Search Results (25)

Side-chain engineering is versatile for tuning the chain mobility of graft polymers and governs their thermal stability. However, it remains elusive to predict the graft effect on chain mobility, especially for competitive side-chain types. Here, relying on molecular dynamics simulation and energy landscape theory, we introduce a three-stage virtual pipeline to sequentially refine the screening of graft chain mobility while minimizing computation cost, by taking the example of grafting similar side-chain types (hydroxyethyl methacrylate (HEMA), methyl methacrylate (MMA), and vinyl acetate (VAC)) onto amorphous polypropylene (PP). Ascribed to their structural similarity, these graft systems exhibit a non-evident chain mobility distinction, with the atom displacement—governing the local “roughness” in potential energy landscape (PEL)—exhibiting only weak-to-modest correlation with their initial atomic energy, volume, and stress. This necessitates the subsequent-stage screening for broader PEL navigation, which confirms a stability and roughness rank of VAC ≥ MMA > HEMA > PP, with their chain activation energy revealing that these side chains enhance the PEL roughness through a counterbalance between possibly lowering the overall energy barrier but extensively wrinkling the landscape. Overall, the three-stage screening establishes a state-of-the-art efficient strategy to evaluate thermal stability of graft polymers in stepwise higher precision from local to ergodic roughness inspection. Full article

Usually, when the computation of limiting distributions of (in)homogeneous (in)finite continuous-time Markov chains (CTMC) has to be performed numerically, the algorithm has to be told when to stop the computation. Such an instruction can be constructed based on available ergodicity bounds. One of the analytical methods to obtain ergodicity bounds for CTMCs is the logarithmic norm method. It can be applied to any CTMC; however, since the method requires a guessing step (search for proper Lyapunov functions), which may not be successful, the obtained bounds are not always meaningful. Moreover, the guessing step in the method cannot be eliminated or automated and has to be performed in each new use-case, i.e., for each new structure of the infinitesimal matrix. However, the simplicity of the method makes attempts to expand its scope tempting. In this paper, such an attempt is made. We present a new technique that allows one to apply, in one unified way, the logarithmic norm method to QBDs with countable state spaces. The technique involves the preprocessing of the infinitesimal matrix of the QBD, finding bounding for its blocks, and then merging them into the single explicit upper bound. The applicability of the technique is demonstrated through a series of examples. Full article

In this paper, we consider a class of stochastic differential equations driven by multiplicative $\alpha$-stable ($0<\alpha <2$) Lévy noises. Firstly, we show that there exists a unique strong solution under a local one-sided Lipschitz condition and a general non-explosion condition. Next, the weak Feller and stationary properties are derived. Furthermore, a concrete sufficient condition for the coefficients is presented, which is different from the conditions for SDEs driven by Brownian motion or general squared-integrable martingales. Finally, some ergodic and mixing properties are obtained by using the Foster–Lyapunov criteria. Full article

This research presents a closed-form mathematical framework for assessing the performance of a wireless communication system in the presence of multipath fading channels with an instantaneous signal-to-noise ratio (SNR) subjected to the inverse power Lomax (IPL) distribution. It is demonstrated that depending on the channel parameters, such a model can describe both severe and light fading covering most cases of the well-renowned simplified models (i.e., Rayleigh, Rice, Nakagami-m, Hoyt, $\alpha -\mu$, Lomax, etc.). This study provides the exact results for a basic statistical description of an IPL channel, including the PDF, CDF, MGF, and raw moments. The derived representation was further used to assess the performance of a communication link. For this purpose, the exact expression and their high signal-to-noise ratio (SNR) asymptotics were derived for the amount of fading (AoF), outage probability (OP), average bit error rate (ABER), and ergodic capacity (EC). The closed-form and numerical hyper-Rayleigh analysis of the IPL channel is performed, identifying the boundaries of weak, strong, and full hyper-Rayleigh regimes (HRRs). An in-depth analysis of the system performance was carried out for all possible fading channel parameters’ values. The practical applicability of the channel model was supported by comparing it with real-world experimental results. The derived expressions were tested against a numerical analysis and statistical simulation and demonstrated a high correspondence. Full article

We revisit the problem of the computation of the limiting characteristics of (in)homogeneous continuous-time Markov chains with the finite state space. In general, it can be performed only numerically. The common rule of thumb is to interrupt calculations after quite some time, hoping that the values at some distant time interval will represent the sought-after solution. Convergence or ergodicity bounds, when available, can be used to answer such questions more accurately; i.e., they can indicate how to choose the position and the length of that distant time interval. The logarithmic norm method is a general technique that may allow one to obtain such bounds. Although it can handle continuous-time Markov chains with both finite and countable state spaces, its downside is the need to guess the proper similarity transformations, which may not exist. In this paper, we introduce a new technique, which broadens the scope of the logarithmic norm method. This is achieved by firstly splitting the generator of a Markov chain and then merging the convergence bounds of each block into a single bound. The proof of concept is illustrated by simple examples of the queueing theory. Full article

