scholarly journals Chimera state in coupled map lattice of matrices

2021 ◽  
Vol 62 ◽  
pp. 57-63
Author(s):  
Kotryna Mačernytė ◽  
Rasa Šmidtaitė
Keyword(s):  
Initial Conditions ◽  
State Parameter ◽  
Coupled Map Lattice ◽  
Supplementary Variable ◽  
Chimera States ◽  
Chimera State ◽  
Nilpotent Matrix ◽  
Wide Range ◽  
The Matrix ◽  
Iterative Maps

In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering. The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix. Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

scholarly journals On the generation of internal waves by river plumes in subcritical initial conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. Mendes ◽  
J. C. B. da Silva ◽  
J. M. Magalhaes ◽  
B. St-Denis ◽  
D. Bourgault ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Internal Waves ◽  
Coastal Waters ◽  
Initial Conditions ◽  
Spatial Scales ◽  
River Plumes ◽  
Wide Range ◽  
Near Shore ◽  
Generation Mechanisms ◽  
Douro River

AbstractInternal waves (IWs) in the ocean span across a wide range of time and spatial scales and are now acknowledged as important sources of turbulence and mixing, with the largest observations having 200 m in amplitude and vertical velocities close to 0.5 m s−1. Their origin is mostly tidal, but an increasing number of non-tidal generation mechanisms have also been observed. For instance, river plumes provide horizontally propagating density fronts, which were observed to generate IWs when transitioning from supercritical to subcritical flow. In this study, satellite imagery and autonomous underwater measurements are combined with numerical modeling to investigate IW generation from an initial subcritical density front originating at the Douro River plume (western Iberian coast). These unprecedented results may have important implications in near-shore dynamics since that suggest that rivers of moderate flow may play an important role in IW generation between fresh riverine and coastal waters.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

scholarly journals Harmonic hybrid inflation

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Federico Carta ◽  
Nicole Righi ◽  
Yvette Welling ◽  
Alexander Westphal
Keyword(s):  
Domain Wall ◽  
Symmetry Breaking ◽  
Initial Conditions ◽  
Scalar Potential ◽  
Field Range ◽  
Slow Roll ◽  
Minimal Form ◽  
Wide Range ◽  
Hybrid Inflation ◽  
Type Iib String Theory

Abstract We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of the scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints f ≲ MP and ∆ϕ60 ≲ MP on the axion periodicity and slow-roll field range, respectively. We discuss controlled ℤ2-symmetry breaking of the adjacent axion vacua as a means of avoiding cosmological domain wall problems. Including a minimal form of ℤ2-symmetry breaking into the minimally tuned setup leads to a prediction of primordial tensor modes with the tensor-to-scalar ratio in the range 10−4 ≲ r ≲ 0.01, directly accessible to upcoming CMB observations. Finally, we outline several avenues towards realizing harmonic hybrid inflation in type IIB string theory.

scholarly journals Influence of Alumina Nanofibers Sintered by the Spark Plasma Method on Nickel Mechanical Properties

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 548 ◽  
Author(s):  
Leonid Agureev ◽  
Valeriy Kostikov ◽  
Zhanna Eremeeva ◽  
Svetlana Savushkina ◽  
Boris Ivanov ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Elastic Modulus ◽  
Strength Properties ◽  
Alumina Nanoparticles ◽  
Metal Powders ◽  
Wide Range ◽  
The Matrix ◽  
Spark Plasma ◽  
Average Size

The article presents the study of alumina nanoparticles’ (nanofibers) concentration effect on the strength properties of pure nickel. The samples were obtained by spark plasma sintering of previously mechanically activated metal powders. The dependence of the grain size and the relative density of compacts on the number of nanofibers was investigated. It was found that with an increase in the concentration of nanofibers, the average size of the matrix particles decreased. The effects of the nanoparticle concentration (0.01–0.1 wt.%) on the elastic modulus and tensile strength were determined for materials at 25 °C, 400 °C, and 750 °C. It was shown that with an increase in the concentration of nanofibers, a 10–40% increase in the elastic modulus and ultimate tensile strength occurred. A comparison of the mechanical properties of nickel in a wide range of temperatures, obtained in this work with materials made by various technologies, is carried out. A description of nanofibers’ mechanisms of influence on the structure and mechanical properties of nickel is given. The possible impact of impurity phases on the properties of nickel is estimated. The tendency of changes in the mechanical properties of nickel, depending on the concentration of nanofibers, is shown.

scholarly journals Estimating the number of usability problems affecting medical devices: modelling the discovery matrix

