Статті в журналах: "Dynamical domains"

1

Mizutani, Masahiro, and Shunji Ito. "Dynamical systems on dragon domains." Japan Journal of Applied Mathematics 4, no. 1 (February 1987): 23–46. http://dx.doi.org/10.1007/bf03167753.

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2

Huang, Yang. "A dynamical construction of Liouville domains." Proceedings of the American Mathematical Society 148, no. 12 (September 4, 2020): 5323–30. http://dx.doi.org/10.1090/proc/15187.

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3

BOYARSKY, ABRAHAM, and PAWEŁ GÓRA. "CHAOS OF DYNAMICAL SYSTEMS ON GENERAL TIME DOMAINS." International Journal of Bifurcation and Chaos 19, no. 11 (November 2009): 3829–32. http://dx.doi.org/10.1142/s0218127409025158.

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We consider dynamical systems on time domains that alternate between continuous time intervals and discrete time intervals. The dynamics on the continuous portions may represent species growth when there is population overlap and are governed by differential or partial differential equations. The dynamics across the discrete time intervals are governed by a chaotic map and may represent population growth which is seasonal. We study the long term dynamics of this combined system. We study various conditions on the continuous time dynamics and discrete time dynamics that produce chaos and alternatively nonchaos for the combined system. When the discrete system alone is chaotic we provide a condition on the continuous dynamical component such that the combined system behaves chaotically. We also provide a condition that ensures that if the discrete time system has an absolutely continuous invariant measure so will the combined system. An example based on the logistic continuous time and logistic discrete time component is worked out.

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4

Kidwingira, F., J. D. Strand, D. J. Van Harlingen, and Y. Maeno. "Dynamical Superconducting Order Parameter Domains in Sr2RuO4." Science 314, no. 5803 (November 24, 2006): 1267–71. http://dx.doi.org/10.1126/science.1133239.

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5

Tsironis, G. P. "Dynamical domains of a nondegenerate nonlinear dimer." Physics Letters A 173, no. 4-5 (February 1993): 381–85. http://dx.doi.org/10.1016/0375-9601(93)90255-x.

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6

Bao, Weizhu, and Qinglin Tang. "Numerical Study of Quantized Vortex Interaction in the Ginzburg-Landau Equation on Bounded Domains." Communications in Computational Physics 14, no. 3 (September 2013): 819–50. http://dx.doi.org/10.4208/cicp.250112.061212a.

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AbstractIn this paper, we study numerically quantized vortex dynamics and their interaction in the two-dimensional (2D) Ginzburg-Landau equation (GLE) with a dimensionless parameter ε > 0 on bounded domains under either Dirichlet or homogeneous Neumann boundary condition. We begin with a review of the reduced dynamical laws for time evolution of quantized vortex centers in GLE and show how to solve these nonlinear ordinary differential equations numerically. Then we present efficient and accurate numerical methods for discretizing the GLE on either a rectangular or a disk domain under either Dirichlet or homogeneous Neumann boundary condition. Based on these efficient and accurate numerical methods for GLE and the reduced dynamical laws, we simulate quantized vortex interaction of GLE with different ε and under different initial setups including single vortex, vortex pair, vortex dipole and vortex lattice, compare them with those obtained from the corresponding reduced dynamical laws, and identify the cases where the reduced dynamical laws agree qualitatively and/or quantitatively as well as fail to agree with those from GLE on vortex interaction. Finally, we also obtain numerically different patterns of the steady states for quantized vortex lattices under the GLE dynamics on bounded domains.

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7

Ha, N. T. T., N. V. Hong, and P. K. Hung. "Distribution of sodium and dynamical heterogeneity in sodium silicate liquid." International Journal of Modern Physics B 33, no. 05 (February 20, 2019): 1950013. http://dx.doi.org/10.1142/s0217979219500139.

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The structural and dynamical properties in sodium silicate liquid were investigated by molecular dynamics method. To clarify the distribution of sodium atoms in model, characteristics of simplex have been investigated. The simulation results reveal that Na2O⋅4SiO2 (NS4) liquid has a lot of simplexes with four sodium atoms inside but about half of simplexes do not have sodium. The spatial distribution of sodium is nonuniform, sodium tends to be in the nonbridging oxygen-simplexes and in larger-radius simplex. Moreover, the sodium density for nonbridging oxygen region is significantly higher than the one for Si-region. Namely, link-cluster function F[Formula: see text](r, t) has been used to clarify dynamical heterogeneity in NS4 liquid. The F[Formula: see text](r, t) for sets of random, immobile and mobile network atoms is quite different, which indicates that the dynamics of network atoms is heterogeneous. The Si–O network has the structure with two separated domains (immobile and mobile domains). These types of domain are significantly different in local microstructure, mobility of atoms and chemical composition.

