2,300 results match your criteria numerically analytically

Stabilizing nanolasers via polarization lifetime tuning.

Sci Rep 2021 Sep 17;11(1):18558. Epub 2021 Sep 17.

Institute for Theoretical Physics, Technische Universiät Berlin, Hardenbergstr. 36, 10623, Berlin, Germany.

We investigate the emission dynamics of mutually coupled nanolasers and predict ways to optimize their stability, i.e., maximize their locking range. Read More

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September 2021

Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics.

Phys Rev E 2021 Aug;104(2-2):025304

Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA.

The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive "full-wave" simulations are typically used, but this is not strictly necessary. Read More

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Attraction and condensation of driven tracers in a narrow channel.

Phys Rev E 2021 Aug;104(2-1):024123

Computational Physics Group, Faculty of Physics, University of Vienna, Vienna 1090, Austria.

Emergent bath-mediated attraction and condensation arise when multiple particles are simultaneously driven through an equilibrated bath under geometric constraints. While such scenarios are observed in a variety of nonequilibrium phenomena with an abundance of experimental and numerical evidence, little quantitative understanding of how these interactions arise is currently available. Here we approach the problem by studying the behavior of two driven "tracer" particles, propagating through a bath in a 1D lattice with excluded-volume interactions. Read More

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Asymmetry-induced order in multilayer networks.

Phys Rev E 2021 Aug;104(2-1):024302

Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.

Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase the stability of synchronization. Yet here we find that general macroscopic features of network solutions such as regularity can be induced by breaking their symmetry of interactions. Read More

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Turbulence and capillary waves on bubbles.

Phys Rev E 2021 Aug;104(2-2):025108

Racah Institute of Physics, The Hebrew University, 9190401 Jerusalem, Israel.

We present a link between the theory of deep water waves and that of bubble surface perturbations. Theory correspondence is shown analytically for small wavelengths in the linear regime and investigated numerically in the nonlinear regime. To do so, we develop the second-order spatial perturbation equations for the Rayleigh-Plesset equation and solve them numerically. Read More

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The effects of heterogeneous mechanical properties on the response of a ductile material.

Sci Rep 2021 Sep 13;11(1):18170. Epub 2021 Sep 13.

Department of Aeronautical Engineering, Imperial College London, Imperial College Road, London, SW7 2AZ, UK.

We investigate numerically the small-strain, elastic-plastic response of statistically isotropic materials with non-uniform spatial distributions of mechanical properties. The numerical predictions are compared to simple bounds derived analytically. We explore systematically the effects of heterogeneity on the macroscopic stiffness, strength, asymmetry, stability and size dependence. Read More

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September 2021

Dynamic behavior and stabilization of brain cell reconstitution after stroke under the proliferation and differentiation processes for stem cells.

Math Biosci Eng 2021 Jul;18(5):6288-6304

Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi Selangor 43600, Malaysia.

Stem cells play a critical role in regulatory operations, overseeing tissue regeneration and tissue homeostasis. In this paper, a mathematical model is proposed and analyzed to study the impact of stem cell transplantation on the dynamical behavior of stroke therapy, which is assumed to be based on transplanting dead brain cells following a stroke. We transform the method of using hierarchical cell systems into a method of using different compartment variables by using ordinary differential equations, each of which elucidates a well-defined differentiation stage along with the effect of mature cells in improving the brain function after a stroke. Read More

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Stability analysis and persistence of a phage therapy model.

Math Biosci Eng 2021 Jun;18(5):5552-5572

School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.

This study deals with a phage therapy model involving nonlinear interactions of the bacteria-phage-innate immune response. The main aim of this work is to analytically and numerically examine the dynamic behavior of the phage therapy model. First, we investigate the positivity and boundedness of the system. Read More

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On the Achievability of Blind Source Separation for High-Dimensional Nonlinear Source Mixtures.

Neural Comput 2021 May;33(6):1433-1468

Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Wako, Saitama 351-0198, Japan, and Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world data that involve nonlinear source mixtures. This work theoretically validates that a cascade of linear PCA and ICA can solve a nonlinear BSS problem accurately-when the sensory inputs are generated from hidden sources via nonlinear mappings with sufficient dimensionality. Read More

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Entanglement Renormalization of Thermofield Double States.

Phys Rev Lett 2021 Aug;127(8):080602

Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.

