Inter-subsystem Interactions Research Articles

Multilayer network analysis to study complex inter-subsystem interactions in a turbulent thermoacoustic system

Thermoacoustic systems are complex systems where the interactions between the hydrodynamic, acoustic and heat release rate fluctuations lead to diverse dynamics such as chaos, intermittency and ordered dynamics. Such complex interactions cause catastrophically high-amplitude acoustic pressure oscillations and the emergence of order in the spatiotemporal dynamics, referred to as thermoacoustic instability. In this work, we use multilayer networks to study the spatial pattern of inter-subsystem interactions between the vorticity dynamics and thermoacoustic power generated due to acoustically coupled combustion in a bluff-body-stabilised turbulent dump combustor. We construct a two-layered network where the layers represent the thermoacoustic power and vorticity fields. The inter-layer links are determined using cross-variable short-window correlations between vorticity and thermoacoustic power fluctuations at any two locations in the flow field. Analysing the topology of inter-layer networks, using network properties such as degree correlations and link-rank distributions, helps us infer the spatial inhomogeneities in inter-subsystem interactions and unravel the fluid mechanical processes involved during different dynamical states. We show that, during chaotic dynamics, interactions between subsystems are non-localised and spread throughout the flow field of the combustor. During the state of thermoacoustic instability (order), we find that intense interactions occur in between regions of coherent vortex shedding and thermoacoustic power generation and we understand that these processes are strongly and locally coupled. Moreover, we discover that such dense inter-layer connections emerge in spatial pockets in the dump plane of the combustor during the state of intermittency much prior to the onset of order.

Thermodynamically consistent master equationbased on subsystem eigenstates.

Master equationsunder appropriate assumptions are efficient tools for the study of open quantum systems. For many-body systems, subsystems of which locally couple to thermal baths and weakly interact with each other, the local approach provides a more convenient description than the global approach. However, these local master equationsare believed to generate inconsistencies with the laws of thermodynamics when intersubsystem interactions exist. Here we develop an alternative local master equationby virtue of similar approximations used in deriving the traditional Gorini-Kossakowski-Lindblad-Sudarshan master equation. In particular, we stick to using eigenstates of each subsystem to construct quantum jump operators, and the secular approximation is also employed to modify the intersubsystem interactions. Our results show that violations of thermodynamic laws will be avoided after correcting intersubsystem interactions. Finally, we study a two-qubit heat transfer model and this further shows the validity of our modified master equation.

Adaptive Subsystem Density Functional Theory.

Subsystem density functional theory (DFT) is emerging as a powerful electronic structure method for large-scale simulations of molecular condensed phases and interfaces. Key to its computational efficiency is the use of approximate nonadditive noninteracting kinetic energy functionals. Unfortunately, currently available nonadditive functionals lead to inaccurate results when the subsystems interact strongly such as when they engage in chemical reactions. This work disrupts the status quo by devising a workflow that extends subsystem DFT's applicability also to strongly interacting subsystems. This is achieved by implementing a fully automated adaptive definition of subsystems which is realized during geometry optimizations or ab initio molecular dynamics simulations. The new method prescribes subsystem merging and splitting events redistributing the resources (both for work and data) in an efficient way making use of modern parallelization strategies and object-oriented programming. We showcase the method with examples probing from moderate-to-strong inter-subsystem interactions, opening the door to using subsystem DFT for modeling chemical reactions in molecular condensed phases with a black box computational tool.

A Semiclassical Framework for Mixed Quantum Classical Dynamics.

Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.

Deep Variational Quantum Eigensolver: A Divide-And-Conquer Method for Solving a Larger Problem with Smaller Size Quantum Computers

We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate variational quantum eigensolver (VQE) with reducing the dimensions of the system, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded by the reduced basis. Then the effective Hamiltonian is further solved by VQE, which we call {\it deep VQE}. Deep VQE allows us to apply quantum-classical hybrid algorithms on small-scale quantum computers to large systems with strong intra-subsystem interactions and weak inter-subsystem interactions, or strongly correlated spin models on large regular lattices. As proof-of-principle numerical demonstrations, we use the proposed method for Heisenberg anti-ferromagnetic models, including one-dimensionally coupled 12-qubit Heisenberg anti-ferromagnetic models on Kagome lattices. The largest problem size of 48 qubits is solved by simulating 12-qubit quantum computers. The proposed scheme enables us to handle the problems of $>1000$ qubits by concatenating VQE with a few tens of qubits. Deep VQE will provide us a promising pathway to solve practically important problems on noisy intermediate-scale quantum computers.

