Aperiodic State Research Articles

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization.

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Control design under actuator saturation and multi-rate sampling

The problem of designing a stabilizing feedback controller in the presence of saturating actuators and multi-rate (asynchronous) aperiodic state measurements is studied. Specifically, we consider a scenario in which measurements of the plant states are collected at the controller end in a sporadic and asynchronous fashion. A hybrid controller is used to perform a fusion of measurements sampled at different times. In between sampling events, the controller behaves as a copy of the plant and provides a feedback control signal based on the reconstruction of the plant state. The presence of saturation at the plant input limits the value of the components of this signal to a bounded range. When a new measurement is available, the controller state undergoes an instantaneous jump. The resulting system is augmented with a set of timers triggering the arrival of new measurements and analyzed in a hybrid systems framework. Relying on Lyapunov tools for hybrid systems and techniques for control design under saturation, we propose sufficient conditions in the form of matrix inequalities to ensure regional exponential stability of a closed-set containing the origin of the plant, i.e., exponential stability with a guaranteed region of attraction. Specifically, explicit estimates of the basin of attraction are provided in the form of ellipsoidal sets. Leveraging those conditions, a design procedure based on semidefinite programming is proposed to design a stabilizing controller with maximized size of the basin attraction. The effectiveness of the proposed methodology is shown in an example.

Networks and Islands of Genome Nano-architecture and Their Potential Relevance for Radiation Biology : (A Hypothesis and Experimental Verification Hints).

The cell nucleus is a complex biological system in which simultaneous reactions and functions take place to keep the cell as an individualized, specialized system running well. The cell nucleus contains chromatin packed in various degrees of density and separated in volumes of chromosome territories and subchromosomal domains. Between the chromatin, however, there is enough "free" space for floating RNA, proteins, enzymes, ATPs, ions, water molecules, etc. which are trafficking by super- and supra-diffusion to the interaction points where they are required. It seems that this trafficking works somehow automatically and drives the system perfectly. After exposure to ionizing radiation causing DNA damage from single base damage up to chromatin double-strand breaks, the whole system "cell nucleus" responds, and repair processes are starting to recover the fully functional and intact system. In molecular biology, many individual epigenetic pathways of DNA damage response or repair of single and double-strand breaks are described. How these responses are embedded into the response of the system as a whole is often out of the focus of consideration. In this article, we want to follow the hypothesis of chromatin architecture's impact on epigenetic pathways and vice versa. Based on the assumption that chromatin acts like an "aperiodic solid state within a limited volume," functionally determined networks and local topologies ("islands") can be defined that drive the appropriate repair process at a given damage site. Experimental results of investigations of the chromatin nano-architecture and DNA repair clusters obtained by means of single-molecule localization microscopy offer hints and perspectives that may contribute to verifying the hypothesis.

Guest-Controlled Incommensurate Modulation in a Meta-Rigid Metal-Organic Framework Material.

Structural transitions of host systems in response to guest binding dominate many chemical processes. We report an unprecedented type of structural flexibility within a meta-rigid material, MFM-520, which exhibits a reversible periodic-to-aperiodic structural transition resulting from a drastic distortion of a [ZnO4N] node controlled by the specific host–guest interactions. The aperiodic crystal structure of MFM-520 has no three-dimensional (3D) lattice periodicity but shows translational symmetry in higher-dimensional (3 + 2)D space. We have directly visualized the aperiodic state which is induced by incommensurate modulation of the periodic framework of MFM-520·H2O upon dehydration to give MFM-520. Filling MFM-520 with CO2 and SO2 reveals that, while CO2 has a minimal structural influence, SO2 can further modulate the structure incommensurately. MFM-520 shows exceptional selectivity for SO2 under flue-gas desulfurization conditions, and the facile release of captured SO2 from MFM-520 enabled the conversion to valuable sulfonamide products. MFM-520 can thus be used as a highly efficient capture and delivery system for SO2.

Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations

We study the scaling of logarithmic negativity between adjacent subsystems in critical fermion chains with various inhomogeneous modulations through numerically calculating its recently established lower and upper bounds. For random couplings, as well as for a relevant aperiodic modulation of the couplings, which induces an aperiodic singlet state, the bounds are found to increase logarithmically with the subsystem size, and both prefactors agree with the predicted values characterizing the corresponding asymptotic singlet state. For the marginal Fibonacci modulation, the prefactors in front of the logarithm are different for the lower and the upper bound and vary smoothly with the strength of the modulation. In the delocalized phase of the quasiperiodic Harper model, the scaling of the bounds of the logarithmic negativity and that of the entanglement entropy are compatible with the logarithmic scaling of the homogeneous chain. At the localization transition, the scaling of the above entanglement characteristics holds to be logarithmic, but the prefactors are significantly reduced compared to those of the translationally invariant case, roughly by the same factor.