Entanglement renormalization is a method for "coarse graining" a quantum state in real space, with the multiscale entanglement renormalization ansatz as a notable example. We obtain an entanglement renormalization scheme for finite-temperature (Gibbs) states by applying the multiscale entanglement renormalization ansatz to their canonical purification, the thermofield double state. As an example, we find an analytically exact renormalization circuit for a finite-temperature two-dimensional toric code that maps it to a coarse-grained system with a renormalized higher temperature, thus explicitly demonstrating its lack of topological order. Read More

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Mutual singularities of overlapping attractor and repeller.

Chaos 2021 Aug;31(8):083127

National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya Ulitsa, 603155 Nizhny Novgorod, Russia.

We apply the concepts of relative dimensions and mutual singularities to characterize the fractal properties of overlapping attractor and repeller in chaotic dynamical systems. We consider one analytically solvable example (a generalized baker's map); two other examples, the Anosov-Möbius and the Chirikov-Möbius maps, which possess fractal attractor and repeller on a two-dimensional torus, are explored numerically. We demonstrate that although for these maps the stable and unstable directions are not orthogonal to each other, the relative Rényi and Kullback-Leibler dimensions as well as the mutual singularity spectra for the attractor and repeller can be well approximated under orthogonality assumption of two fractals. Read More

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Fragmentation in trader preferences among multiple markets: market coexistence versus single market dominance.

R Soc Open Sci 2021 Aug 18;8(8):202233. Epub 2021 Aug 18.

Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK.

Technological advancement has led to an increase in the number and type of trading venues and a diversification of goods traded. These changes have re-emphasized the importance of understanding the effects of market competition: does proliferation of trading venues and increased competition lead to dominance of a single market or coexistence of multiple markets? In this paper, we address these questions in a stylized model of zero-intelligence traders who make repeated decisions at which of three available markets to trade. We analyse the model numerically and analytically and find that the traders' decision parameters-memory length and how strongly decisions are based on past success-make the key difference between consolidated and fragmented steady states of the population of traders. Read More

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Dynamic analysis of a micro-cantilever beam in noncontact mode: Classic and strain gradient theories.

Microsc Res Tech 2021 Aug 25. Epub 2021 Aug 25.

Center of Advanced Systems & Technologies (CAST), School of Mechanical Engineering, University of Tehran, Tehran, Iran.

This article investigates the dynamic behavior of the micro-cantilever beam in a noncontact atomic force microscope based on classic and strain gradient continuum theories. Governing equation of the system is derived using Euler-Bernoulli and strain gradient theories as a nonlinear partial differential equation. Then, the equation is converted to a nonlinear ordinary differential equation using the Galerkin method, and the lumped model is derived. Read More

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Dimensional Interpolation for Random Walk.

J Phys Chem A 2021 Sep 24;125(34):7581-7587. Epub 2021 Aug 24.

Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States.

We employ a simple and accurate dimensional interpolation formula for the shapes of random walks at = 3 and = 2 based on the analytically known solutions at both limits = ∞ and = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at = 3 and = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. Read More

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September 2021

Multiscale representations of community structures in attractor neural networks.

PLoS Comput Biol 2021 Aug 23;17(8):e1009296. Epub 2021 Aug 23.

Okinawa Institute of Science and Technology, Onna-son, Okinawa, Japan.

Our cognition relies on the ability of the brain to segment hierarchically structured events on multiple scales. Recent evidence suggests that the brain performs this event segmentation based on the structure of state-transition graphs behind sequential experiences. However, the underlying circuit mechanisms are poorly understood. Read More

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Wound opening in a thin incompressible viscoelastic tissue.

Phys Rev E 2021 Jul;104(1-2):015001

Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal.

We develop a model to investigate analytically and numerically the mechanics of wound opening made in a viscoelastic, isotropic, homogeneous, and incompressive thin tissue. This process occurs just immediately after the wound infliction. Before any active biological action has taken place, the tissue relaxes, and the wound opens mostly due to the initial homeostatic tension of the tissue, its elastic and viscous properties, and the existing friction between the tissue and its substrate. Read More

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Optimal and efficient generation of sine-Gordon breathers.

Phys Rev E 2021 Jul;104(1-1):014209

Key Laboratory of Modern Acoustics (MOE) and Institute of Acoustics, Nanjing University, Nanjing 210093, P.R. China.