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8

Padmanabhan, T. "Gravity and quantum theory: Domains of conflict and contact." International Journal of Modern Physics D 29, no. 01 (November 5, 2019): 2030001. http://dx.doi.org/10.1142/s0218271820300013.

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There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer-dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength limit should be described in thermodynamic language and not in a geometric language. Second clue is related to the existence of the cosmological constant. Its understanding from first-principles will require the dynamical principles of the theory to be invariant under the shift [Formula: see text]. This puts strong constraints on the nature of gravitational dynamics and excludes metric tensor as a fundamental dynamical variable. In fact, these two clues are closely related to each other. When the dynamical principles are recast, respecting the symmetry [Formula: see text], they automatically acquire a thermodynamic interpretation related to the first clue. The first part of this review provides a pedagogical introduction to thermal properties of the horizons, including some novel derivations. The second part describes some aspects of cosmological constant problem and the last part provides a perspective on gravity which takes into account these principles.

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9

Kobine, J. J., T. Mullin, and T. J. Price. "The dynamics of driven rotating flow in stadium-shaped domains." Journal of Fluid Mechanics 294 (July 10, 1995): 47–69. http://dx.doi.org/10.1017/s0022112095002801.

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Results are presented from an experimental investigation of the dynamics of driven rotating flows in stadium-shaped domains. The work was motivated by questions concerning the typicality of low-dimensional dynamical phenomena which are found in Taylor-Couette flow between rotating circular cylinders. In such a system, there is continuous azimuthal symmetry and travelling-wave solutions are found. In the present study, this symmetry is broken by replacing the stationary outer circular cylinder with one which has a stadium-shaped cross-section. Thus there is now only discrete symmetry in the azimuthal direction, and travelling waves are no longer observed. To begin with, the two-dimensional flow field was investigated using numerical techniques. This was followed by an experimental study of the dynamics of flow in systems with finite vertical extent. Configurations involving both right-circular and tapered inner cylinders were considered. Dynamics were observed which correspond to known mechanisms from the theory of finite-dimensional dynamical systems. However, flow behaviour was also observed which cannot be classified in this way. Thus it is concluded that while certain low-dimensional dynamical phenomena do persist with breaking of the continuous azimuthal symmetry embodied in the Taylor-Couette system, sufficient reduction of symmetry admits behaviour at moderately low Reynolds number which is without any low-dimensional characteristics.

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10

ELLIS, GEORGE F. R. "DYNAMICAL PROPERTIES OF COSMOLOGICAL SOLUTIONS." Journal of Hyperbolic Differential Equations 02, no. 02 (June 2005): 381–95. http://dx.doi.org/10.1142/s0219891605000464.

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I will consider how there are FOSH formulations and associated results in relativistic cosmology expressed in 1+3 tetrad form. The characteristics of scalar and vector perturbations are timelike, hence the real domains of dependence in cosmology are much smaller than implied by the light cone, associated with gravitational wave perturbations.

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11

Ha, N. T. T., M. T. Lan, N. V. Hong, and P. K. Hung. "Structural transformation and dynamical heterogeneity in Germania melt under compression: molecular dynamic simulation." Canadian Journal of Physics 99, no. 12 (December 2021): 1086–94. http://dx.doi.org/10.1139/cjp-2020-0493.

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The structural transformation and dynamical heterogeneity in Germania (GeO2) are investigated via molecular dynamics (MD) simulation. The MD model with 5499 atoms was constructed under pressure up to 150 GPa and at a temperature of 3500 K. The structural transformation mechanism has been studied by observing domain structures and boundary oxygen atoms. The simulation result reveals that GeO2 consists of separate domains and boundaries in its melt structure. Under compression, the structure of GeO2 changes gradually and represents many types of structures. The melt structure exhibits many structural domains Dx, and polymorphism appears at pressures of 12 and 20 GPa. The change of tetrahedral structure to octahedral structure in germanium coordination occurred in parallel with the process of merging and splitting of domain structure. Moreover, the existence of high- and low-density phases in GeO2 melt is indicated. The high-density phase is D6 domain and boundary oxygen while the low-density phase is D4 and D5 domain. The compression mechanism in GeO2 melt mainly is a reduction of average Voronoi volume of oxygen and Voronoi volume of D6, boundary atoms oxygen. Furthermore, we find the dynamical heterogeneity at ambient pressure. The separate “fast” regions and “slow” regions in GeO2 are detected via link-cluster function.

