Dynamical Decomposition Research Articles

Controlled Synthesis of Nickel Encapsulated into Nitrogen-Doped Carbon Nanotubes with Covalent Bonded Interfaces: The Structural and Electronic Modulation Strategy for an Efficient Electrocatalyst in Dye-Sensitized Solar Cells

Developing an efficient and low-cost synthetic approach to controllably synthesize non-precious-metal counter electrode (CE) electrocatalysts with superior catalytic activity and electrochemical stability is critically important for the mass production of dye-sensitized solar cells (DSSCs). Herein, we proposed a simple, economical, and easily scalable synthetic route for copyrolysis of melamine and nickel acetate precursors to access the well-defined Ni-encapsulated and nitrogen-doped carbon nanotubes (Ni-NCNTs). The synthetic mechanism was comprehensively investigated by creatively analyzing the phase structure evolution and dynamical decomposition behaviors, and revealed the construction of Ni-NCNTs based on the Ni-catalyzed tip-growth mechanism. Furthermore, the meticulous structural design of Ni nanoparticles intercalated in N-doped CNTs endows Ni-NCNTs with homogeneously distributed Ni–C interfaces, abundant structural defects, and a porous architecture, as well as good electrical conductivity and co...

Direct numerical simulation of turbulent boundary layer over a compliant wall

The performance of compliant wall with different parameters in a spatially developing turbulent boundary layer is investigated by direct numerical simulation. The Reynolds number based on the external flow velocity and the momentum thickness ranges from 300 to approximately 860. The compliant wall is placed in the region starting from 200 to 600 in the streamwise direction, scaled by the inlet momentum thickness. The monoharmonic analysis is carried out for selection of the parameters of compliant wall in numerical simulations. The instantaneous flow fields and the turbulence statistics are presented to show the impact of the compliant wall. A dynamical decomposition of the skin-friction coefficient Cf is performed for examining the sources bringing the variations in Cf. The spatial evolution of compliant wall motion is disclosed, which is a special feature of the boundary layer flow. The spatial–temporal self-correlation of the wall displacement is calculated for obtaining the convection velocity of the wavy motion of compliant wall. The frequency–wavenumber power spectrum of wall pressure fluctuation is presented for studying the interaction of the compliant wall and the above turbulent flow. The effect of the fixed boundaries of the compliant wall is also examined.

Gravitational waves from axion monodromy

Large field inflation is arguably the simplest and most natural variant of slow-roll inflation. Axion monodromy may be the most promising framework for realising this scenario. As one of its defining features, the long-range polynomial potential possesses short-range, instantonic modulations. These can give rise to a series of local minima in the post-inflationary region of the potential. We show that for certain parameter choices the inflaton populates more than one of these vacua inside a single Hubble patch. This corresponds to a dynamical phase decomposition, analogously to what happens in the course of thermal first-order phase transitions. In the subsequent process of bubble wall collisions, the lowest-lying axionic minimum eventually takes over all space. Our main result is that this violent process sources gravitational waves, very much like in the case of a first-order phase transition. We compute the energy density and peak frequency of the signal, which can lie anywhere in the mHz-GHz range, possibly within reach of next-generation interferometers. We also note that this ``dynamical phase decomposition" phenomenon and its gravitational wave signal are more general and may apply to other inflationary or reheating scenarios with axions and modulated potentials.

Renormalizations and Wandering Jordan Curves of Rational Maps

We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations.

Low-frequency variability of the shallow meridional overturning circulation in the South China Sea

The low-frequency variability of the shallow meridional overturning circulation (MOC) in the South China Sea (SCS) is investigated using a Simple Ocean Data Assimilation (SODA) product for the period of 1900–2010. A dynamical decomposition method is used in which the MOC is decomposed into the Ekman, external mode, and vertical shear components. Results show that all the three dynamical components contribute to the formation of the seasonal and annual mean shallow MOC in the SCS. The shallow MOC in the SCS consists of two cells: a clockwise cell in the south and an anticlockwise cell in the north; the former is controlled by the Ekman flow and the latter is dominated by the external barotropic flow, with the contribution of the vertical shear being to reduce the magnitude of both cells. In addition, the strength of the MOC in the south is found to have a falling trend over the past century, due mainly to a weakening of the Luzon Strait transport (LST) that reduces the transport of the external component. Further analysis suggests that the weakening of the LST is closely related to a weakening of the westerly wind anomalies over the equatorial Pacific, which leads to a southward shift of the North Equatorial Current (NEC) bifurcation and thus a stronger transport of the Kuroshio east of Luzon.