We investigate analytically and numerically whether an optimally designed defect structure can significantly reduce the threshold for breather train generation by almost two orders of magnitude in a sine-Gordon chain. By optimizing the parameters of defects based on a variational approach, we show that the decoupling of in-phase and antiphase branches allows us to independently minimize the driving threshold and reach the goal of emission of high-amplitude and well-formed breathers by an ultraweak driving. These results not only provide an optimal way for highly controllable and efficient emission of breathers, but also provide some insights into the mechanism of breather excitations in such processes as the DNA-protein interaction during transcription. Read More

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Effect of individual differences on the jamming transition in traffic flow.

Phys Rev E 2021 Jul;104(1-1):014311

Department of Physics, National Tsing Hua University, 30013 Hsinchu, Taiwan.

The individual difference, particularly in drivers' distance perception, is introduced in the microscopic one-dimensional optimal velocity model to investigate its effect on the onset of the jamming instability seen in traffic systems. We show analytically and numerically that the individual difference helps to inhibit the traffic jam at high vehicle densities while it promotes jamming transition at low vehicle densities. In addition, the jamming mechanism is further investigated by tracking how the spatial disturbance travels through traffics. Read More

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Power requirements for the hovering flight of insects with different sizes.

Yu Zhu Lyu Mao Sun

J Insect Physiol 2021 Aug 11;134:104293. Epub 2021 Aug 11.

Ministry-of-Education Key Laboratory of Fluid Mechanics, Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.

Winged insects vary greatly in size, from tiny wasps (0.015 mg) to large moths (1.6 g). Read More

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Theoretical framework for mixer design for noise reduction and gradient fidelity.

J Chromatogr A 2021 Sep 21;1653:462357. Epub 2021 Jun 21.

Waters Corporation, 34 Maple Street, Milford, MA 01757, USA. Electronic address:

The mixing of two or more solvent streams to deliver a stable and accurate solvent composition is crucial to the performance, repeatability and reproducibility of a liquid chromatographic separation. We provide a theoretical treatment of axial mixing of a sequence of solvent packets with the framework of continuous stirred tank reactors (CSTRs) in series and investigate the tradeoffs presented between the primary goal of mixers (noise reduction) and it's necessary side-effects of gradient deformation and asymmetry. An experimental setup to mimic CSTR conditions was created using a stop-flow setup where the fluid flow was periodically paused and sonicated within pods of a certain volume. Read More

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September 2021

A Vibration Sensor-Based Method for Generating the Precise Rotor Orbit Shape with General Notch Filter Method for New Rotor Seal Design Testing and Diagnostics.

Sensors (Basel) 2021 Aug 3;21(15). Epub 2021 Aug 3.

NTIS-New Technologies for the Information Society, Faculty of Applied Sciences, The University of West Bohemia, 30100 Pilsen, Czech Republic.

Verification of the behaviour of new designs of rotor seals is a crucial phase necessary for their use in rotary machines. Therefore, experimental equipment for the verification of properties that have an effect on rotor dynamics is being developed in the test laboratories of the manufacturers of these components all over the world. In order to be able to compare the analytically derived and experimentally identified values of the seal parameters, specific requirements for the rotor vibration pattern during experiments are usually set. Read More

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Fractional Derivative Modification of Drude Model.

Sensors (Basel) 2021 Jul 22;21(15). Epub 2021 Jul 22.

Institute of Mathematics and Physics, UTP University of Science and Technology, 85-796 Bydgoszcz, Poland.

A novel, two-parameter modification of a Drude model, based on fractional time derivatives, is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing good agreement between theoretical description and numerical results. The absorption coefficient and wave vector are shown to follow a power law in the frequency domain, which is a common phenomenon in electromagnetic and acoustic wave propagation in complex media such as biological tissues. Read More

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Effect of Kinesin-5 Tail Domain on Motor Dynamics for Antiparallel Microtubule Sliding.

Int J Mol Sci 2021 Jul 23;22(15). Epub 2021 Jul 23.

Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.

Kinesin-5 motor consists of two pairs of heads and tail domains, which are situated at the opposite ends of a common stalk. The two pairs of heads can bind to two antiparallel microtubules (MTs) and move on the two MTs independently towards the plus ends, sliding apart the two MTs, which is responsible for chromosome segregation during mitosis. Prior experimental data showed that the tails of kinesin-5 Eg5 can modulate the dynamics of single motors and are critical for multiple motors to generate high steady forces to slide apart two antiparallel MTs. Read More

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Synchronizability of double-layer dumbbell networks.