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12

Baxter, G. William, and C. David Andereck. "Formation of Dynamical Domains in a Circular Couette System." Physical Review Letters 57, no. 24 (December 15, 1986): 3046–49. http://dx.doi.org/10.1103/physrevlett.57.3046.

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13

ICHIMIYA, AYAHIKO, and YUSUKE OHNO. "STRUCTURAL ANALYSIS OF IMPERFECT CRYSTAL SURFACES BY REFLECTION HIGH-ENERGY ELECTRON DIFFRACTION: ANTIPHASE DOMAINS OF A ${\rm Si}(111)(\sqrt 3 \times\sqrt 3)$-Ag SURFACE." Surface Review and Letters 04, no. 05 (October 1997): 985–90. http://dx.doi.org/10.1142/s0218625x97001164.

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For dynamical calculations of reflection high-energy electron diffraction (RHEED) for imperfect crystal surfaces, a general formula of Fourier coefficients of crystal potential with domain structures is developed. Using the formula, RHEED intensity rocking curves are calculated for a [Formula: see text]-Ag surface with antiphase domains. We discuss effects of antiphase domains of surfaces in structure determinations by RHEED.

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14

Chaves, Rui, Selma Dahmane, Michael Odorico, Gerry Nicolaes, and Jean-Luc Pellequer. "Factor Va alternative conformation reconstruction using atomic force microscopy." Thrombosis and Haemostasis 112, no. 12 (2014): 1167–73. http://dx.doi.org/10.1160/th14-06-0481.

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SummaryProtein conformational variability (or dynamics) for large macromolecules and its implication for their biological function attracts more and more attention. Collective motions of domains increase the ability of a protein to bind to partner molecules. Using atomic force microscopy (AFM) topographic images, it is possible to take snapshots of large multi-component macromolecules at the single molecule level and to reconstruct complete molecular conformations. Here, we report the application of a reconstruction protocol, named AFM-assembly, to characterise the conformational variability of the two C domains of human coagulation factor Va (FVa). Using AFM topographic surfaces obtained in liquid environment, it is shown that the angle between C1 and C2 domains of FVa can vary between 40° and 166°. Such dynamical variation in C1 and C2 domain arrangement may have important implications regarding the binding of FVa to phospholipid membranes.

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15

Chacon, Juan, Mo Chen, and Razvan C. Fetecau. "Safe Coverage of Compact Domains For Second Order Dynamical Systems." IFAC-PapersOnLine 53, no. 2 (2020): 15167–73. http://dx.doi.org/10.1016/j.ifacol.2020.12.2286.

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16

Yang, Peicai, Geli Wang, Ziniu Xiao, Anastasios A. Tsonis, Guolin Feng, Shida Liu, and Xiuji Zhou. "Climate: a dynamical system with mismatched space and time domains." Climate Dynamics 56, no. 9-10 (February 14, 2021): 3305–11. http://dx.doi.org/10.1007/s00382-021-05646-7.

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17

Scarabelli, Guido, and Barry J. Grant. "Mapping the Structural and Dynamical Features of Kinesin Motor Domains." PLoS Computational Biology 9, no. 11 (November 7, 2013): e1003329. http://dx.doi.org/10.1371/journal.pcbi.1003329.

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18

Granata, Daniele, Luca Ponzoni, Cristian Micheletti, and Vincenzo Carnevale. "Patterns of coevolving amino acids unveil structural and dynamical domains." Proceedings of the National Academy of Sciences 114, no. 50 (November 28, 2017): E10612—E10621. http://dx.doi.org/10.1073/pnas.1712021114.