Primarily Disrupted Default Subsystems Cause Impairments in Inter-system Interactions and a Higher Regulatory Burden in Alzheimer's Disease.

Background: Intrinsically organized large-scale brain networks and their interactions support complex cognitive function. Investigations suggest that the default network (DN) is the earliest disrupted network and that the frontoparietal control network (FPCN) and dorsal attention network (DAN) are subsequently impaired in Alzheimer's disease (AD). These large-scale networks comprise different subsystems (DN: medial temporal lobe (MTL), dorsomedial prefrontal cortex (DM) subsystems and a Core; FPCN: FPCNA and FPCNB). Our previous research has indicated that different DN subsystems are not equally damaged in AD. However, changes in the patterns of interactions among these large-scale network subsystems and the underlying cause of the alterations in AD remain unclear. We hypothesized that disrupted DN subsystems cause specific impairments in inter-system interactions and a higher regulatory burden for the FPCNA.Method: To test this hypothesis, Granger causality analysis (GCA) was performed to explore effective functional connectivity (FC) pattern of these networks. The regional information flow strength (IFS) was calculated and compared across groups to explore changes in the subsystems and their inter-system interactions and the relationship between them. To investigate specific inter-system changes, we summed the inter-system IFS and performed correlation analyses of the bidirectional inter-system IFS, which was compared across groups. Additionally, correlation analyses of dynamic effective FC patterns were performed to reveal alterations in the temporal co-evolution of sets of inter-subsystem interactions. Furthermore, we used partial correlation analysis to quantify the FPCN's regulatory effects. Finally, we applied a support vector machine (SVM) linear classifier to probe which network most effectively discriminated patients from controls.Results: Compared with controls, AD patients showed a decreased intra-DN regional IFS, which was significantly related to the inter-network's IFS. The IFS between the DN subsystems and FPCN subsystems/DAN decreased. Critically, the correlation values of the decreased bidirectional IFS between the DN subsystems and FPCNA diminished. Additionally, the Core and DM play pivotal roles in disordered temporal co-evolution. Furthermore, the FPCNA showed enhanced regulation of the Core. Finally, the MTL subsystem and Core were effective at discriminating patients from controls.Conclusion: The predominantly disrupted DN subsystems caused impaired inter-system interactions and created a higher regulatory burden for the FPCNA.

Network decomposition for distributed control through community detection in input–output bipartite graphs

This paper addresses the decomposition of network systems for distributed control. We construct a novel weighted input–output bipartite graph representation of control systems, in which the input–output edge weights capture topological connectivity and short-time response sensitivities. We then introduce community detection as a network-theoretic tool to generate a decomposition with strong intra-subsystem interactions and weak inter-subsystem interactions. A modularity-based graph bisection procedure is applied recursively to determine the optimal decomposition. The proposed method is applied to a chemical process network example.

Interaction among subsystems within default mode network diminished in schizophrenia patients: A dynamic connectivity approach

Default mode network (DMN) has been reported altered in schizophrenia (SZ) using static connectivity analysis. However, the studies on dynamic characteristics of DMN in SZ are still limited. In this work, we compare dynamic connectivity within DMN between 82 healthy controls (HC) and 82 SZ patients using resting-state fMRI. Firstly, dynamic DMN was computed using a sliding time window method for each subject. Then, the overall connectivity strengths were compared between two groups. Furthermore, we estimated functional connectivity states using K-means clustering, and then investigated group differences with respect to the connectivity strengths in states, the dwell time in each state, and the transition times between states. Finally, graph metrics of time-varying connectivity patterns and connectivity states were assessed. Results suggest that measured by the overall connectivity, HC showed stronger inter-subsystem interaction than patients. Compared to HC, patients spent more time in the states with nodes sparsely connected. For each state, SZ patients presented relatively weaker connectivity strengths mainly in inter-subsystem. Patients also exhibited lower values in averaged node strength, clustering coefficient, global efficiency, and local efficiency than HC. In summary, our findings indicate that SZ show impaired interaction among DMN subsystems, with a reduced central role for posterior cingulate cortex (PCC) and anterior medial prefrontal cortex (aMPFC) hubs as well as weaker interaction between dorsal medial prefrontal cortex (dMPFC) subsystem and medial temporal lobe (MTL) subsystem. For SZ, decreased integration of DMN may be associated with impaired ability in making self-other distinctions and coordinating present mental states with episodic decisions about future.