Dynamical decomposition theorems of homeomorphisms with zero-dimensional sets of periodic points

In this note, we study some dynamical decomposition theorems of spaces related to given homeomorphisms. First, we prove that if f:X→X is a homeomorphism of an n-dimensional separable metric space X with zero-dimensional set of periodic points, then X can be decomposed into a zero-dimensional bright space of f except n times and an (n−1)-dimensional dark space of f except n times, and also by use of dark spaces, we prove some decomposition theorems of X related to dimension theory and dynamical systems. Finally, we study dynamical decompositions of continuum-wise expansive homeomorphisms.

Direct numerical simulation of spatially developing turbulent boundary layers with opposition control

Opposition control of spatially developing turbulent boundary layers for skin friction drag reduction is studied by direct numerical simulations. The boundary layer extends 800θ0 in the streamwise (x) direction, with θ0 denoting the momentum thickness at the flow inlet. The Reynolds number, based on the external flow velocity and the momentum thickness, ranges from 300 to 860. Opposition control applied in different streamwise ranges, i.e. and as well as the uncontrolled case, are simulated. Statistical results and instantaneous flow fields are presented, with special attention paid to the spatial evolution properties of the boundary layer flow with control and the underlying mechanism. It is observed that a long spatial transient region after the control start and a long recovery region after the control end are present in the streamwise direction. A maximum drag reduction rate of about 22% is obtained as the transient region is passed, and an overshoot in the local skin friction coefficient (Cf) occurs in the recovery region. A new identity is derived for dynamical decomposition of Cf. Reduction of Cf by opposition control and overshoot of Cf in the recovery region are explained by quantifying the contributions from the viscous shear stress term, the Reynolds shear stress term, the mean convection term and other terms.

A Dynamical Decomposition of the Hamiltonian for Analyzing the Time Evolution of Quantum Mechanically Driven Harmonic Oscillator Systems

A Dynamical Decomposition of the Hamiltonian for Analyzing the Time Evolution of Quantum Mechanically Driven Harmonic Oscillator Systems

Analytical Design of Multivariable Control Systems by Dynamical Decomposition Method

Design of multivariable control systems for complex technical plants with several interrelated channels and controlled variables is difficult problem. Usually here it is necessary to provide either independent (autonomous, unrelated) or coherent control of output variables. This design problem can be solved by using the analytical method implying exact, dynamical decomposition of the multivariable plant to the set of an independent single input–single output channels. The dynamic decomposition method is based on decomposing property of the adjunct matrix and provides realized of control action as function of output variables, reference input and measured disturbances (control on output and inputs) of the system. The efficiency of this analytical method is shown by the numerical example of control system design for the turbojet engine of the gas-pumping station with three interrelated channels.

Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems.

We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.

Dynamical Spectrum in Random Dynamical Systems

Dynamical spectrum is a concept in terms of exponential dichotomy. The theory of dynamical spectrum, due to Sacker and Sell, plays important roles in many fields of dynamical systems and differential equations. Noticing its significance and importance, we study in this paper the theory of dynamical spectrum for some general random dynamical systems. More precisely, after introducing a random version of the concept of exponential dichotomy, by using some methods and techniques from dynamical systems and ergodic theory, under some general integrability conditions, we establish the dynamical spectral decomposition theorem in framework of random dynamical systems, which can be regarded as a random version of the deterministic dynamical systems due to Sacker and Sell. In our result, the dynamical spectral intervals and the corresponding spectral subbundles will be given.

An inverse problem for a third order PDE arising in high-intensity ultrasound: Global uniqueness and stability by one boundary measurement

Abstract. In this paper, we consider an inverse problem for the linearized Jordan–Moore–Gibson–Thompson equation, which is a third-order (in time) PDE that arises in nonlinear acoustic waves modeling high-intensity ultrasound. Both canonical recovery problems are investigated: (i) uniqueness and (ii) stability, by use of just one boundary measurement. Our approach relies on the dynamical decomposition of the Jordan–Moore–Gibson–Thompson equation given in [Math. Methods Appl. Sci. 35 (2012), 1896–1929].