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Patterns of interacting amino acids are so preserved within protein families that the sole analysis of evolutionary comutations can identify pairs of contacting residues. It is also known that evolution conserves functional dynamics, i.e., the concerted motion or displacement of large protein regions or domains. Is it, therefore, possible to use a pure sequence-based analysis to identify these dynamical domains? To address this question, we introduce here a general coevolutionary coupling analysis strategy and apply it to a curated sequence database of hundreds of protein families. For most families, the sequence-based method partitions amino acids into a few clusters. When viewed in the context of the native structure, these clusters have the signature characteristics of viable protein domains: They are spatially separated but individually compact. They have a direct functional bearing too, as shown for various reference cases. We conclude that even large-scale structural and functionally related properties can be recovered from inference methods applied to evolutionary-related sequences. The method introduced here is available as a software package and web server (spectrus.sissa.it/spectrus-evo_webserver).

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19

Gu, Wei, and Volkhard Helms. "Dynamical binding of proline-rich peptides to their recognition domains." Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics 1754, no. 1-2 (December 2005): 232–38. http://dx.doi.org/10.1016/j.bbapap.2005.07.033.

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20

Rault, Jean-François. "The Fujita phenomenon in exterior domains under dynamical boundary conditions." Asymptotic Analysis 66, no. 1 (2010): 1–8. http://dx.doi.org/10.3233/asy-2009-0954.

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21

Lazebnik, Kirill. "Quadrature domains and the real quadratic family." Conformal Geometry and Dynamics of the American Mathematical Society 25, no. 6 (September 15, 2021): 104–25. http://dx.doi.org/10.1090/ecgd/361.

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We study several classes of holomorphic dynamical systems associated with quadrature domains. Our main result is that real-symmetric polynomials in the principal hyperbolic component of the Mandelbrot set can be conformally mated with a congruence subgroup of P S L ( 2 , Z ) \mathrm {PSL}(2,\mathbb {Z}) , and that this conformal mating is the Schwarz function of a simply connected quadrature domain.

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22

CRAUEL, H., P. E. KLOEDEN, and MEIHUA YANG. "RANDOM ATTRACTORS OF STOCHASTIC REACTION–DIFFUSION EQUATIONS ON VARIABLE DOMAINS." Stochastics and Dynamics 11, no. 02n03 (September 2011): 301–14. http://dx.doi.org/10.1142/s0219493711003292.

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It is shown that a stochastic partial differential equation of the reaction–diffusion type on time-varying domains obtained by a temporally continuous dependent spatially diffeomorphic transformation of a reference domain, which is bounded with a smooth boundary, generates a "partial-random" dynamical system, which has a pathwise nonautonomous pullback attractor.

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23

Kenrick, Douglas T., Jon K. Maner, Jon Butner, Norman P. Li, D. Vaughn Becker, and Mark Schaller. "Dynamical Evolutionary Psychology: Mapping the Domains of the New Interactionist Paradigm." Personality and Social Psychology Review 6, no. 4 (November 2002): 347–56. http://dx.doi.org/10.1207/s15327957pspr0604_09.

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Dynamical systems and evolutionary theories have both been proposed as integrative approaches to psychology. These approaches are typically applied to different sets of questions. Dynamical systems models address the properties of psychological systems as they emerge and change over time; evolutionary models address the specific functions and contents of psychological structures. New insights can be achieved by integrating these two paradigms, and we propose a framework to begin doing so. The framework specifies a set of six evolutionarily fundamental social goals that place predictable constraints on emergent processes within and between individuals, influencing their dynamics over the short-term, and across developmental and evolutionary time scales. These social goals also predictably influence the dynamic emergence and change of cultural norms. This framework has heuristic as well as integrative potential, generating novel hypotheses within a number of unexplored areas atpsychology's interface with the other biological and social sciences.

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24

Akashi, Shigeo. "Embedding of nonlinear dynamical systems with compact and totally disconnected domains into the product symbolic dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e1817-e1821. http://dx.doi.org/10.1016/j.na.2005.01.073.

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25

Vitillaro, Enzo. "Global existence for the heat equation with nonlinear dynamical boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, no. 1 (February 2005): 175–207. http://dx.doi.org/10.1017/s0308210500003838.

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This paper deals with local and global existence for the solutions of the heat equation in bounded domains with nonlinear boundary damping and source terms. The typical problem studied is where Ω ⊂ Rn (n ≥ 1) is a regular and bounded domain, ∂Ω = Γ0 ∪ Γ1, m > 1, 2 ≤ p < r, where r = 2(n − 1)/(n − 2) when n ≥ 3, r = ∞ when n = 1, 2 and u0 ∈ H1(Ω), u0 = 0 on Γ0. We prove local existence of the solutions in H1(Ω) when m > r/(r + 1−p) or n = 1, 2 and global existence when p ≤ m or the initial datum is inside the potential well associated to the stationary problem.