Approximation of the exit probability of a stable Markov modulated constrained random walk

Let X be the constrained random walk on \({\mathbb {Z}}_+^2\) having increments (1, 0), \((-\,1,1)\), \((0,-\,1)\) with jump probabilities \(\lambda (M_k)\), \(\mu _1(M_k)\), and \(\mu _2(M_k)\) where M is an irreducible aperiodic finite state Markov chain. The process X represents the lengths of two tandem queues with arrival rate \(\lambda (M_k)\), and service rates \(\mu _1(M_k)\), and \(\mu _2(M_k)\); the process M represents the random environment within which the system operates. We assume that the average arrival rate with respect to the stationary measure of M is less than the average service rates, i.e., X is assumed stable. Let \(\tau _n\) be the first time when the sum of the components of X equals n for the first time. Let Y be the random walk on \({{\mathbb {Z}}} \times {{\mathbb {Z}}}_+\) having increments \((-\,1,0)\), (1, 1), \((0,-\,1)\) with probabilities \(\lambda (M_k)\), \(\mu _1(M_k)\), and \(\mu _2(M_k)\). Supposing that the queues share a joint buffer of size n, \(p_n =P_{(x_n,m)}(\tau _n < \tau _0)\) is the probability that this buffer overflows during a busy cycle of the system. To the best of our knowledge, the only methods currently available for the approximation of \(p_n\) are classical large deviations analysis giving the exponential decay rate of \(p_n\) and rare event simulation. Let \(\tau \) be the first time the components of Y are equal. For \(x \in {{\mathbb {R}}}_+^2\), \(x(1) + x(2) < 1\), \(x(1) > 0\), and \(x_n = \lfloor nx \rfloor \), we show that \(P_{(n-x_n(1),x_n(2),m)}( \tau < \infty )\) approximates \(P_{(x_n,m)}(\tau _n < \tau _0)\) with exponentially vanishing relative error as \(n\rightarrow \infty \). For the analysis we define a characteristic matrix in terms of the jump probabilities of (X, M). The 0-level set of the characteristic polynomial of this matrix defines the characteristic surface; conjugate points on this surface and the associated eigenvectors of the characteristic matrix are used to define (sub/super) harmonic functions which play a fundamental role both in our analysis and the computation/approximation of \(P_{(y,m)}(\tau < \infty )\).

Multifaceted nonlinear dynamics in $$\mathcal {PT}$$-symmetric coupled Liénard oscillators

We propose a generalized parity-time ($$\mathcal {PT}$$)-symmetric Lienard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of the Jacobian and evaluate the stability threshold thereafter. In the first-order nonlinear damping model, we discover that the temporal evolution of both gain and lossy oscillators attains a complete convergence towards the stable stationary state leading to the emergence of oscillation and amplitude deaths. Also, the system displays a remarkable manifestation of transient chaos in the lossy oscillator while the gain counterpart exhibits growing oscillations for certain choice of initial conditions and control parameters. Employing an external driving force on the loss oscillator, we find that the growing temporal evolution can be controlled and a pure aperiodic state is achievable. On the other hand, the second-order nonlinear damping model yields a completely different dynamics on contrary to the first order where the former reveals a conventional quasiperiodic route to chaos upon decreasing the natural frequency of both gain and loss oscillators. An electronic circuit scheme for the experimental realization of the proposed system has also been put forward.

Separation Principle for Linear Sampled-Data Control Systems Under Observer-Based Output Feedback With Aperiodic Sampling

This paper studies a separation principle for a class of linear sampled-data control systems with aperiodic sampling. The concerned problem is to show that in aperiodic sampling, the design of observer-based output feedback controller can be broken into two separate designs: aperiodic sampled-data static state feedback controller and observer designs. It is proved that asymptotic (respectively, exponential) stabilization by the sampled-data static state feedback and asymptotic (respectively, exponential) observation by the sampled-data Luenberger observer imply asymptotic (respectively, exponential) stabilization by the sampled-data observer-based output feedback. An example is given to check the validity of the proposed theoretical claims.