An integrated approach to vehicle and subsystem sizing and analysis for novel subsystem architectures

The aerospace industry is currently transitioning to More Electric subsystem architectures due to steadily improving electric technologies and the technology saturation of established conventional architectures. For aircraft with such unconventional architectures, the lack of historical information and the presence of increased inter-subsystem interactions create a significant design challenge. These necessitate a greater focus on subsystems design earlier in the design process than typically seen for aircraft with conventional subsystem architectures. At the same time, however, to be suitable for the early design phases, the subsystem analyses must be computationally inexpensive and not require detailed aircraft definition. This work presents an integrated, modular, and tool-independent approach to the sizing and performance analysis of the aircraft and its subsystems, in which inter-dependencies are established between relevant aircraft and subsystem level parameters. The approach allows the assessment of subsystem architectures using vehicle and mission level metrics for a fixed vehicle design, and also the amplified effect of re-sizing the vehicle in accordance with a pre-defined rule-set. The proposed approach was demonstrated through a comparative assessment of a predominantly electric subsystem architecture and a conventional one for a representative single-aisle aircraft. In this assessment, the impacts of changing the form of secondary power extraction, the change in vehicle empty weight, and re-sizing of the vehicle were successively identified.

Hybridization of magnetic excitations between quasi-one-dimensional spin chains and spin dimers in Cu3Mo2O9observed using inelastic neutron scattering

We have studied the exchange interactions and the hybridization effects of two kinds of magnetic excitations in Cu${}_{3}$Mo${}_{2}$O${}_{9}$ by using inelastic neutron scattering. This compound has two magnetic subsystems, i.e., the quasi-one-dimensional (q1D) antiferromagnetic (AF) spin system and the quantum spin dimers. We observe two branches in the magnetic excitations and obtain the magnetic parameters as follows. We evaluate the intrachain interaction ${J}_{4}=4.0$ meV in the q1D AF spin system and the intradimer interaction ${J}_{3}=5.8$ meV in the spin dimers. Applying the interchain mean-field theory (CMF) with the random-phase approximation (RPA), we estimate the mass gap of the q1D AF spin system as 1.2 meV. Using the CMF-RPA theory, the ferromagnetic interchain interaction between the magnetic chain along the $a$ axis and the AF one between the magnetic chains at the center and the corner of the unit cell are estimated to be $\ensuremath{-}{J}_{a}={J}_{\ensuremath{\alpha}\ensuremath{\beta}}=0.19$ meV, respectively. The hybridization parameter, which represents the intersubsystem interaction, has the wave-vector dependence as ${E}_{\mathrm{int}}\mathrm{sin}(\ensuremath{\pi}k)$, where ${E}_{\mathrm{int}}=1.6$ meV and ${\mathit{kb}}^{*}$ denotes the wave vector of magnetic excitation along the ${b}^{*}$ direction. The modulation of the molecular field generated by the magnetic excitation of the q1D AF spin system plays an important role in this hybridization.

Structural and physical properties of a novel misfit-layered cobalt oxide (CaOH)1.14CoO2

We have studied crystal structure and physical properties of a new layered cobalt oxide (CaOH)1.14CoO2. The compound is a composite crystal which consists of two interpenetrating subsystems of the CdI2-type CoO2 layer and the rock-salt-type double CaOH atomic layer. The two subsystems have incommensurate periodicity along the a-axis, resulting in modulated crystal structure due to the inter-subsystem interaction. We found that the observed physical properties originate in the electronic state with a “low-carrier-density limit” in the cobalt t2g band.

Modulated Structure of the Composite Crystal [2CaOH]kCoO2(k=0.576)

We have studied the crystal structure of the new misfit-layer calcium cobaltite [2CaOH] k CoO 2 ( k =0.576) by means of superspace-group formalism using synchrotron x-ray diffraction data. This compound is a kind of a composite crystal which consists of two interpenetrating subsystems: (a) [CoO 2 ] ∞ containing triangular lattices formed by edge-sharing CoO 6 octahedra and (b) [2CaOH] ∞ double-layered rock-salt-type slabs. The two subsystems have incommensurate periodicity along the a -axis ( a 1 / a 2 = k =0.576), resulting in a modulated crystal structure due to the inter-subsystem interaction. It was found that the significant structural modulation is realized in the [2CaOH] subsystem. Modulation in the [CoO 2 ] subsystem is less marked than in the [2CaOH] ones owing to tight bonding of the closed-pack CoO 6 octahedra. Thick CoO 6 octahedra indicate insufficient hole-doping level in this compound.

