Finite Time Duration Research Articles

Response of a three-species cyclic ecosystem to a short-lived elevation of death rate

A balanced ecosystem with coexisting constituent species is often perturbed by different natural events that persist only for a finite duration of time. What becomes important is whether, in the aftermath, the ecosystem recovers its balance or not. Here we study the fate of an ecosystem by monitoring the dynamics of a particular species that encounters a sudden increase in death rate. For exploration of the fate of the species, we use Monte-Carlo simulation on a three-species cyclic rock-paper-scissor model. The density of the affected (by perturbation) species is found to drop exponentially immediately after the pulse is applied. In spite of showing this exponential decay as a short-time behavior, there exists a region in parameter space where this species surprisingly remains as a single survivor, wiping out the other two which had not been directly affected by the perturbation. Numerical simulations using stochastic differential equations of the species give consistency to our results.

Observer and fault reconstruction-based control design for interval type-2 fuzzy systems

In this study, the finite-time stabilization and multiple faults reconstruction issues are scrutinized for nonlinear control systems in the presence of time-varying state delay, actuator faults and sensor faults in which the underlying system is approximated by dint of fuzzy approach. To be specific, the interval type-2 (IT2) fuzzy technique is deployed in tandem with a non-parallel distribution compensation scheme to linearize such a faulty system. Further, the existence of unknown inputs in both the system and its output are effectively reconstructed with the aid of IT2 fuzzy-based observer, namely the IT2 fuzzy unknown input (UI) observer. Simultaneously, the designed observer also ensures the reconstruction of system state vectors that are not able to be measured. With the help of this reconstruction information, a fault-tolerant control scheme is established to maintain the performance of the addressed system even in the occurrence of unknown faults. Particularly, in this work, the sampling strategy is incorporated with the developed controller design. Overall, the proposed IT2 fuzzy UI observer-based sampled fault-tolerant controller guarantees the stability of the resulting system within a finite-time duration. Furthermore, the Lyapunov stability theory enables to formulate the delay-dependent adequate constraints in the framework of linear matrix inequalities. On the grounds of established criteria, the relations are also constructed for obtaining the controller and observer gain matrices. Eventually, the simulation study is conducted with two numerical examples to validate the theoretical and practical significance of the developed control procedure.

SchröWave: Realistic voice generation by solving two-stage conditional Schrödinger bridge problems

In recent years, methods based on discrete diffusion models have achieved state-of-the-art performances in voice generation [1,2]. In theory, the voice data can be transformed into the exact Gaussian prior distributions only when the diffusion time tends to infinity. But in real applications, the Gaussian prior distribution can only be achieved approximately in a limited time duration run by these diffusion-based methods, thus resulting in sub-optimal sound quality. In this paper, we present the SchröWave to realize the continuous transformation from exact Dirac's deltas to the target voice data distribution in finite time duration, conditioned on middle voice representation with different sizes. At the same time, in order to overcome the difficulty in calculating the score on the low-dimensional manifold of voice data during the generation process, we propose to use a two-stage diffusion and generation method, while each stage implemented by solving a conditional Schrödinger bridge problem. Our experiments on the public data set LJSpeech show that the effect is significant in both objective and subjective evaluation, and achieve the new state-of-the-art MOS of 4.53. Audio samples are available at https://schrowave.github.io.

Extensive Stable Physical Contacts between a Nanoparticle and a Highly Repulsive Polymeric Layer.

Interaction between nanoparticles (NPs) and a layer of grafted and solvated polymer molecules has been widely explored for a variety of applications ranging from fabrication of nanocomposites and sensors to developing nanocoating for virus deactivation. In all of these applications, the solvated polymer molecules are necessarily philic to the NPs, and consequently, driven by the favorable NP-polymer interactions, there is the formation of numerous stable direct (i.e., without any intervening solvent molecule) NP-monomer (monomer of the polymer) contact pairs. In this paper, we propose a paradigm shift in this problem: we employ molecular dynamics (MD) simulations and establish that under appropriate conditions, it is possible to develop numerous stable direct contacts between a NP and a solvated polymer layer even when the polymer molecules are extremely phobic to the NP. Here, by "stable" contacts, we refer to the NP-Polymer contacts that remain intact for a finite duration of time; of course, such contacts, after being intact for a finite time duration, might get broken and reformed. In terms of the mechanism of the process, the NP is driven inside a grafted layer of collapsed (in the absence of solvent) and phobic (to the NP) polymer molecules by a liquid drop (polymer is philic to the liquid). Subsequently, the liquid molecules imbibe and diffuse inside the polymer layer, but the NPs, due to the large steric effect imposed by the polymer molecules, remain localized within the polymer layer. This ensures the establishment of several stable direct contacts between the NP and the highly phobic polymer molecules. We quantify these contacts by their numbers, stability, and frequency of occurrences as well as their dependences on the NP-polymer interaction energies and NP sizes. We also quantify the associated NP dynamics inside the polymeric layer. Finally, we argue that our finding will open up avenues for leveraging NP-polymer interactions for a myriad of applications even for cases where the polymer molecules are phobic to the NPs.

Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model

BackgroundFacing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations.Methods and resultsIn this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention.ConclusionsThis study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications.

Quantum metrology based on symmetry-protected adiabatic transformation: imperfection, finite time duration, and dephasing

The aim of quantum metrology is to estimate target parameters as precisely as possible. In this paper, we consider quantum metrology based on symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising model with a transverse field as a probe and consider the estimation of a longitudinal field. Without the transverse field, the ground state of the probe is given by the Greenberger–Horne–Zeilinger state, and thus the Heisenberg limit estimation of the longitudinal field can be achieved through parity measurement. In our scheme, full information of the longitudinal field encoded on parity is exactly mapped to global magnetization by symmetry-protected adiabatic transformation, and thus the parity measurement can be replaced with global magnetization measurement. Moreover, this scheme requires neither accurate control of individual qubits nor that of interaction strength. We discuss the effects of the finite transverse field and nonadiabatic transitions as imperfection of adiabatic transformation. By taking into account finite time duration for state preparation, sensing, and readout, we also compare performance of the present scheme with a classical scheme in the absence and presence of dephasing.

Controllability Robustness of Henneberg-Growth Complex Networks

It is important for a networked-system to have both good controllability and robustness, where the former measures the ability that the networked system can be properly steered via control to any target state form any initial state within a finite time duration, while the later reflects how well this system can regain its controllability after being destructively attacked. Empirical observations suggest that multi-loop structures are beneficial for enhancing the controllability robustness. The Henneberg-growth mechanism in social networks offers a natural manner to generate multi-clique structures that can be developed to multi-loops by assigning proper edge directions. In this paper, a series of random polygon networks are generated, forming random triangle, rectangle, pentagon and hexagon networks. Then, their controllability robustness is investigated. A realistic measure is designed for characterizing their controllability robustness, which can be used to filter out trivial performances after the network is severely destructed, so that the computation and analysis become much more efficient. Extensive simulation results suggest that, for random polygon networks, 1) non-loop polygon structures are inferior to the loop polygons, confirming that the multi-loop structures are indeed beneficial for controllability robustness; 2) polygons with more sides possess better controllability robustness; and 3) the correlation between controllability robustness and connectivity robustness is weak, implying that the two objectives cannot be enhanced in the same way.

Iterative Control Framework with Application to Guidance Control of Rockets with Impulsive Thrusters

In contrast with traditional control techniques that require a priori verification of complex mathematical conditions, in this paper, we develop a fundamentally new framework of control logic that can be readily applied to a general class of nonlinear systems. Our approach, called the Iterative Control Framework (ICF), uses a novel control logic to guarantee the stability of a closed-loop system without a priori verification of Lyapunov-like conditions. The underlying idea is in repetitive reconfiguration of the control vector provided by a computational routine running in the background in real time during each iteration. The control approach is applicable to a broad class of complex nonlinear systems but is particularly suitable for systems inherently admitting only control action of finite-time duration such as short- and long-range missiles, satellites, and spacecrafts. In this work, we focus on the application of ICF to guidance control of rockets and missiles where actuation is provided via single-use thrusters.

Quantum Otto refrigerators in finite-time cycle period

Finite-time cycle period for a quantum Otto machine implies that either an adiabatic stroke or an isochoric process proceeds in finite time duration. The quantum Otto refrigerators under consideration consist of two adiabatic strokes, where the system (isolated from the heat reservoir) undergoes finite-time unitary transformation, and two isochoric steps, where the system may not reach thermal equilibrium even at the respective ends of the two stages due to finite-time interaction intervals. Using two-time projective measurement method, we find the probability distribution functions of both coefficient of performance and cooling load, which are dependent on the time duration along each process. With these distributions we find the analytical expressions for the performance parameters as well as their fluctuations. We then numerically determine the performance and fluctuations for the refrigerator operating with a two-level system employed in a recent experimental implementation. Our results clarify the role of finite-time durations of four processes on the performance and fluctuations of the quantum Otto refrigerators.