Optimization of sampling intervals for tracking control of nonlinear systems: A game theoretic approach

This paper presents a near optimal adaptive event-based sampling scheme for tracking control of an affine nonlinear continuous-time system. A zero-sum game approach is proposed by introducing a novel performance index. The optimal value function, i.e., the solution to the associatedHamilton–Jacobi–Issac (HJI) equation is approximated using a functional link neural network (FLNN) with event-based aperiodic state feedback information as inputs. The saddle point approximated optimal solution is employed to design the near optimal event-based control policy and the sampling condition. An impulsive weight update scheme is designed to guarantee local ultimate boundedness of the closed-loop parameters, which is analyzed via extension of Lyapunov stability theory for the impulsive hybrid dynamical systems. Zeno-freeness of the event-sampling scheme is enforced and its effect on stability is analyzed. Finally, numerical simulation results are included to corroborate the analytical design, which shows a 48.82% reduction of feedback communication and computational load.

Separated periodic/aperiodic state feedback control using periodic/aperiodic separation filter based on lifting

Automatic machines have recently advanced into diverse environments. A periodic state and an aperiodic state of the system usually have different physical meanings and require different control objectives in the diverse environments. To enable a new control approach based on the periodic and aperiodic states for the different control objectives, a periodic/aperiodic separation filter (PASF) that separates a state into a periodic state and an aperiodic state is proposed in this paper. Furthermore, using the PASF, the periodic/aperiodic state feedback control and the separation principle are established.

基于Soret和Dufour效应的方腔内双扩散自然对流振荡特性研究

The lattice Boltzmann method was adopted to study the oscillating characteristics of double diffusive natural convection in square cavities with Soret and Dufour effects. The inner heating cylinder with high concentration was located at the center of the cavity and the 4 surrounding walls were assumed to be at low concentrations and temperatures. The impacts of buoyancy ratio B_r(2.0≤B_r≤10.0), Soret number S_r(-0.6≤S_r≤0.0) and Dufour number D_f(-0.6≤D_f≤0.0) on the oscillating characteristics in the cavity were analyzed with the time history method and the power spectrum method. The results show that the flow state is steady at S_r=0.0 and D_f=0.0. With decreasing S_rand D_f from 0.0 to -0.6, the state of double diffusive natural convection turns into the periodic state and in turn the aperiodic oscillatory state gradually. Moreover, the positive buoyancy ratio enhances the oscillating characteristics.

Bifurcation Analysis of a Rotor Supported by Five-Pad Tilting Pad Journal Bearings Using Numerical Continuation

This paper presents analytical bifurcations analysis of a “Jeffcott” type rigid rotor supported by five-pad tilting pad journal bearings (TPJBs). Numerical techniques such as nonautonomous shooting/arc-length continuation, Floquet theory, and Lyapunov exponents are employed along with direct numerical integration (NI) to analyze nonlinear characteristics of the TPJB-rotor system. A rocker pivot type five-pad TPJB is modeled with finite elements to evaluate the fluid pressure distribution on the pads, and the integrated fluid reaction force and moment are utilized to determine coexistent periodic solutions and bifurcations scenarios. The numerical shooting/continuation algorithms demand significant computational workload when applied to a rotor supported by a finite element bearing model. This bearing model may be significantly more accurate than the simplified infinitely short-/long-bearing approximations. Consequently, the use of efficient computation techniques such as deflation and parallel computing methods is applied to reduce the execution time. Loci of bifurcations of the TPJB-rigid rotor are determined with extensive numerical simulations with respect to both rotor spin speed and unbalance force magnitude. The results show that heavily loaded bearings and/or high unbalance force may induce consecutive transference of response in forms of synchronous to subsynchronous, quasi-periodic responses, and chaotic motions. It is revealed that the coexistent responses and their solution manifolds are obtainable and stretch out with selections of pad preload, pivot offset, and lubricant viscosity so that the periodic doubling bifurcations, saddle node bifurcations, and corresponding local stability are reliably determined by searching parameter sets. In case the system undergoes an aperiodic state, the rate of divergence/convergence of the attractor is examined quantitatively by using the maximum Lyapunov exponent (MLE).

Stability analysis of bilinear systems under aperiodic sampled-data control

This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.

Protein crystals can be incommensurately modulated

For a normal periodic crystal, the X-ray diffraction pattern can be described by an orientation matrix and a set of three integers that indicate the reciprocal lattice points. Those integers determine the spacing along the reciprocal lattice directions. In aperiodic crystals, the diffraction pattern is modulated and the standard periodic main reflections are surrounded by satellite reflections. The successful indexing and refinement of the main unit cell andqvector usingTWINSOLVE, developed by Svensson [(2003). Lund University, Sweden], are reported here for an incommensurately modulated, aperiodic crystal of a profilin:actin complex. The indexing showed that the modulation is along thebdirection in the crystal, which corresponds to an `actin ribbon' formed by the crystal lattice. Interestingly, the transition to the aperiodic state was shown to be reversible and the diffraction pattern returned to the periodic state during data collection. It is likely that the protein underwent a conformational change that affected the neighbouring profilin:actin molecules in such a way as to produce the observed modulation in the diffraction pattern. Future work will aim to trap the incommensurately modulated crystal state, for example using cryocooling or chemical crosslinking, thus allowing complete X-ray data to be collected.