Adaptive spiral flight and multi-strategy fusion are the foundations of a new FOX optimization algorithm that aims to address the drawbacks of the original method, including weak starting individual ergodicity, low diversity, and an easy way to slip into local optimum. In order to enhance the population, inertial weight is added along with Levy flight and variable spiral strategy once the population is initialized using a tent chaotic map. To begin the process of implementing the method, the fox population position is initialized using the created Tent chaotic map in order to provide more ergodic and varied individual beginning locations. To improve the quality of the solution, the inertial weight is added in the second place. The fox random walk mode is then updated using a variable spiral position updating approach. Subsequently, the algorithm’s global and local searches are balanced, and the Levy flying method and greedy approach are incorporated to update the fox location. The enhanced FOX optimization technique is then thoroughly contrasted with various swarm intelligence algorithms using engineering application optimization issues and the CEC2017 benchmark test functions. According to the simulation findings, there have been notable advancements in the convergence speed, accuracy, and stability, as well as the jumping out of the local optimum, of the upgraded FOX optimization algorithm. Full article

This article, based on network science, aims to contribute to overcoming its geometric and technological phases. The novelty consists in considering links of networks as linked by superimposed networks, termed here multiple superimposed soft networks (MSSN), which is introduced as a research issue. Such links of links (termed here as passive links) concern, for instance, correspondences, incompatibilities, and temporal synchronizations between the occurrences of pairs of active links of effective networks, such as those based on electrical and telecommunication. A possible constitutive mechanism of such passive linkage consists of linkage representations for practices and histories of use expressed by their validating statistical reoccurrences. We consider the possible emergent nature of the passive linkage. The reason for introducing the design and usage of MSSN properties as a research issue involves making new approaches to profile and manage networks available. Correspondence between active linkage and MSSN properties should be a matter for an experiential, machine-learning approach. Research issues relate their possible usage on the active linkage such as for classification, comparations, detection of criticalities, diagnosis, performance evaluation, and regulatory as weak forces. Furthermore, the possible identification of standard corresponding configurations of passive and active linkage is finalized to avoid their establishment or, conversely, in facilitating their establishment and keeping their replication in different contexts (or partially and in combinations) and identifying related standardized approaches (also for classes of configurations having significant levels of equivalence). This research project has methodological generalizing aspects of trans-disciplinarity. We conclude by mentioning related research issues. Full article

This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper’s findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator’s asymptotic $(1-\alpha )$-confidence interval is provided for $0<\alpha <1$ as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology. Full article

In this paper, we consider the ergodic semilinear stochastic partial differential equation driven by additive noise and the long-time behavior of its full discretization realized by a spectral Galerkin method in spatial direction and an Euler scheme in the temporal direction, which admits a unique invariant probability measure. Under the condition that the nonlinearity is once differentiable, the optimal convergence orders of the numerical invariant measures are obtained based on the time-independent weak error, but not relying on the associated Kolmogorov equation. More precisely, the obtained convergence orders are $O({\lambda }_N^{-\gamma })$ in space and $O({\tau }^{\gamma })$ in time, where $\gamma \in (0,1]$ from the assumption $\parallel A^{\frac{\gamma -1}{2}}{Q}^{\frac{1}{2}}{\parallel }_{{\mathcal{L}}_2}$ is used to characterize the spatial correlation of the noise process. Finally, numerical examples confirm the theoretical findings. Full article

Bi_0.5Na_0.5TiO₃-0.06BaTiO₃ (BNT-BT) thin films were prepared via both chemical solution (CSD) and pulsed laser deposition (PLD). The structural, dielectric, and ferroelectric properties were investigated. High stability of the dielectric permittivity or TCC (∆ε/ε (150 °C) ≤ ±15%) over a wide temperature range from room temperature to 300 °C was obtained. Distinctly, the CSD film showed high TCC stability with variation of ±5% up to 250 °C. Furthermore, the CSD film showed an unsaturated ferroelectric hysteresis loop characteristic of the ergodic relaxor phase. However, the PLD one exhibited an almost saturated loop characteristic of the coexistence of both ergodic and non-ergodic states. The energy storage properties of the prepared films were determined using P–E loops obtained at different temperatures. The results show that these films exhibited a stable and improved energy storage density comparable to ceramic capacitors. Moreover, the CSD film exhibited more rigidity and better energy storage density, which exceeded 1.3 J/cm³ under a weak applied field of 317 kV/cm, as well as interesting efficiency in a large temperature range. The obtained results are very promising for energy storage capacitors operating at high temperatures. Full article