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Vincent Vandewalle ◽  
Alexandre Caron ◽  
Coralie Delettrez ◽  
Renaud Périchon ◽  
Sylvia Pelayo ◽  
...  
Keyword(s):  
Medical Devices ◽  
Market Access ◽  
Real Life ◽  
Usability Testing ◽  
Probability Of Detection ◽  
Usability Problems ◽  
Usability Problem ◽  
Wide Range ◽  
The Matrix ◽  
Problem Detection

Abstract Background Usability testing of medical devices are mandatory for market access. The testings’ goal is to identify usability problems that could cause harm to the user or limit the device’s effectiveness. In practice, human factor engineers study participants under actual conditions of use and list the problems encountered. This results in a binary discovery matrix in which each row corresponds to a participant, and each column corresponds to a usability problem. One of the main challenges in usability testing is estimating the total number of problems, in order to assess the completeness of the discovery process. Today’s margin-based methods fit the column sums to a binomial model of problem detection. However, the discovery matrix actually observed is truncated because of undiscovered problems, which corresponds to fitting the marginal sums without the zeros. Margin-based methods fail to overcome the bias related to truncation of the matrix. The objective of the present study was to develop and test a matrix-based method for estimating the total number of usability problems. Methods The matrix-based model was based on the full discovery matrix (including unobserved columns) and not solely on a summary of the data (e.g. the margins). This model also circumvents a drawback of margin-based methods by simultaneously estimating the model’s parameters and the total number of problems. Furthermore, the matrix-based method takes account of a heterogeneous probability of detection, which reflects a real-life setting. As suggested in the usability literature, we assumed that the probability of detection had a logit-normal distribution. Results We assessed the matrix-based method’s performance in a range of settings reflecting real-life usability testing and with heterogeneous probabilities of problem detection. In our simulations, the matrix-based method improved the estimation of the number of problems (in terms of bias, consistency, and coverage probability) in a wide range of settings. We also applied our method to five real datasets from usability testing. Conclusions Estimation models (and particularly matrix-based models) are of value in estimating and monitoring the detection process during usability testing. Matrix-based models have a solid mathematical grounding and, with a view to facilitating the decision-making process for both regulators and device manufacturers, should be incorporated into current standards.

Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results

1996 ◽  
Vol 324 ◽  
pp. 163-179 ◽  
Author(s):  
A. Levy ◽  
G. Ben-Dor ◽  
S. Sorek
Keyword(s):  
Porous Materials ◽  
Initial Conditions ◽  
Computer Code ◽  
Experimental Results ◽  
Numerical Code ◽  
Materials Development ◽  
Numerical Predictions ◽  
Wide Range ◽  
Dimensional Version ◽  
The One

The governing equations of the flow field which is obtained when a thermoelastic rigid porous medium is struck head-one by a shock wave are developed using the multiphase approach. The one-dimensional version of these equations is solved numerically using a TVD-based numerical code. The numerical predictions are compared to experimental results and good to excellent agreements are obtained for different porous materials and a wide range of initial conditions.

Ni Content Surface Layer Produced by Laser Surface Treatment on Amorphisable Cu Base Alloy

2010 ◽  
Vol 649 ◽  
pp. 101-106
Author(s):  
Mária Svéda ◽  
Dóra Janovszky ◽  
Kinga Tomolya ◽  
Jenő Sólyom ◽  
Zoltán Kálazi ◽  
...  
Keyword(s):  
Surface Layer ◽  
Surface Treatment ◽  
Laser Cladding ◽  
Base Alloy ◽  
Laser Surface ◽  
Laser Alloying ◽  
Laser Surface Treatment ◽  
Ni Content ◽  
Wide Range ◽  
The Matrix

The aim of our research was to comparatively examine Ni content surface layers on amorphisable Cu base alloy produced by different laser surface treatments. Laser surface treatment (LST) techniques, such as laser surface melting, laser alloying and laser cladding, provide a wide range of interesting solutions for the production of wear and corrosion resistant surfaces. [1,2] With LST techniques, the surface can be: i) coated with a layer of another material by laser cladding, ii) the composition of the matrix can be modified by laser alloying. [3] Two kinds of laser surface treatment technologies were used. In the case of coating-melting technology a Ni content surface layer was first developed by galvanization, and then the Ni content layer was melted together with the matrix. In the case of powder blowing technology Ni3Al powder was blown into the layer melted by laser beam and Argon gas. LST was performed using an impulse mode Nd:YAG laser. The laser power and the interaction time were 2 kW and 20÷60 ms. The characterization of the surface layer microstructure was performed by XRD, scanning electron microscopy and microhardness measurements.

