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Using the frequency domain approach, we prove the rational stability for a wave equation with distributed delay on the dynamical control, after establishing the strong stability and the lack of uniform stability.

The aim of this study is to apply a novel technique to control the accuracy and error of the Adomian decomposition method (ADM) for solving nonlinear shallow water wave equation. The ADM is among semi-analytical and powerful methods for solving many mathematical and engineering problems. We apply the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method which is based on stochastic arithmetic (SA). Also instead of applying mathematical packages we use the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. In this library we will write all codes using C++ programming codes. Applying the method we can find the optimal numerical results, error and step of the ADM and they are the main novelties of this research. The numerical results show the accuracy and efficiency of the novel scheme.

In this paper, high-order fully actuated (HOFA) models with multiple orders for general dynamical control systems are firstly proposed, for which controllers can be easily designed such that the cl...

Objective. To analyze the possibilities and efficacy of application of the intervention sonography in complex surgical treatment of patients with bacterial hepatic abscesses. Materials and methods. Results of treatment of 39 patients with hepatic abscesses in Department of Surgery № 3 through period from 2012 till June 2019 yr was presented. The patients were treated, using the puncture aspiration or drainage of abscesses under sonographic guidance. In hepatic abscesses with diameter up to 40 mm a puncture sanation was applied. In all the patients transcutaneous drainage was performed, not depending from the abscesses dimensions and localization. Results. Treatment and application of the intervention sonography was effective in 37 (94.9%) patients. Postoperative complications have occurred in 4 (10.3%) patients: hemorrhage inside the abscess cavity (in 2), durable bile leakage via the drain (in 1), migration of the drain from the abscess cavity (in 1). Average stationary stay of the patients was (19,2 ± 1,6) bed-days. Conclusion. Application of the puncture-draining procedures under sonographic control in treatment of patients, suffering hepatic abscesses constitutes a method of choice, what is caused by their small traumaticity, availability of dynamical control and efficacy in 94.9% patients. But these procedures owe some limitations, connected by the abscesses quantity, their localization, as well as complex configuration and big possibility of presence of large sequesters of necrotized hepatic parenchyma.

In this study, we consider a parametric uncertain Lotka-Volterra cancer model including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. The biological parameter (i.e., cell growth rate) is described as a form of the triangular fuzzy number. By using grade mean value conversion, the imprecise fuzzy parameter is translated into the degree of optimism (λ-integral value λ ∈ [0,1]) interval. We derive the sufficient conditions for the existence of the region of asymptotic stability (RAS) in the fuzzy cancer model. The boundary crisis of transient chaos and properties of RAS are investigated under fuzzy environment. We present a dynamical perturbation control to avoid uncontrolled tumor cell growth and prevent healthy cell extinction.

Marine dissolved organic matter (DOM) holds ~660 billion metric tons of carbon, making it one of Earth’s major carbon reservoirs that is exchangeable with the atmosphere on annual to millennial time scales. The global ocean scale dynamics of the pool have become better illuminated over the past few decades, and those are very briefly described here. What is still far from understood is the dynamical control on this pool at the molecular level; in the case of this Special Issue, the role of microgels is poorly known. This manuscript provides the global context of a large pool of marine DOM upon which those missing insights can be built.

The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function $f$. The relative controllability of the presented semilinear system is discussed. Rothe's fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time $t>0$ is presented. A numerical example is provided to illustrate the obtained theoretical results and a practical example is given to show a possible application of the study.

We study the topological properties of the technology set (the set of all technologically admissible net production output vectors) in the continuous-time dynamic Leontief model in which the control is a function of unproductive consumption. Necessary conditions for the technology set to be closed are obtained.

We consider the wave equation with a delay term in the dynamical control. If the delay term is small enough, we establish the strong stability of this system, but show that it is not exponentially stable. We then prove that the system with delay has the same rational decay rate than the one without delay.

We propose to dynamically control the conductivity of a Josephson junction composed of two weakly coupled one dimensional condensates of ultracold atoms. A current is induced by a periodically modulated potential difference between the condensates, giving access to the conductivity of the junction. By using parametric driving of the tunneling energy, we demonstrate that the low-frequency conductivity of the junction can be enhanced or suppressed, depending on the choice of the driving frequency. The experimental realization of this proposal provides a quantum simulation of optically enhanced superconductivity in pump-probe experiments of high temperature superconductors., Comment: 10 pages, 6 figures

In this paper, we address exponential stablization of transmission problem of the wave equation with dynamical boundary conditions. Using the classical energy method and multiplier technique, we prove that the energy of system exponentially decays.