Modulated crystal structure of the composite crystal (CaOH)1.14CoO2

The crystal structure of the new misfit-layer calcium cobaltite (CaOH)1.14CoO2 was determined by means of superspace-group formalism using synchrotron X-ray diffraction data. The compound belongs to the class of incommensurate composite crystals that are isostructural to an orthorhombic form of sulfide, (PbS)1.18TiS2. The structure of the present compound consists of two interpenetrating subsystems: (i) [CoO2]-containing triangular lattices formed by edge-sharing CoO6 octahedra and (ii) [CaOH] double-layered rock-salt-type slabs. The two subsystems have incommensurate periodicity along the a-axis (a 1/a 2 = 0.576), resulting in a modulated crystal structure due to the inter-subsystem interaction. In this study, it was found that there is a significant structural modulation in the [CaOH] subsystem.

Spin-wave spectrum of copper metaborate in the incommensurate phase [formula omitted

The high-energy branch of the spin-wave spectrum of CuB 2 O 4 in the incommensurate magnetic phase was investigated by means of a linear spin-wave theory. The influence of the intersubsystem interactions on the spectrum of the “strong” subsystem was taken into account as the effective field in the framework of the mean-field approach. The comparison with the inelastic neutron scattering experiment leads to the conclusion about the additional “spiral anisotropy” appearance due to the dynamical interaction through the “weak” subsystem fluctuations (the “order due to disorder” mechanism) in the incommensurate phase.

Neutron scattering study ofSr2Cu3O4Cl2

We report a neutron scattering study on the tetragonal compound ${\mathrm{Sr}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{4}{\mathrm{Cl}}_{2},$ which has two-dimensional (2D) interpenetrating ${\mathrm{Cu}}_{\mathrm{I}}$ and ${\mathrm{Cu}}_{\mathrm{II}}$ subsystems, each forming a $S=1/2$ square lattice quantum Heisenberg antiferromagnet (SLQHA). The mean-field ground state is degenerate, since the intersubsystem interactions are geometrically frustrated. Magnetic neutron scattering experiments show that quantum fluctuations lift the degeneracy and cause a 2D Ising ordering of the ${\mathrm{Cu}}_{\mathrm{II}}$ subsystem. Due to quantum fluctuations a dramatic increase of the ${\mathrm{Cu}}_{\mathrm{I}}$ out-of-plane spin-wave gap is also observed. The temperature dependence and the dispersion of the spin-wave energy are quantitatively explained by spin-wave calculations which include quantum fluctuations explicitly. The values for the nearest-neighbor superexchange interactions between the ${\mathrm{Cu}}_{\mathrm{I}}$ and ${\mathrm{Cu}}_{\mathrm{II}}$ ions and between the ${\mathrm{Cu}}_{\mathrm{II}}$ ions are determined experimentally to be ${J}_{\mathrm{I}\ensuremath{-}\mathrm{I}\mathrm{I}}=\ensuremath{-}10(2)$ meV and ${J}_{\mathrm{II}}=10.5(5)$ meV, respectively. Due to its small exchange interaction ${J}_{\mathrm{II}},$ the 2D dispersion of the ${\mathrm{Cu}}_{\mathrm{II}}$ SLQHA can be measured over the whole Brillouin zone with thermal neutrons, and a dispersion at the zone boundary, predicted by theory, is confirmed. The instantaneous magnetic correlation length of the ${\mathrm{Cu}}_{\mathrm{II}}$ SLQHA is obtained up to a very high temperature, ${T/J}_{\mathrm{II}}\ensuremath{\approx}0.75.$ This result is compared with several theoretical predictions as well as recent experiments on the $S=1/2$ SLQHA.