Ceramic matrices for plutonium disposition

One of the major issues related to the expanded use of nuclear power and the development of advanced nuclear fuel cycles is the fate of plutonium and “minor” actinides. In addition, substantial quantities of plutonium and highly enriched uranium from dismantled nuclear weapons now require disposition. There are two basic strategies for the disposition of the actinides: (1) to “burn” or transmute the actinides using nuclear reactors or accelerators; (2) to “sequester” the actinides in chemically durable, radiation-resistant materials that are suitable for geologic disposal. This paper deals with actinide-bearing materials that support the latter approach. During the past two decades, a considerable amount of research and development has been done in an effort to develop matrices for the immobilization of plutonium and the “minor actinides”, Np, Am and Cm. A variety of waste form materials – oxides, silicates and phosphates – have been developed that have a high capacity for the incorporation of actinides, are chemically durable and, in some cases, resistant to the radiation-induced transformation to the aperiodic state. These waste forms can be selected depending on the composition of the waste stream that contains the actinides, the desired materials' properties of the waste form, and the geochemical and hydrologic conditions of the specific repository. The present state-of-knowledge for these materials is such that now one can design materials for very specific conditions, such as the thermal history and accumulated radiation dose, in a repository.

Effect of Structure and Thermodynamic Stability on the Response of Lanthanide Stannate Pyrochlores to Ion Beam Irradiation

The lanthanide stannates, Ln2Sn2O7, Ln=La-Lu and Y, have the isometric pyrochlore structure, A2B2O7, and their structural properties have been refined by Rietveld analysis of powder neutron and synchrotron X-ray diffraction data. In this study, the enthalpies of formation of selected stannate pyrochlores, Ln=La, Nd, Sm, Eu, Dy, and Yb, were measured by high-temperature oxide melt solution calorimetry. Their radiation response was determined by 1 MeV Kr2+ ion irradiation combined with in situ TEM observation over the temperature range of 25 to 1000 K. The enthalpy of formation from binary oxides of stannate pyrochlores became more endothermic (from -145 to -40 kJ/mol) as the size of the lanthanide in the A-site decreases. A more exothermic trend of the enthalpy of formation was observed in stannate pyrochlores with larger lanthanide ions, particularly La, possibly as a result of increased covalency in the Sn-O bond. In contrast to lanthanide titanate pyrochlores, Ln2Ti2O7, that are generally susceptible to radiation-induced amorphization and zirconate pyrochlores, Ln2Zr2O7, that are generally resistant to radiation-induced amorphization, the lanthanide stannate pyrochlores show a much greater variation in their response to ion irradiation. La, Nd, and Gd stannates experience the radiation-induced transformation to the aperiodic state, and the critical amorphization temperatures are approximately 960, 700, and 350 K, respectively. Y and Er stannate pyrochlores cannot be amorphized by ion beam irradiation, even at 25 K, and instead disorder to a defect fluorite structure. Comparison of the calorimetric and ion irradiation data for titanate, zirconate, and stannate pyrochlores reveals a strong correlation among subtle changes in crystal structure with changing composition, the energetics of the disordering process, and the temperature above which the material can no longer be amorphized. In summary, as the structure approaches the ideal, ordered pyrochlore structure, radiation-induced amorphization is more easily attained. This is consistent with an increasingly exothermic trend in the enthalpies of formation of pyrochlores from the oxides, that is, the greater the thermochemical stability of the pyrochlore structure, the more likely it will be amorphized upon radiation damage rather than recover to a disordered fluorite structure.