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26

Sakai, Kazutaka. "Baire's Category Theoretic Classification of Compact Expansive Dynamical Systems." Open Systems & Information Dynamics 09, no. 04 (December 2002): 315–23. http://dx.doi.org/10.1023/a:1021802200549.

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A revised version of the estimation inequality of Akashi [2] is given, and this result is applied to Baire's category theoretic classification of ∊-expansive dynamical systems. Moreover, this classification method is applied to topological classification of shift dynamical systems on finite-dimensional compact domains.

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27

Hauswirth, Adrian, Saverio Bolognani, and Florian Dörfler. "Projected Dynamical Systems on Irregular, Non-Euclidean Domains for Nonlinear Optimization." SIAM Journal on Control and Optimization 59, no. 1 (January 2021): 635–68. http://dx.doi.org/10.1137/18m1229225.

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28

Elin, Mark, Simeon Reich, and David Shoikhet. "Complex dynamical systems and the geometry of domains in Banach spaces." Dissertationes Mathematicae 427 (2004): 1–62. http://dx.doi.org/10.4064/dm427-0-1.

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29

Lone, Waseem Z., and Firdous A. Shah. "Shift-invariant spaces and dynamical sampling in quadratic-phase Fourier domains." Optik 260 (June 2022): 169063. http://dx.doi.org/10.1016/j.ijleo.2022.169063.

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30

Markiewicz, R. S. "Condon domains in the two-dimensional electron gas. III. Dynamical effects." Physical Review B 34, no. 6 (September 15, 1986): 4183–86. http://dx.doi.org/10.1103/physrevb.34.4183.

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31

Guttalu, R. S., and H. Flashner. "A numerical method for computing domains of attraction for dynamical systems." International Journal for Numerical Methods in Engineering 26, no. 4 (April 1988): 875–90. http://dx.doi.org/10.1002/nme.1620260409.

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32

Elghobashi-Meinhardt, Nadia. "Cholesterol Transport in Wild-Type NPC1 and P691S: Molecular Dynamics Simulations Reveal Changes in Dynamical Behavior." International Journal of Molecular Sciences 21, no. 8 (April 22, 2020): 2962. http://dx.doi.org/10.3390/ijms21082962.

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The Niemann–Pick C1 (NPC1) protein is the main protein involved in NPC disease, a fatal lysosomal lipid storage disease. NPC1, containing 1278 amino acids, is comprised of three lumenal domains (N-terminal, middle lumenal, C-terminal) and a transmembrane (TM) domain that contains a five helix bundle referred to as the sterol-sensing domain (SSD). The exact purpose of the SSD is not known, but it is believed that the SSD may bind cholesterol, either as a part of the lipid trafficking pathway or as part of a signaling mechanism. A recent cryo-EM structure has revealed an itraconazole binding site (IBS) in the SSD of human NPC1. Using this structural data, we constructed a model of cholesterol-bound wild-type (WT) and mutant P691S and performed molecular dynamics (MD) simulations of each cholesterol-bound protein. For WT NPC1, cholesterol migrates laterally, in the direction of the lipid bilayer. In the case of P691S, cholesterol is observed for the first time to migrate away from the SSD toward the N-terminal domain via a putative tunnel that connects the IBS with the lumenal domains. Structural features of the IBS are analyzed to identify the causes for different dynamical behavior between cholesterol-bound WT and cholesterol-bound P691S. The side chain of Ser691 in the P691S mutant introduces a hydrogen bond network that is not present in the WT protein. This change is likely responsible for the altered dynamical behavior observed in the P691S mutant and helps explain the disrupted cholesterol trafficking behavior observed in experiments.

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33

MARANGI, C., G. NARDULLI, and G. PASQUARIELLO. "DYNAMICAL PROPERTIES OF NEURAL NETWORKS WITH CORRELATED PATTERNS." International Journal of Modern Physics C 02, no. 03 (September 1991): 773–86. http://dx.doi.org/10.1142/s0129183191000998.

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We investigate the retrieval properties of fully connected saturated neural networks trained by the Edinburgh algorithm with correlated patterns {ξi}. We evaluate the effect of the correlation on the overlap between {ξi} and the network configuration after one time step and on the basins of attraction. We also show that the introduction of the thermal noise does not change the domains of attraction of the correlated memories.