Chaos 2021 Jul;31(7):073101

School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.

Synchronization of multiplex networks has been a topical issue in network science. Dumbbell networks are very typical structures in complex networks which are distinguished from both regular star networks and general community structures, whereas the synchronous dynamics of a double-layer dumbbell network relies on the interlink patterns between layers. In this paper, two kinds of double-layer dumbbell networks are defined according to different interlayer coupling patterns: one with the single-link coupling pattern between layers and the other with the two-link coupling pattern between layers. Read More

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Symmetry kills the square in a multifunctional reservoir computer.

Chaos 2021 Jul;31(7):073122

School of Mathematical Sciences, University College Cork, Cork T12 XF62, Ireland.

The learning capabilities of a reservoir computer (RC) can be stifled due to symmetry in its design. Including quadratic terms in the training of a RC produces a "square readout matrix" that breaks the symmetry to quell the influence of "mirror-attractors," which are inverted copies of the RC's solutions in state space. In this paper, we prove analytically that certain symmetries in the training data forbid the square readout matrix to exist. Read More

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Analytical solutions for contaminant fate and transport in parallel plate fracture-rock matrix systems with poiseuille flow.

J Hydrol (Amst) 2021 May;596

Department of Systems Engineering and Management, Air Force Institute of Technology, 2950 Hobson Way, WPAFB OH, 45433, USA.

Modeling contaminant transport in fractured-rock matrix systems often approximates the effect of the parabolic flow field in the fractures (i.e., Poiseuille flow) on transport by adding a dispersion term to the uniform flow field. Read More

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Thermoelectrics in ice slabs: charge dynamics and thermovoltages.

Phys Chem Chem Phys 2021 Aug;23(30):16277-16288

Department of Mechanical Engineering, Virginia Tech, Blaksburg, VA 24061, USA.

Thermoelectric effects of ice play an important role in many natural and engineering phenomena. We investigate, numerically and analytically, the electrification of finite-thickness ice slabs due to an imposed temperature difference across them. When exposed to a temperature gradient, thermoelectrification involves a fast initial stage dominated by Bjerrum defects and a subsequent slow stage driven by ionic defects. Read More

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Transfer-RLS method and transfer-FORCE learning for simple and fast training of reservoir computing models.

Neural Netw 2021 Jul 6;143:550-563. Epub 2021 Jul 6.

Graduate School of Engineering, The University of Tokyo, 113-8656 Tokyo, Japan; International Research Center for Neurointelligence, The University of Tokyo, 113-0033 Tokyo, Japan.

Reservoir computing is a machine learning framework derived from a special type of recurrent neural network. Following recent advances in physical reservoir computing, some reservoir computing devices are thought to be promising as energy-efficient machine learning hardware for real-time information processing. To realize efficient online learning with low-power reservoir computing devices, it is beneficial to develop fast convergence learning methods with simpler operations. Read More

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Electrically Tuneable Optical Diffraction Gratings Based on a Polymer Scaffold Filled with a Nematic Liquid Crystal.

Polymers (Basel) 2021 Jul 13;13(14). Epub 2021 Jul 13.

Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.

We present an experimental and theoretical investigation of the optical diffractive properties of electrically tuneable optical transmission gratings assembled as stacks of periodic slices from a conventional nematic liquid crystal (E7) and a standard photoresist polymer (SU-8). The external electric field causes a twist-type reorientation of the LC molecules toward a perpendicular direction with respect to initial orientation. The associated field-induced modification of the director field is determined numerically and analytically by minimization of the Landau-de Gennes free energy. Read More

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Temporal aiming.

Light Sci Appl 2020 Jul 20;9(1):129. Epub 2020 Jul 20.

Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, 19104, USA.

Deflecting and changing the direction of propagation of electromagnetic waves are needed in multiple applications, such as in lens-antenna systems, point-to-point communications and radars. In this realm, metamaterials have been demonstrated to be great candidates for controlling wave propagation and wave-matter interactions by offering manipulation of their electromagnetic properties at will. They have been studied mainly in the frequency domain, but their temporal manipulation has become a topic of great interest during the past few years in the design of spatiotemporally modulated artificial media. Read More

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