Phytoplankton biomass in estuarine and continental shelf regions are regulated and modified by physical processes, but these interactions have mostly been investigated at a scale of tens of kilometers, and the role of meso- to sub-mesoscale dynamical processes of freshwater plumes in regulating the spatial and temporal variations of algal biomass is largely unknown. To assess the importance of features at these scales, high-resolution (horizontal spacing smaller than 1 km) cross-sectional profiles of hydrographic and biogeochemical variables were collected in the lower Changjiang Estuary and adjacent continental shelf with a towed, undulating vehicle equipped with sensors measuring fluorescence, turbidity and irradiance. Discrete stations were also occupied to allow for the characterization of nutrients. Multiple physical features at different scales regulated the spatial variation of phytoplankton biomass. Phytoplankton biomass was initialized by an improved irradiance field driven by reduced turbidity together with a rapid development of subsurface stratification at the main plume front (isohaline of 23) downstream from the turbidity maximum zone. Phytoplankton blooms did not occur until outcrops located within the main front that were characterized by surface convergence and downwelling, which contributed to large algal biomass by mass trapping and enhanced light penetration. Wave-like features were detected seaward of the main front, coinciding with deacceleration of currents, indicating that they are front-released internal waves that increase algal retention time. This study revealed the critical role of small-scale processes near the plume front in triggering phytoplankton blooms under the large-scale context of improved light conditions, coastal upwelling and nutrient additions from intruding oceanic waters.

An advanced material interface is modified by using a substrate-independent coating of detachable poly-para-xylylene, enabling dynamical control of the immobilization and detachment of biomolecules, and a previously installed biological function is deactivated or tuned with reduced activity. The induction of osteogenesis activity, and subsequent deactivation of such osteogenesis activity, is demonstrated.

In this work, we study two seemingly unrelated aspects of core genetic nonlinear dynamical control of the competence phenotype in Bacillus subtilis, a common Gram-positive bacterium living in the soil. We focus on hitherto unchartered aspects of the dynamics by exploring the effect of time-scale separation between transcription and translation and, as well, the effect of intrinsic molecular stochasticity. We consider these aspects of regulatory control as two possible evolutionary handles. Hence, using theory and computations, we study how the onset of oscillations breaks the excitability-based competence phenotype in two topologically close evolutionary-competing circuits: the canonical “wild-type” regulation circuit selected by Evolution and the corresponding indirect-feedback inverted circuit that failed to be selected by Evolution, as was shown elsewhere, due to dynamical reasons. Relying on in-silico perturbation of the living state, we show that the canonical core genetic regulation of excitability-based competence is more robust against switching to phenotype-breaking oscillations than the inverted feedback organism. We show how this is due to time-scale separation and stochasticity.

Metamaterials/metasurfaces, which have subwavelength resonating unit cells (i.e., meta‐atoms), can enable unprecedented control over the flow of light. Despite their significant progress, achieving dynamical control of both energy and momentum of light remains a challenge. Here, a mechanically tunable metawall capable of either absorbing light energy or modulating light momentum, by incorporating the magnetic meta‐atoms into a 3D printed origami grating, is theoretically designed and experimentally realized. Through mechanical stretching or compressing of the Miura‐ori pattern, the function of metawall can transit from an absorber, a mirror, to a negative reflector. Particularly, the continuously geometric deformation of the Miura‐ori lattice is a promising approach to compensate the angular dispersion in gradient metasurfaces. Considering the prominent mechanical properties and strong deformation abilities of origami structures, the findings may open an alternative avenue toward lightweight and deployable metadevices with diversified and continuously alterable electromagnetic properties., Here, an origami metawall capable of either absorbing light energy or modulating light momentum is proposed. With external mechanical stimuli, the functions of metawall can be switched among an absorber, a reflective mirror or a negative reflector. The findings may open an alternative avenue toward lightweight and deployable metadevices with diversified and continuously alterable electromagnetic properties.

Annealing of block copolymers has become a tool of great importance for the reconfiguration of nanoparticles. Here, we present the experimental results of annealing block copolymer nanoparticles and a theoretical model to describe the morphological transformation of ellipsoids with striped lamellae into onionlike spheres. A good correspondence between the experimental findings and predictions of the model was observed. The model based on finding the steepest direction of descent of an appropriate free energy leads to a set of Cahn-Hilliard equations that correctly describe the dynamical transformation of striped ellipsoids into onionlike spheres and reverse onionlike particles, regardless of the nature of the annealing process. This universality makes it possible to describe a variety of experimental conditions involving nanoparticles underlying a heating process. A notable advantage of the proposed approach is that it enables selective control of the interaction between the confined block copolymer and the surrounding medium. This feature endows the model with a great versatility to enable the reproduction of several combined effects of surfactants in diverse conditions, including cases with reverse affinities for the block copolymer segments. A phase diagram to describe a variety of morphologies is presented. We employ the relationship between the temperature-dependent Flory-Huggins parameter and the width of the interfaces to account for changes in temperature due to the heating process. Simulation results correctly show how the transformation evolves as the temperature increases. This increment in temperature corresponds to progressively smaller values of the interfacial width. We anticipate that the proposed approach will facilitate the design and more precise control of experiments involving various kinds of annealing processes.