The predictability of large-scale wind-driven flows

Abstract. The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving examples of wind-driven, double-gyre circulations in different flow regimes are explored. By changing the Reynolds number in simple quasi-geostrophic models of the wind-driven circulation, steady, weakly aperiodic and chaotic states may be examined. The singular vectors of the steady state reveal some of the physical mechanisms responsible for optimally growing perturbations. In time-dependent cases, the dominant singular values show significant variability in time, indicating strong variations in the predictability of the flow. When the underlying flow is weakly aperiodic, the dominant singular values co-vary with integral measures of the large-scale flow, such as the basin-integrated upper ocean kinetic energy and the transport in the western boundary current extension. Furthermore, in a reduced gravity quasi-geostrophic model of a weakly aperiodic, double-gyre flow, the behaviour of the dominant singular values may be used to predict a change in the large-scale flow, a feature not shared by an analogous two-layer model. When the circulation is in a strongly aperiodic state, the dominant singular values no longer vary coherently with integral measures of the flow. Instead, they fluctuate in a very aperiodic fashion on mesoscale time scales. The dominant singular vectors then depend strongly on the arrangement of mesoscale features in the flow and the evolved forms of the associated singular vectors have relatively short spatial scales. These results have several implications. In weakly aperiodic, periodic, and stationary regimes, the mesoscale energy content is usually relatively low and the predictability of the wind-driven circulation is determined by the large-scale structure of the flow. In the more realistic, strongly chaotic regime, in which energetic mesoscale eddies are produced by the meandering of the separated western boundary current extension, the predictability of the flow locally tends to be a stronger function of the local mesoscale eddy structure than of the larger scale structure of the circulation. This has a broader implication for the effectiveness of different approaches to forecasting the ocean with models which sequentially assimilate new observations.

Biologically Modeled Noise Stabilizing Neurodynamics for Pattern Recognition

We present a distributed KIII model for the olfactory neural system. Low-level Gaussian noise is introduced to the receptors and anterior olfactory nucleus, which biologically models the peripheral and central sources of noise. The additive noise numerically makes the model stable and robust in respect to repeated input-induced state transitions, while improving the simulations of EEG potentials and multiunit activity from the olfactory system. This hybrid dynamics generates a 1/f aperiodic state, which provides an unpatterned basal state for every module to stay in while there is no significant stimulus. Any external input may guide the system to a certain patterned state. The mechanism is fast, fully parallel, under modulatory control, and flexible in absorbing new patterns from unpredictable environments.

Breaking waves: Bifurcations leading to a singular wave state

We examine free surface wave singularities that show a violent focusing of energy. Periodic, modulated, and frequency locked wave states lead to a state with fluid spikes. When the excitation of free surface waves exceeds a well defined threshold, the waves break leading to a low-dimensional aperiodic state with spikes, droplet ejection, and air entrainment. Return maps formed from wave height measurements lead to a low-dimensional model of the dynamics. Surprisingly, only a slight increase in power dissipation is observed past the transition to ejecting waves.

Radial evolution of corotating merged interaction regions and flows between ≈14 AU and ≈43 AU

During 1993 and 1994 the solar coronal holes and the heliospheric current sheet were relatively stationary, and recurrent streams and interaction regions with periods of the order of the solar rotation period were present within 5 AU. One expects that during 1994 Voyager 2 (V2) (located at ≈43 AU and at ≈12°S latitude, in the sector zone) would have observed some evolutionary form of corotating streams and interaction regions. The “sector zone” is the latitude band in which a spacecraft observes both positive and negative sectors [Burlaga and Ness, 1996]. We present the observations of the magnetic field strength (B), the speed (V), density (N), and proton temperature (T) made by V2‐94, and for reference we also discuss the observations made by V2 at ≈14 AU during 1983 (V2‐83) a solar cycle earlier. Correlated, quasiperiodic variations in B and N with a period of ≈26 days (corotating merged interaction regions) were observed at ≈14 AU but not at ≈43 AU. The speed and temperature profiles were irregular at ≈14 AU but quasiperiodic at ≈43 AU. An ƒ−2 spectrum of the magnetic field strength B (indicating the dominance of shocks) was observed at ≈14 AU, but an ƒ−5/3 spectrum (indicating the dominance of Kolmogorov turbulence) was observed at ≈43 AU in the range (2.7 × 10−6 to 2.3 × 10−5)Hz. An ƒ−2.5 spectrum of the speed fluctuations was observed at ≈14 AU, but an ƒ−2 spectrum was observed at ≈43 AU in the range (8.8 × 10−7 to 2.3 × 10−5)Hz. We suggest the hypothesis that the qualitative differences between the observations at ≈14 AU and ≈43 AU represent a change in the state of the solar wind as it moves between these two positions. This change involves a transition from a quasiperiodic (ordered) state in B and N at ≈14 AU to a disordered state at ≈43 AU and from an aperiodic state in V and T at ≈14 AU to a quasiperiodic state at ≈43 AU. The standard MHD models for the radial evolution of corotating streams and interaction regions have not predicted such a transition. Our results suggest that it would be fruitful to develop a new MHD model of such flows, which should include (1) three‐dimensional effects, (2) the intermediate‐scale fluctuations, and (3) the interstellar pickup ion pressure.