Synchronization control of externally disturbed chaotic spacecraft in pre-assigned settling time

This article reports the design of a novel finite-time robust nonlinear controller for the synchronization of two identical chaotic spacecraft. The proposed controller does not cancel nonlinear terms appearing in the chaotic spacecraft dynamics. Avoiding the cancelation of the nonlinear terms of the plant by the controller makes the closed-loop robust stable in the presence of uncertainties in the chaotic spacecraft parameters; this concept blooms base for the design of computationally efficient simple control law. The proposed finite-time robust nonlinear controller (1) synchronizes two nearly identical chaotic spacecraft in finite-time duration, (2) expedites the convergence of errors vector to zero without oscillation, and (3) eradicates the effects of external disturbances. Analysis based on the Lyapunov second theorem proves that the synchronization error converges fast and verifying the closed-loop’s robust global stability. The finite-time stability technique affirms the convergence of the synchronization error to zero in settling time. This research article also studies the effects of the exogenous disturbances and the controller parameter’s slowly smooth variations on the closed-loop performance. The controller parameter variation analysis sets the procedure for tuning the controller parameters. The computer-based simulation results validate the theoretical findings and provide a comparative performance analysis with the other recently proposed synchronization feedback controllers. This article uses Mathematica 12.0 version in the Microsoft 10 environment for all the simulations.

Fluctuations in irreversible quantum Otto engines

We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent work fluctuations, average work, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. The effects of the irreversibility originating from finite-time cycle operation on the thermodynamic efficiency, work fluctuations, and relative power fluctuations are discussed.

Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness

The initial energy density produced in heavy ion collisions can be estimated with the Bjorken energy density formula after choosing a proper formation time $\tau{_{\rm F}}$. However, the Bjorken formula breaks down at low energies because it neglects the finite nuclear thickness. Here we include both the finite time duration and finite longitudinal extension of the initial energy production. When $\tau{_{\rm F}}$ is not too much smaller than the crossing time of the two nuclei, our results are similar to those from a previous study that only considers the finite time duration. In particular, we find that at low energies the initial energy density has a much lower maximum value but evolves much longer than the Bjorken formula, while at large-enough $\tau{_{\rm F}}$ and/or high-enough energies our result approaches the Bjorken formula. We also find a qualitative difference in that our maximum energy density $\epsilon^{\rm max}$ at $\tau{_{\rm F}}=0$ is finite, while the Bjorken formula diverges as $1/\tau{_{\rm F}}$ and the previous result diverges as $\ln (1/\tau{_{\rm F}})$ at low energies but as $1/\tau{_{\rm F}}$ at high energies. Furthermore, our solution of the energy density approximately satisfies a scaling relation. As a result, the $\tau{_{\rm F}}$-dependence of $\epsilon^{\rm max}$ determines the $A$-dependence, and the weaker $\tau{_{\rm F}}$-dependence of $\epsilon^{\rm max}$ in our results at low energies means a slower increase of $\epsilon^{\rm max}$ with $A$.

Ergodic Tendencies in Sub-Systems Coupled to Finite Reservoirs—Classical and Quantal

Whereas ergodic theories relate to limiting cases of infinite thermal reservoirs and infinitely long times, some ergodicity tendencies may appear also for finite reservoirs and time durations. These tendencies are here explored and found to exist, but only for extremely long times and very soft ergodic criteria. “Weak ergodicity breaking” is obviated by a judicious time-weighting, as found in a previous work [Found. Phys. (2015) 45: 673–690]. The treatment is based on an N-oscillator (classical) and an N-spin (quantal) model. The showing of ergodicity is facilitated by pictorial presentations.

Caching Policies for Transient Data

This work focuses on designing caching policies for transient data, i.e., data which can be used to serve requests only for a finite duration of time after which it becomes redundant. We first characterize the fundamental limit on the performance of caching policies for transient data and characterize the performance of traditional caching policies like LRU for this setting. Traditional caching policies often make decisions based on the popularity of the data being cached. We propose a new caching policy which uses both the popularity and the residual life-time (time remaining before the data becomes redundant) to make caching decisions. We show that in the setting where data being cached is transient, our policy outperforms traditional caching policies.