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34

Chen, Xingchao, Robert G. Nystrom, Christopher A. Davis, and Colin M. Zarzycki. "Dynamical Structures of Cross-Domain Forecast Error Covariance of a Simulated Tropical Cyclone in a Convection-Permitting Coupled Atmosphere–Ocean Model." Monthly Weather Review 149, no. 1 (January 2021): 41–63. http://dx.doi.org/10.1175/mwr-d-20-0116.1.

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AbstractUnderstanding the dynamics of the flow-dependent forecast error covariance across the air–sea interface is beneficial toward revealing the potential influences of strongly coupled data assimilation on tropical cyclone (TC) initialization in coupled models, and the fundamental dynamics associated with TC air–sea interactions. A 200-member ensemble of convection-permitting forecasts from a coupled atmosphere–ocean regional model is used to investigate the forecast error covariance across the oceanic and atmospheric domains during the rapid intensification of Hurricane Florence (2018). Forecast uncertainties in both atmospheric and oceanic domains, from an Eulerian perspective, increase with forecast lead time, mainly from TC displacement errors. In a storm-relative framework, the ensemble forecast uncertainties in both domains are predominantly caused by differences in the simulated storm intensity and structure. The largest ensemble spread in the atmospheric pressure, temperature, and wind fields can be found within the TC inner-core region. Alternatively, the largest ensemble spread in the upper-ocean currents and temperature fields are located along the cold wake behind the storm. Cross-domain ensemble correlations between simulated atmospheric (oceanic) observations and oceanic (atmospheric) state variables in the storm-relative coordinates are highly anisotropic, variable dependent, and ultimately driven by the dynamics of TC air–sea interactions. Meaningful and dynamically consistent cross-domain ensemble correlations suggest that it is possible to use atmospheric and oceanic observations to simultaneously update state variables associated with the coupled ocean–atmosphere prediction of TCs using strongly coupled data assimilation. Sensitivity experiments demonstrate that at least 60–80 ensemble members are required to represent physically consistent cross-domain correlations and minimize sampling errors.

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35

Mayne, N. J., I. Baraffe, D. M. Acreman, C. Smith, N. Wood, D. S. Amundsen, J. Thuburn, and D. R. Jackson. "Using the UM dynamical cores to reproduce idealised 3-D flows." Geoscientific Model Development 7, no. 6 (December 18, 2014): 3059–87. http://dx.doi.org/10.5194/gmd-7-3059-2014.

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Abstract. We demonstrate that both the current (New Dynamics), and next generation (ENDGame) dynamical cores of the UK Met Office global circulation model, the UM, reproduce consistently, the long-term, large-scale flows found in several published idealised tests. The cases presented are the Held–Suarez test, a simplified model of Earth (including a stratosphere), and a hypothetical tidally locked Earth. Furthermore, we show that using simplifications to the dynamical equations, which are expected to be justified for the physical domains and flow regimes we have studied, and which are supported by the ENDGame dynamical core, also produces matching long-term, large-scale flows. Finally, we present evidence for differences in the detail of the planetary flows and circulations resulting from improvements in the ENDGame formulation over New Dynamics.

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36

Faivre, G., and J. Mergy. "Dynamical wavelength selection by tilt domains in thin-film lamellar eutectic growth." Physical Review A 46, no. 2 (July 1, 1992): 963–72. http://dx.doi.org/10.1103/physreva.46.963.

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37

Burch, Matthew J., Chris M. Fancher, Srikanth Patala, Marc De Graef, and Elizabeth C. Dickey. "Mapping 180° polar domains using electron backscatter diffraction and dynamical scattering simulations." Ultramicroscopy 173 (February 2017): 47–51. http://dx.doi.org/10.1016/j.ultramic.2016.11.013.

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38

Nakamura, Hiroaki, Susumu Fujiwara, and Tetsuya Sato. "Dynamical process of coalescence of domains in a short chain-molecule system." Computer Physics Communications 142, no. 1-3 (December 2001): 127–30. http://dx.doi.org/10.1016/s0010-4655(01)00350-2.

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39

Zelik, S. V. "Spatial and Dynamical Chaos Generated by Reaction–Diffusion Systems in Unbounded Domains." Journal of Dynamics and Differential Equations 19, no. 1 (June 28, 2006): 1–74. http://dx.doi.org/10.1007/s10884-006-9007-4.