Dynamical Decomposition of Markov Processes without Detailed Balance

We introduce a dynamical decomposition view in dealing with Markov processes without detailed balance. This work generalizes a previous decomposition framework on continuous-state Markov processes and explicitly gives its correspondence in discrete-state case. We investigate the dynamical roles of decomposed parts by studying the evolution of relative-entropy-like functions. We find a special definition of relative entropy to unify the dynamical roles played by the detailed balance part and the breaking detailed balance part. The evolution of the relative entropy naturally bounds the convergence of the process.

On dynamics of Out(F n ) on PSL2(ℂ) characters

We introduce and study an open set of PSL2(ℂ) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of discrete, faithful convex-cocompact (i.e. Schottky) characters. This implies, in particular, that the outer automorphism group does not act ergodically on the set of characters with dense image. Hence there is a difference between the geometric (discrete vs. dense) decomposition of the characters, and a natural dynamical decomposition.

Direct numerical simulation of spatially developing turbulent boundary layer for skin friction drag reduction by wall surface-heating or cooling

Direct numerical simulation (DNS) of zero-pressure-gradient spatially developing turbulent boundary layer with uniform heating (UH) or cooling (UC) is performed aiming at skin friction drag reduction. The Reynolds number based on the free-stream velocity, U ∞, the 99% boundary layer thickness at the inlet, δ0, and the kinematic viscosity, ν, is set to be 3000 and the Prandtl number is 0.71. The computational domain is set to be 9πδ0×3δ0×πδ0 in the streamwise, wall-normal, and spanwise directions, respectively. A constant temperature is imposed on the wall. The Richardson number Ri for the buoyancy is varied in the range of −0.1⩽Ri⩽0.1. The DNS results show that UC reduces skin friction drag with a maximum drag reduction rate of 65%, while UH enhances it. The trend is similar to that in channel flow studied by Iida and Kasagi in 1997 and Iida et al.in 2002 and that in spatially developing boundary layer flow by Hattori et al. in 2007. Dynamical decomposition of skin friction drag using the identity equation (FIK identity, discussed by Fukagata et al.in 2002) quantitatively shows that drag reduction by UC is due to reduced Reynolds shear stress (RSS), while drag increase by UH is augmentation of RSS. The control efficiency of UC, however, is found to be largely negative; namely, net power saving is not achieved.

High frequency variability of the Atlantic meridional overturning circulation

Abstract. We compare the variability of the Atlantic meridional overturning circulation (AMOC) as simulated by the coupled climate models of the RAPID project, which cover a wide range of resolution and complexity, and observed by the RAPID/MOCHA array at about 26° N. We analyse variability on a range of timescales, from five-daily to interannual. In models of all resolutions there is substantial variability on timescales of a few days; in most AOGCMs the amplitude of the variability is of somewhat larger magnitude than that observed by the RAPID array, while the time-mean is within about 10 % of the observational estimate. The amplitude of the simulated annual cycle is similar to observations, but the shape of the annual cycle shows a spread among the models. A dynamical decomposition shows that in the models, as in observations, the AMOC is predominantly geostrophic (driven by pressure and sea-level gradients), with both geostrophic and Ekman contributions to variability, the latter being exaggerated and the former underrepresented in models. Other ageostrophic terms, neglected in the observational estimate, are small but not negligible. The time-mean of the western boundary current near the latitude of the RAPID/MOCHA array has a much wider model spread than the AMOC does, indicating large differences among models in the simulation of the wind-driven gyre circulation, and its variability is unrealistically small in the models. In many RAPID models and in models of the Coupled Model Intercomparison Project Phase 3 (CMIP3), interannual variability of the maximum of the AMOC wherever it lies, which is a commonly used model index, is similar to interannual variability in the AMOC at 26° N. Annual volume and heat transport timeseries at the same latitude are well-correlated within 15–45° N, indicating the climatic importance of the AMOC. In the RAPID and CMIP3 models, we show that the AMOC is correlated over considerable distances in latitude, but not the whole extent of the North Atlantic; consequently interannual variability of the AMOC at 50° N, where it is particularly relevant to European climate, is not well-correlated with that of the AMOC at 26° N, where it is monitored by the RAPID/MOCHA array.

Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction

Direct numerical simulation (DNS) of spatially developing turbulent boundary layer with uniform blowing (UB) or uniform suction (US) is performed aiming at skin friction drag reduction. The Reynolds number based on the free stream velocity and the 99% boundary layer thickness at the inlet is set to be 3000. A constant wall-normal velocity is applied on the wall in the range, −0.01U∞ ≤ Vctr ≤ 0.01U∞. The DNS results show that UB reduces the skin friction drag, while US increases it. The turbulent fluctuations exhibit the opposite trend: UB enhances the turbulence, while US suppresses it. Dynamical decomposition of the local skin friction coefficient cf using the identity equation (FIK identity) (Fukagata, Iwamoto & Kasagi, Phys. Fluids, vol. 14, 2002, pp. L73–L76) reveals that the mean convection term in UB case works as a strong drag reduction factor, while that in US case works as a strong drag augmentation factor: in both cases, the contribution of mean convection on the friction drag overwhelms the turbulent contribution. It is also found that the control efficiency of UB is much higher than that of the advanced active control methods proposed for channel flows.

Node adaptive domain decomposition method by radial basis functions

AbstractDuring the last years, there has been increased interest in developing efficient radial basis function (RBF) algorithms to solve partial differential problems of great scale. In this article, we are interested in solving large PDEs problems, whose solution presents rapid variations. Our main objective is to introduce a RBF dynamical domain decomposition algorithm which simultaneously performs a node adaptive strategy. This algorithm is based on the RBFs unsymmetric collocation setting. Numerical experiments performed with the multiquadric kernel function, for two stationary problems in two dimensions are presented. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

E-Science in high energy density science research

We present three achievements related to e-Science in high energy density science research. We have developed a test module of new data base system for nation-wide users of the high power lasers at Osaka University with web technology, flexible control system and XML-database, which provide efficient, accurate and flexible R&D processing. We also constructed a EUV-GRID portal system for integrated computer simulations of laser produced plasma–extreme ultraviolet (LPP–EUV) light source development, which provides flexible framework for automatic sequencing of workflow for the integrated simulations. A dynamical domain decomposition method in molecular dynamic (MD) simulations is required to obtain a good adaptive load balancing for heterogeneous computing environments such as grid. We have developed a new algorithm of the dynamical domain decomposition. We successfully performed large scale MD-message passing interface (MPI) simulations on cluster computers connected through Super-SINET using the National Research Grid Initiative (NAREGI GRID) grid middleware and the new algorithm.

Mechanisms of Interannual Variations of the Meridional Overturning Circulation of the North Atlantic Ocean

Abstract The authors investigate the nature of the interannual variability of the meridional overturning circulation (MOC) of the North Atlantic Ocean using an Estimating the Circulation and Climate of the Ocean (ECCO) assimilation product for the period of 1993–2003. The time series of the first empirical orthogonal function of the MOC is found to be correlated with the North Atlantic Oscillation (NAO) index, while the associated circulation anomalies correspond to cells extending over the full ocean depth. Model sensitivity experiments suggest that the wind is responsible for most of this interannual variability, at least south of 40°N. A dynamical decomposition of the meridional streamfunction allows a further look into the mechanisms. In particular, the contributions associated with 1) the Ekman flow and its depth-independent compensation, 2) the vertical shear flow, and 3) the barotropic gyre flowing over zonally varying topography are examined. Ekman processes are found to dominate the shorter time scales (1.5–3 yr), while for longer time scales (3–10 yr) the MOC variations associated with vertical shear flow are of greater importance. The latter is primarily caused by heaving of the pycnocline in the western subtropics associated with the stronger wind forcing. Finally, how these changes in the MOC affect the meridional heat transport (MHT) is examined. It is found that overall, Ekman processes explain a larger part of interannual variability (3–10 yr) for MHT (57%) than for the MOC (33%).