introduced. Based on this method, graphene magneto-plasmons in graphene rings of four kinds are investigated. The strongest magneto-optic effect is observed in circular ring, which is consistent with its highest rotational symmetry. In all the rings, the lowest dipolar graphene magneto-plasmon always supports symmetric mode splitting, which can be further modified by the interaction between inner edge and outer edge of ring. As the hole size is very small, the edge current confined to the outer edge dominates, and that confined to the inner edge can be ignored; while increasing the hole size, the interaction between these two edges increases, which results in the reduction of the symmetric mode splitting; when the hole size is larger than a critical value, the symmetric mode splitting will disappear.

A symmetric splitting sequential quadratic optimization algorithm for two-block nonlinearly constrained nonconvex optimization

In this paper, a double-step-length symmetric splitting sequential quadratic optimization (DSL-SS-SQO) algorithm for solving two-block nonconvex optimization with nonlinear constraints is proposed. First, at each iteration, the idea of symmetric splitting is embedded into solving the quadratic optimization (QO) subproblem approximating the discussed problem. As a result, the QO subproblem is split into two small-scale QOs, which can generate two improved search directions for the two primal variables. Second, the augmented Lagrangian function is used as the merit function, and two step sizes are yielded by performing the Armijo line search along the two improved directions. Third, under mild conditions, the global convergence, strong convergence, iterative complexity, and Maratos effect of the DSL-SS-SQO algorithm are proven. Finally, some numerical results are reported, comparisons with the results obtained by the IPOPT solver are also provided, which preliminarily show that the proposed algorithm is promising.