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40

Aleksiev, T., R. Potestio, F. Pontiggia, S. Cozzini, and C. Micheletti. "PiSQRD: a web server for decomposing proteins into quasi-rigid dynamical domains." Bioinformatics 25, no. 20 (August 20, 2009): 2743–44. http://dx.doi.org/10.1093/bioinformatics/btp512.

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41

Miller, Bruce D., and Jonathan E. Clark. "Towards highly-tuned mobility in multiple domains with a dynamical legged platform." Bioinspiration & Biomimetics 10, no. 4 (June 16, 2015): 046001. http://dx.doi.org/10.1088/1748-3190/10/4/046001.

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42

Buck, Wolfgang, and Jürgen Parisi. "Temporal Behavior of the Breakdown of Superconductivity." Zeitschrift für Naturforschung A 44, no. 3 (March 1, 1989): 247–56. http://dx.doi.org/10.1515/zna-1989-0313.

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On a very short time scale, breakdown of superconductivity with increasing transport current turns out to be a highly dynamical process, called “current-induced resistive state”. Magnetic flux domains rapidly move perpendicular to the direction of the transport current applied, with increasing velocity as the current is further increased. At sufficiently high currents, superconductivity is completely destroyed, and the sample ends up in the normal state. In this paper, the first timeresolved measurements of voltage signals induced by the motion of single flux domains are reported. A stability analysis of the superconducting state based on the “Gibbs free energy barrier model” describes the temporal voltage profile generated by a single flux domain, which is solitarily moving across the sample cross-section, as well as the superimposed signals of a series of competing domains, existing simultaneously in the sample. In the latter case, the interaction among the flux domains is taken into account by a monopole ansatz. Studying the onset of the breakdown of superconductivity in type I materials, an oscillatory behavior of the domain size was found. After a few periods, these transients change into a stationary number of flux quanta per domain.

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43

Fan, Jinjun, Shuangshuang Li, and Ge Chen. "On Dynamical Behavior of a Friction-Induced Oscillator with 2-DOF on a Speed-Varying Traveling Belt." Mathematical Problems in Engineering 2017 (2017): 1–19. http://dx.doi.org/10.1155/2017/1208563.

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The dynamical behavior of a friction-induced oscillator with 2-DOF on a speed-varying belt is investigated by using the flow switchability theory of discontinuous dynamical systems. The mechanical model consists of two masses and a speed-varying traveling belt. Both of the masses on the traveling belt are connected with three linear springs and three dampers and are harmonically excited. Different domains and boundaries for such system are defined according to the friction discontinuity. Based on the above domains and boundaries, the analytical conditions of the passable motions, stick motions, and grazing motions for the friction-induced oscillator are obtained mathematically. An analytical prediction of periodic motions is performed through the mapping dynamics. With appropriate mapping structure, the simulations of the stick and nonstick motions in the two-degree friction-induced oscillator are illustrated for a better understanding of the motion complexity.

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44

Noelle, David C. "Is the dynamical hypothesis falsifiable? On unification in theories of cognition." Behavioral and Brain Sciences 21, no. 5 (October 1998): 647–48. http://dx.doi.org/10.1017/s0140525x98441736.

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The dynamical hypothesis is strong in that, for it to be true, every cognitive phenomenon must be best modeled by a dynamical system. Depending on how it is interpreted, however, the hypothesis may be seen as probably false or even unfalsifiable. Strengthening the hypothesis to require unification, or at least coherence, across models in different cognitive domains alleviates this problem.

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45

VITILLARO, ENZO. "ON THE LAPLACE EQUATION WITH NON-LINEAR DYNAMICAL BOUNDARY CONDITIONS." Proceedings of the London Mathematical Society 93, no. 2 (August 7, 2006): 418–46. http://dx.doi.org/10.1112/s0024611506015875.