A uniform mathematical framework based on probabilistic graphical models drives the digital twin technologies towards dynamical control with real-time data.

In this paper, a rotating thin-walled beam theory incorporating fiber-reinforced and piezo-composite is developed and used to study the active control for vibration suppression. The structural model accounts for transverse shear strain, primary and secondary warpings, pretwist and presetting angles. In addition, the centrifugal stiffening effect, tennis-racket effect, flapping-lagging-transverse shear and extension-twist couplings are accounted as well. Based on a negative velocity feedback control algorithm, the effective damping performance is optimized by studying anisotropic characteristics of piezo-actuators and elastic tailoring of the host structure. Moreover, relations between damping control authority and design factors, such as rotor speed, presetting and pretwist angles are investigated in detailed.

The problem of guaranteed closed-loop guidance by a given time under incomplete information on the initial state is studied for a dynamical control system with delay by means of the method of open-loop control packages. A solvability criterion is proved for this problem in the case of a finite set of admissible initial states. The proposed technique is illustrated by a specific linear control system of differential equations with delay.

We study pulse control assisted dynamical decoupling through a central spin model in a total Hilbert space. We find that the effective decoupling can be realized by applying a sequence of external pulses. Compared with the bang-bang control which needs infinite strength and infinitesimal short pulses, we show that there is a large parameter space that allows an effective nonperturbative dynamical control. Furthermore, our numerical calculation shows that the reliability can be held for random pulses, such as random pulse time interval or random strength.

In a single two-level trapped ion system, dynamical control of decoherence induced by phase damping involving electric motion of ion and heating effect involving vibrational motion of ion has been investigated. We have found that two kinds of decoherences can be simultaneously suppressed by applying a series of blue sideband and red sideband pulses to drive alternately the ion in a precision-designed manner, thus best results can be obtained with minimal resources.

We consider a dual-core nonlinear waveguide with the parity-time (PT) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce "management" in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features strong robustness when amplitudes of the variation of the LG and ICC coefficients keep a ratio equal to that of their constant counterparts, allowing one to find exact solutions for PT-symmetric solitons. A stability region for the solitons is identified in terms of the management amplitude and period, as well as the soliton's amplitude. In the long-period regime, the solitons evolve adiabatically, making it possible to predict their stability boundaries in an analytical form. The system keeping the Galilean invariance, collisions between moving solitons are considered too., Comment: 12 pages, 9 figures, to be published in Commun. Nonlin. Sci. Numerical Simul

So far the concept is extremely general. The next series of definitions provides for various more concrete restrictions.

In this chapter, the complexity of the dynamical control system in the optimal control problem under extension increases. Herein, it is not linear w.r.t. x and u but is still linear w.r.t. the impulsive control variable. Moreover, the matrix-multiplier for the impulsive control depends on the conventional control \(u(\cdot )\) given by Borel functions. The right-hand side of the dynamical system is assumed to be Borel w.r.t. u. The results of the first chapter are derived for this more general formulation. The concept of extension itself does not change so far, as the space of Borel measures yet suffices to describe all feasible trajectories. The chapter ends with seven exercises.

In this paper, the nonlinear shallow water wave equation is illustrated. The famous semi-analytical method, homotopy analysis method (HAM) is applied for solving this equation. The main novelty, of this study is to validate the numerical results using the stochastic arithmetic, the CESTAC method and the CADNA library. Based on this method, we can find the optimal iteration of the HAM, optimal approximation of the shallow water wave equation and optimal error. The main theorem of the CESTAC method is proved. Based on this theorem, we can show that the number of common significant digits for two successive approximations are almost equal to the number of common significant digits for exact and approximate solutions. Thus instead of traditional absolute error to show the accuracy of method we can apply the new termination criterion depends on two successive approximations. In order to find the convergence region of the HAM, several ħ-curves are demonstrated.

In this paper, a reliable scheme is proposed to solve fuzzy differential equations by fuzzy Runge-Kutta method of order $m$. For this purpose, the stochastic arithmetic and CESTAC method are applied to validate the results. In order to implement the C++ codes, the CADNA library is used. In this case, the optimal step size is found. The examples illustrate the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic.

The aim of this paper is to investigate the Uniqueness solution of Abstract Cauchy Problem represented for fractional order nonlinear dynamical control system involving certain control input and their approach of investigated depended on commutative composite semigroup and some certain conditions in certain space.

In order to achieve a laser output at 1550 nm and a dynamical control, we perform an optimization design for one-dimensional PT-symmetric structure. The optimization is based on the structure parameters and the modulation of the external electric field. The optimization is performed by three steps: to achieve the defect mode, to achieve the amplification of the defect mode and to move the defect mode with a large peak value to the special wavelength 1550 nm. The maximum transmittance can reach 687.4. Through changing the electric field, the transmittance of the structure can be modulated to an arbitrary value from the cut-off state to its maximum value.