In this paper, we consider general Markov chains with discrete time in an arbitrary measurable (phase) space. Markov chains are given by a classical transition function that generates a pair of conjugate linear Markov operators in a Banach space of measurable bounded functions and in a Banach space of bounded finitely additive measures. We study sequences of Cesaro means of powers of Markov operators on the set of finitely additive probability measures. It is proved that the set of all limit measures (points) of such sequences in the weak topology generated by the preconjugate space is non-empty, weakly compact, and all of them are invariant for this operator. We also show that the well-known Doeblin condition $\left(D\right)$ for the ergodicity of a Markov chain is equivalent to condition $(\ast )$: all invariant finitely additive measures of the Markov chain are countably additive, i.e., there are no invariant purely finitely additive measures. We give all the proofs for the most general case. Full article

A dynamic reconfiguration method based on the improved multi-objective dung beetle optimizer (IMODBO) is proposed to reduce the operating cost of the distribution network with distributed generation (DG) and ensure the quality of the power supply, while also minimizing the number of switch operations during dynamic reconfiguration. First, a multi-objective model of distribution network dynamic reconfiguration with the optimization goal of minimizing active power loss and voltage deviation is established. Secondly, the K-means++ clustering algorithm is used to divide the daily load of the distribution network into periods. Finally, using the IMODBO algorithm, the distribution network is reconstructed into a single period. The IMODBO algorithm uses the chaotic tent map to initialize the population, which increases the ergodicity of the initial population and solves the problem of insufficient search space. The algorithm introduces an adaptive weight factor to solve the problem of the algorithm easily falling into a locally optimal solution in the early stage with weak searchability in the later stage. Levy flight is introduced in the perturbation strategy, and a variable spiral search strategy improves the search range and convergence accuracy of the dung beetle optimizer. Reconfiguration experiments on the proposed method were conducted using a standard distribution network system with distributed power generation. Multiple sets of comparative experiments were carried out on the IEEE 33-nodes and PG&E 69-nodes. The results demonstrated the effectiveness of the proposed method in addressing the multi-objective distribution network dynamic reconfiguration problem. Full article

We are studying the quasi-birth-death process and the property of weak ergodicity. Using the C-matrix method, we derive estimates for the rate of convergence to the limiting regime for the general case of the $PH/M/1$ model, as well as the particular case when $m=3$. We provide a numerical example for the case $m=3$, and construct graphs showing the probability of an empty queue and the probability of $p_1\left(t\right)$. Full article

The outdoor terrestrial terahertz (THz) communication links have recently attracted great research and commercial interest in response to the emerging bandwidth-hungry demands for extremely high-speed wireless data transmissions. However, their development is hindered by the random behavior of the atmospheric channel due to the molecular attenuation, adverse weather effects, and atmospheric turbulence (along with free space path loss (FSPL) and pointing errors) due to the stochastic misalignments between the transmitter and the receiver. Thus, in this work, we investigate the joint influence of these detrimental effects on both capacities, i.e., average (ergodic) and outage, of such a typical line of sight (LOS) THz communication link. Specifically, atmospheric turbulence-induced intensity fluctuations can be modeled by using either the suitable gamma or the well-known gamma–gamma distribution for weak and moderate to strong turbulence conditions, respectively. Additionally, weak to strong stochastic misalignment-induced intensity fluctuations, due to generalized pointing errors with non-zero boresight (NZB), are emulated by the appropriate Beckman distribution. Taking into additional consideration the unavoidable presence of FSPL and the different but realistic water vapor concentration values along with the influence of weather conditions, an outage performance analysis has been conducted. Considering the abovementioned significant effects, novel analytical mathematical expressions have been extracted for both average (ergodic) and outage capacity, which are critical metrics that first incorporate the total influence of all of the above significant effects on the THz links’ performance. Through the derived expressions, proper analytical results verified by simulations are presented and demonstrate the validity of our analysis. It is notable that the derived expressions can accommodate realistic parameter values involved in all the above-mentioned major effects and link characteristics. In this context, they provide encouraging quantitative results and outcomes for both capacity metrics under investigation. The latter enables the design and the establishment of modern and future high-speed THz links, which are expected to cover longer propagation distances and thus become even more vulnerable to atmospheric turbulence effect. This is modeled and incorporated in our analysis and expressions contrary to most of the previous works in the open technical literature. Full article

We consider the time-inhomogeneous Prendiville model with failures and repairs. The property of weak ergodicity is considered, and estimates of the rate of convergence for the main probabilistic characteristics of the model are obtained. Several examples are considered showing how such estimates are obtained and how the limiting characteristics themselves are constructed. Full article