Dependence of Granular Matrix Demagnetizing Factor on the Matrix Relative Size

2015 ◽  
Vol 1083 ◽  
pp. 32-36 ◽  
Author(s):  
Alexander Sandulyak ◽  
Anna Sandulyak ◽  
Petr Shkatov
Keyword(s):  
Magnetic Permeability ◽  
Relative Size ◽  
Dramatic Effect ◽  
Comparative Estimate ◽  
Magnetic Filter ◽  
Wide Range ◽  
Demagnetizing Factor ◽  
The Matrix ◽  
Granular Matrix ◽  
Operating Units

We note that for a wide range of porous, especially granular, ferromagnetics used as matrices of magnetic filter-separators, there is still an issue of defining their demagnetizing factor N which has a dramatic effect on the values of average magnetic permeability of these operating units of filter-separators. The work aims at filling the existent gaps in the issue, we supply N values depending on the relative size of such magnets as well as a respective generalizing phenomenological dependence which is characterized by an exponential realtion between the demagnetizing factor and relative size radical. The established relation allows obtaining real values of magnetic permeability of a short filter matrix thus providing an unbiased comparative estimate of its technological workability.

Effects of fines on liquefaction behaviour in well-graded materials

2017 ◽  
Vol 54 (10) ◽  
pp. 1460-1471 ◽  
Author(s):  
Katherine A. Kwa ◽  
David W. Airey
Keyword(s):  
Critical State ◽  
Soil Mechanics ◽  
State Parameter ◽  
Triaxial Tests ◽  
Particle Sizes ◽  
Graded Materials ◽  
Fines Content ◽  
Cyclic Resistance ◽  
Wide Range ◽  
Soil Behaviour

This study uses a critical state soil mechanics perspective to understand the mechanics behind the liquefaction of metallic ores during transport by ship. These metallic ores are transported at relatively low densities and have variable gradings containing a wide range of particle sizes and fines contents. The effect of the fines content on the location of the critical state line (CSL) and the cyclic liquefaction behaviour of well-graded materials was investigated by performing saturated, standard drained and undrained monotonic and compression-only cyclic triaxial tests. Samples were prepared at four different gradings containing particle sizes from 9.5 mm to 2 μm with fines (<75 μm) contents of 18%, 28%, 40%, and 60%. In the e versus log[Formula: see text] plane, where e is void ratio and [Formula: see text] is mean effective stress, the CSLs shifted upwards approximately parallel to one another as the fines content was increased. Transitional soil behaviour was observed in samples containing 28%, 40%, and 60% fines. A sample’s cyclic resistance to liquefaction depended on a combination of its density and state parameter, which were both related to the fines content. Samples with the same densities were more resistant to cyclic failure if they contained higher fines contents. The state parameter provided a useful prediction for general behavioural trends of all fines contents studied.

MODELING NANOSECOND-PULSED SPARK DISCHARGE AND FLAME KERNEL EVOLUTION

2021 ◽  
pp. 1-22
Author(s):  
Joohan Kim ◽  
Vyaas Gururajan ◽  
Riccardo Scarcelli ◽  
Sayan Biswas ◽  
Isaac Ekoto
Keyword(s):  
Electrical Discharge ◽  
Internal Combustion Engines ◽  
Initial Conditions ◽  
Fuel Mixture ◽  
Spark Ignition ◽  
Combustion Stability ◽  
Flame Kernel ◽  
Wide Range ◽  
Challenging Environment ◽  
Kernel Growth

Abstract Dilute combustion, either using exhaust gas recirculation or with excess-air, is considered a promising strategy to improve the thermal efficiency of internal combustion engines. However, the dilute air-fuel mixture, especially under intensified turbulence and high-pressure conditions, poses significant challenges for ignitability and combustion stability, which may limit the attainable efficiency benefits. In-depth knowledge of the flame kernel evolution to stabilize ignition and combustion in a challenging environment is crucial for effective engine development and optimization. To date, comprehensive understanding of ignition processes that result in the development of fully predictive ignition models usable by the automotive industry does not yet exist. Spark-ignition consists of a wide range of physics that includes electrical discharge, plasma evolution, joule-heating of gas, and flame kernel initiation and growth into a self-sustainable flame. In this study, an advanced approach is proposed to model spark-ignition energy deposition and flame kernel growth. To decouple the flame kernel growth from the electrical discharge, a nanosecond pulsed high-voltage discharge is used to trigger spark-ignition in an optically accessible small ignition test vessel with a quiescent mixture of air and methane. Initial conditions for the flame kernel, including its thermodynamic state and species composition, are derived from a plasma-chemical equilibrium calculation. The geometric shape and dimension of the kernel are characterized using a multi-dimensional thermal plasma solver. The proposed modeling approach is evaluated using a high-fidelity computational fluid dynamics procedure to compare the simulated flame kernel evolution against flame boundaries from companion schlieren images.

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