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The main part of the paper deals with local existence and global existence versus blow-up for solutions of the Laplace equation in bounded domains with a non-linear dynamical boundary condition. More precisely, we study the problem consisting in: (1) the Laplace equation in $(0, \infty) \times \Omega$; (2) a homogeneous Dirichlet condition $(0, \infty) \times \Gamma_0$; (3) the dynamical boundary condition $ \frac {\partial u}{\partial \nu} = - |u_t|^{m-2} u_t + |u|^{p - 2} u$ on $(0, \infty) \times \Gamma_1$; (4) the initial condition $u(0, x) = u_0 (x)$ on $\partial \Omega$. Here $\Omega$ is a regular and bounded domain in $\mathbb{R}^n$, with $n \ge 1$, and $\Gamma_0$ and $\Gamma_1$ endow a measurable partition of $\partial \Omega$. Moreover, $m>1$, $2 \le p < r$, where $r = 2 (n - 1) / (n - 2)$ when $n \ge 3$, $r = \infty$ when $n = 1,2$, and $u_0 \in H^{1/2} (\partial \Omega)$, $u_0 = 0$ on $\Gamma_0$.The final part of the paper deals with a refinement of a global non-existence result by Levine, Park and Serrin, which is applied to the previous problem.

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46

Das, D. B., and V. Nassehl. "Development of a new mathematical model for subsurface water quality management." Water Science and Technology 45, no. 9 (May 1, 2002): 301–7. http://dx.doi.org/10.2166/wst.2002.0264.

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The interfaces between free (e.g., groundwater) and porous (e.g., soil) flow zones in the subsurface represent important transition zones across which many important transfer/exchange processes occur. The understanding of these interactive phenomena and the way these regions behave in combination is, therefore, critical for management of subsurface water quality. Indispensable to this is numerical modelling and simulation as they can handle complex flow domains and minimise the analysis cost and time. In the present work, the hydrodynamic conditions for a combined free and porous flow domain in the subsurface are analysed. An investigation into the fluid dynamical behaviour for different aspect ratios of the domains is of most interest.

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47

SHI, YUMING, and GUANRONG CHEN. "CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS GOVERNED BY CONTINUOUS MAPS." International Journal of Bifurcation and Chaos 15, no. 02 (February 2005): 547–55. http://dx.doi.org/10.1142/s0218127405012351.

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This paper is concerned with chaotification of discrete dynamical systems in finite-dimensional real spaces, via feedback control techniques. A chaotification theorem for one-dimensional discrete dynamical systems and a chaotification theorem for general higher-dimensional discrete dynamical systems are established, respectively. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the maps corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions on two very small disjoint closed subsets in the domains of interest. This condition is weaker than those in the existing relevant literature.

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48

Altukhov, I. V., S. E. Dizhur, M. S. Kagan, N. A. Khvalkovskiy, S. K. Paprotskiy, I. S. Vasil'evskii, and A. N. Vinichenko. "Transport in Short-Period GaAs/AlAs Superlattices with Electric Domains." Физика и техника полупроводников 52, no. 4 (2018): 472. http://dx.doi.org/10.21883/ftp.2018.04.45821.10.

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AbstractElectronic transport in short-period GaAs/AlAs superlattices with resonant cavities was studied at room temperature. The evolution of tunneling current at forward and backward bias sweep was investigated. The step-like decrease in current at some threshold voltage was referred to moving domain formation. The current hysteresis observed in current-voltage characteristics was explained by changes in electrical domain regimes. The series of maxima in the current-voltage characteristics was attributed to resonant tunneling of electrons through several barriers inside the domain. The change of threshold voltage for the domain formation at the change of the cavity parameters explained by the excitation of high-amplitude oscillations in the cavity which demonstrated the possibility to excite oscillations in the THz cavity by dynamical negative resistance of SLs with domains.

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49

Brooke, John M., Sebastian S. James, Alejandro Jimenez-Rodriguez, and Stuart P. Wilson. "Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication." PLOS Computational Biology 18, no. 3 (March 28, 2022): e1009963. http://dx.doi.org/10.1371/journal.pcbi.1009963.

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Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organize in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of ‘subbarrel’ patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.

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Chin, Jonathan, and Peter V. Coveney. "Chirality and domain growth in the gyroid mesophase." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2076 (June 23, 2006): 3575–600. http://dx.doi.org/10.1098/rspa.2006.1741.

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We describe the first dynamical simulations of domain growth during the self-assembly of the gyroid mesophase from a ternary amphiphilic mixture, using the lattice Boltzmann method. The gyroid is a chiral structure; we demonstrate that, for a symmetric amphiphile with no innate preference for left- or right-handed morphologies, the self-assembly process may give rise to a racemic mixture of domains. We use measurements of the averaged mean curvature to analyse the behaviour of domain walls, and suggest that diffusive domain growth may be present in this system.

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