Statistical Performance Modeling of Solar and Wind-Powered UAV Communications

We develop novel statistical models of the harvested energy from renewable energy sources considering harvest-store-consume (HSC) architecture. We consider three renewable energy harvesting scenarios, i.e., (i) harvesting from the solar power, (ii) harvesting from the wind power, and (iii) hybrid solar and wind power. In this context, we first derive the closed-form expressions for the density functions and moments of the harvested power solar and wind power. Then, we calculate the probability of energy outage at UAVs and signal-to-noise ratio (SNR) outage at ground cellular users. The energy outage occurs when the UAV is unable to support the flight consumption and transmission consumption from its battery power and the harvested power. Due to the intricate distribution of the hybrid solar and wind power, we derive novel closed-form expressions for the moment generating function (MGF) of the harvested solar power and wind power. Then, we apply Gil-Pelaez inversion to evaluate the energy outage at the UAV and SNR outage at the ground users. In addition, we formulate the SNR outage minimization problem and obtain closed-form solutions for the transmit power and flight time of the UAV. Furthermore, we demonstrate the application of moments in computing novel metrics such as the probability of charging the UAV battery within the flight time, average UAV battery charging time, probability of energy outage at UAVs, and the probability of eventual energy outage (i.e., the probability of energy outage in a finite duration of time) at UAVs. Numerical results validate the analytical expressions and reveal interesting insights related to the optimal flight time and transmit power of the UAV as a function of the harvested energy.

Improving the double-exponential windowing method to identify modal frequencies and damping ratios of dynamically large structures

Dynamically large structures can have many closely spaced modes. A particular example is an extruded aluminium panel used for building high-speed trains. Such a structure may be modelled deterministically with a large number of degrees of freedom (dofs), or statistically represented as a statistical energy analysis (SEA) system having particular SEA parameters. In both cases, experimental modal parameter identification may be required. Although there are several commercial packages which can be used for modal parameter identification, alternative methods with different strengths and/or convenience are still desirable. In this paper, the double-exponential windowing method developed by the second author is revisited and improved. Improvements are achieved by taking into account the effect of the finite time duration of Fourier transforms and making use of the real parts of driving point mobilities. The method is easy to implement and the improvements make the choice of the decay rate in the exponential window much flexible: for a very lightly damped structure, it allows to use a large positive decay rate to depress measurement noise, and for a highly damped structure, it allows to use a negative decay rate to make modes more evident or to separate overlapped modes. The usefulness of the improved method are demonstrated for a 30-bladed wheel model with known modal parameters, and for an extruded aluminium panel.

Defining Lagrangian coherent vortices from their trajectories

We study the transport properties of mesoscale eddies (i.e., vortices of 100–200 km in diameter) over a finite time duration. While these oceanic structures are well-known to stir and mix surrounding water, they can also carry and transport water properties in a coherent manner. In this paper, we are interested in dynamic transport properties of these coherent structures, despite their chaotic environment. Here, we reveal that such vortices can be identified based a simple decomposition of their Lagrangian trajectories. We identify and extract coherent vortices as material lines along which particles’ trajectories share similar polar rotations. The proposed method identifies coherent vortices and their centers in an automatic manner. We illustrate our new method by identifying and extracting Lagrangian coherent vortices in different two-dimensional flows.

A Fourier approach to Lagrangian vortex detection.

We study the transport properties of coherent vortices over a finite-time duration. Here, we reveal that such vortices can be identified based on the frequency-domain representation of Lagrangian trajectories. We use Fourier analysis to convert particles' trajectories from their time domain to a presentation in the frequency domain. We then identify and extract coherent vortices as material surfaces along which particles' trajectories share similar frequencies. Our method identifies all coherent vortices in an automatic manner, showing high vortices' monitoring capacity. We illustrate our new method by identifying and extracting Lagrangian coherent vortices in different two- and three-dimensional flows.

Hybrid NOMA for an Energy Harvesting MAC With Non-Ideal Batteries and Circuit Power

We consider a multiple-access channel (MAC), where transmitters are powered by energy harvesting. They are equipped with batteries having non-ideal charging and discharging characteristics, resulting in a fractional loss of power driven into or drawn from them. Assuming that each user consumes constant power for circuit operation during transmission, we optimize the throughput region, the set of all tuples of the number of bits delivered by the users over a finite duration of time. When circuit powers are zero, it is known that a non-orthogonal multiple access (NOMA) strategy, called Pure-NOMA (P-NOMA), where user transmissions always overlap, achieves all points on the largest throughput region. We show that P-NOMA is no longer optimal with non-zero circuit power and propose a hybrid strategy called H-NOMA that combines P-NOMA with time-division multiple access (TDMA). H-NOMA allocates fixed time windows for single-user and non-orthogonal multi-user transmissions. We maximize the sum-throughput in H-NOMA with non-casual and causal knowledge of the harvested powers and channel power gains. With causal knowledge, we obtain the optimal online policy via dynamic programming and deduce some structural properties and propose a simpler suboptimal online policy that performs significantly better than a naive greedy policy. We numerically show the largest throughput regions of P-NOMA and TDMA are contained within that of H-NOMA.

Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates

We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the existence and uniqueness of the solution to the optimality equation out of a class of possibly unbounded functions, to which the Feynman–Kac formula was also justified to hold.