Nonlinear feedback effects in coupled boson-fermion systems

We address ourselves to a class of systems composed of two coupled subsystems without any intra-subsystem interaction: itinerant Fermions and localized Bosons on a lattice. Switching on an interaction between the two subsystems leads to feedback effects which result in a rich dynamical structure in both of them. Such feedback features are studied on the basis of the flow equation technique - an infinite series of infinitesimal unitary transformations - which leads to a gradual elimination of the inter-subsystem interaction. As a result the two subsystems get decoupled but their renormalized kinetic energies become mutually dependent on each other. Choosing for the inter - subsystem interaction a charge exchange term (the Boson-Fermion model) the initially localized Bosons acquire itinerancy through their dependence on the renormalized Fermion dispersion. This latter evolves from a free particle dispersion into one showing a pseudogap structure near the chemical potential. Upon lowering the temperature both subsystems simultaneously enter a macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a soundwave like dispersion while the Fermions develop a true gap in their dispersion. The essential physical features described by this technique are already contained in the renormalization of the kinetic terms in the respective Hamiltonians of the two subsystems. The extra interaction terms resulting in the process of iteration only strengthen this physics. We compare the results with previous calculations based on selfconsistent perturbative approaches.

Sliding mode and breaking of analyticity in the double-chain model of incommensurate composites

The double chain model (DCM) generalizes the Frenkel-Kontorova model for composite systems, coping with situations when both subsystems are deformable. We show how the shape and amplitude of the intermodulation of subsystems depend on the intersubsystem interaction potential, elastic constants, and average repeat distances of the subsystems. We characterize and study the behavior of the sliding mode, that is a pseudo-Goldstone mode of the system. DCM undergoes an analyticity breaking transition that leads to intrinsic pinning of the sliding mode, when the strength of the intersubsystem coupling is increased above a threshold value.

Ordering due to Quantum Fluctuations inSr2Cu3O4Cl2

Sr{sub 2}Cu {sub 3}O{sub 4}Cl{sub 2} has Cu{sub I } and Cu{sub II } subsystems, forming interpenetrating S=1/2 square lattice Heisenberg antiferromagnets. The classical ground state is degenerate, due to frustration of the intersubsystem interactions. Magnetic neutron scattering experiments show that quantum fluctuations cause a two dimensional Ising ordering of the Cu{sub II } `s, lifting the degeneracy, and a dramatic increase of the Cu{sub I } out-of-plane spin-wave gap, unique for {ital order out of disorder}. The spin-wave energies are quantitatively predicted by calculations which include quantum fluctuations. {copyright} {ital 1999} {ital The American Physical Society }

Dynamics of lattice vibrations for one-dimensional commensurate and incommensurate composites with harmonic interaction

We introduce a model thr.t generalizes the Frenkel-Kontorova model and describes :i one-dimensional (ID ) composite system made of iwo subsystems which are treated on an equal footing. The gap structure of the phonon energy spectrum and the character of lattice vibration are studied. We show that the phason mode may be pinned or not depending on the form of the intersubsystem potential. For a weak intersubsystem interaction the structure of the phonon energy spectrum is universal and may be revealed by a gnomonic projection of l ) onto the plane. For a short-range harmonic interaction there are similarities between this model of composite and ID quasi crystals. The ratio of the periods of the two subsystems along different directions in a composite may be rational or irrational We speak then of commensurate and incommensurate composites, respectively. The incommensurate composites belong to the larger class of incommensurate crystals. The incommensurability of the composites comes neither from the modulation of a basic three-dimensional (3D) crystalline structure (as for the modulated incommensurate crystals) nor from the quasiperiodic repetition of some structural units (as for the quasicrystals and polytypes), but from the existence of several interpenetrating, mutually incommensurate crystalline structures.

Self-consistent embedded clusters: Building block equations for localized orthogonal orbitals

In order to be able to study a large electronic system following a building block approach, in which smaller tractable subsystems are handled at a time rather than the system as a whole, equations are proposed in this paper whose solutions are variational orthogonal orbitals localized on the subsystems. The equations for a given subsystem correspond to a molecular cluster embedded in the field created by the rest of the system, and are coupled to the corresponding equations for all subsystems under consideration, so that they must be solved self-consistently. While the localized nature of the solutions makes the equations appropriate for use in conjunction with local basis sets in practical implementations without significant loss of precision due to truncation errors, their orthogonality properties allow for the use of the advantages of the theory of separability of McWeeny in order to calculate total energies and (generalized product) wave functions. Since the building block equations proposed involve inter-subsystem interactions very cumbersome to calculate, an approximation is proposed in order to make their application to actual problems feasible: the representation of the cumbersome interaction operators by ab initio model potentials which are obtained directly from them, without resorting to any parametrization procedure based on a reference. This ab initio model potential approximation has been found to provide considerable computational savings without significant loss of accuracy in frozen-core calculations on molecules and frozen-lattice calculations on imperfect crystals.