Transition Probability Rates Research Articles

Er3+ -doped oxyfluoroborosilicate glass ceramics with embedded CaF2 nanoparticles for 1.53 μm broad band applications

The CaF2 based oxyfluoroborosilicate glasses and glass ceramics doped with Er3+ ions were prepared via melt quench process followed by heat treatment and characterized for 1.53 μm broadband applications. The optimized glass ceramic sample was obtained at 450oC/1h heat treatment. The Er3+ concentration was optimized as 1.0 mol% for efficient emission at 460 nm excitation through concentration dependent luminescence analysis. The spectroscopic parameters such as Ωλ=2,4,6 parameters and the radiative parameters such as spontaneous transition probability rates (AR), branching ratios (βR) and decay times (τR) were calculated applying the standard Judd-Ofelt theory. The effective bandwidth (Δλeff), stimulated emission cross-section (σe), gain bandwidth (σe×Δλeff), quantum efficiency (η) and figure of merit (σe×τR) were calculated as 25.78 nm, 13.42×10-21 cm2, 3.46×10-26 cm3, 82.83% and 5.32×10-23 cm2s, respectively for the optimized glass ceramic sample. The exchange type of energy transfer among the excited Er3+ ions results the quenching in luminescence and the non-exponentiality in decay curves. The systematic investigations carried out indicate that the glass ceramic obtained at 450oC/1h heat treatment was proficient for 1.53 μm broadband fiber lasers and optical amplifiers in S and C band communication window.

Probability rate optimization of positive Markov jump linear systems via DC programming

AbstractWe investigate the stabilization problem of positive Markov jump linear systems by optimizing their transition probability rates. By using the convex property of posynomials and the standard mathematical programming that deals with the difference in convex functions, we show that transition probability rate synthesis problems can be solved via difference‐of‐convex (DC) programming. A numerical example is used to illustrate the effectiveness of our results.

Tailoring Interfacial Electric Field by Gold Nanoparticles Enable Electrocatalytic Lithium Polysulfides Conversion for Lithium-Sulfur Batteries.

Although lithium-sulfur batteries (LSBs) are considered as the promising next rechargeable storage system ascribing to their decent specific capacity of inorganic sulfur, the development is partially impeded by inferior electronic conductivity, severe shuttle effect, and large volume variation. To tackle the issues above, a great deal of effort is made on sulfur-containing polymer (SCP) that shows better electrochemical performance. Nevertheless, sluggish conversion of lithium polysulfides (LiPSs) obstructs battery performance yet. Herein, electrocatalytic LiPSs with full conversion by tailoring the interfacial electric field are discovered based on gold nanoparticles (AuNPs) anchored on sulfurized polyaniline (SPANI). A downhill path of Gibbs free energy from organosulfur polymer to intermediate product means more spontaneously and favorable for full conversion, as the significant enhancement of electron density of state in the vicinity of the HOMO level for the AuNPs increase the electron transition probability rate. This composite delivers satisfactory electrochemical performance, especially increased rate capacity of >300 mAh g-1. Furthermore, catalyst mechanism on molecule level is proposed that AuNPsdominate chemical enhancement and higher electron delocalizablility betweenAuNPs and LiPSs molecules. These results can erect a promising strategy for enhancing lithium polysulfides full conversion.

PREDICTIONS FOR DEMENTIA PREVALENCE IN CHINA BY 2050: A MARKOV MODELING STUDY

Abstract Dementia brings a heavy burden on older adults, their family and the society at large. Accurate prediction of dementia prevlance is important for preventive strategy for fast- ageing China. The purpose of this study is to predict dementia prevalence in China by 2050, taking into account variations in dementia incidence rates and mortality rates in future. Based on two nationally representative Chinese ageing cohorts (i.e. CLHLS, CHARLS), a ten-state Markov model (IMPACT-CAM), including prevalence, transition probability and mortality rate of dementia and its associated cardiovaiscualr diseases and disability, was constructed to predict dementia prevalence in people aged above 60 years by 2050, with different assumptions on the furture trends of dementia incidence and mortality rates. IMPACT-CAM projected there were approximately 57.9 million (95% uncententiy interval 56.3-59.6 m) people with dementia by 2050, assuming constant incidence rate of dementia and declining mortality rates over coming years. In comparison with this assumption, if the incidence rate of dementia decreasing by 1.0% annually coupled with declining mortality rates, the projected number of dementia cases would be 9.8 million less; if dementia incidence and mortality rates both remained constant since 2022, the projection would be 18.5 million less. The estimated dementia prevlance for people aged 60 years in 2050 were 12.0%, 9.9% and 9.5%, respectively. Alongside the irreversible population ageing trend, the number of people with dementia in China is likely to increase rapidly in the near furture. Nevertheless, effective preventing measures of dementia would restrain the surge substantially.

Effects of Na/Al ratio on phonon sideband spectra and luminescent characteristics of Eu3+ doped sodium aluminosilicate glasses

In this work, sodium aluminosilicate (NAS) glass systems were fabricated via traditional melting technique with various Na/Al ratios. Structure and surface morphology of the fabricated glasses were investigated by X-ray diffractometer, Raman spectroscopy and SEM images. Optical characteristics of the fabricated glasses were inspected by photoluminescence (PL) and photoluminescence excitation (PLE) spectra, and the observations showed that intensity of the excitation peak of Eu3+ ions in the NAS glasses at 392 nm increases while one at 463 nm decreases with the increasing of Na/Al ratio. Analysis of the phonon sideband spectra shown a change of multiphonon relative rate (Wmp/W0) of the synthesized glasses relates to Na/Al ratio. By applying the Judd-Ofelt theory, Ωλ = 2,4,6 parameters were evaluated from the PL spectra and used these parameters to estimate the radiative parameters like calculated lifetime (τcal), effective line width (Δλeff), transition probability rate (A), emission cross-section (σp) and branching ratio (βR). Decay curves were measured to investigate luminescence quantum efficiency (η) of Eu3+ emission and η gets value in the 53%–65% region. The color coordinates (x, y) and correlated color temperature (CCT) were also estimated for the synthesized NAS glasses.

On the Cauchy problem for Boltzmann equation modeling a polyatomic gas

In the present article, we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogeneous setting for the full non-linear case, under an extended Grad-type assumption on transition probability rates, which comprises hard potentials for both the relative speed and internal energy with the rate in the interval 0,2, multiplied by an integrable angular part and integrable partition functions. The Cauchy problem is resolved by means of an abstract ordinary differential equation (ODE) theory in Banach spaces for the initial data with finite and strictly positive gas mass and energy, finite momentum, and additionally finite K* polynomial moment, with K* depending on the rate of the transition probability and the structure of a polyatomic molecule or its internal degrees of freedom. Moreover, we prove that polynomially and exponentially weighted Banach space norms associated with the solution are both generated and propagated uniformly in time.

Optical, emission, and excitation dynamics of Eu3+ -doped bismuth-based phosphate glass for visible display laser applications.

Eu3+ -doped-bismuth-based phosphate glasses with chemical equation (60 - x)P2 O5 -20Bi2 O3 -10Na2 CO3 -10SrF2 -xEu2 O3 (PBNSEu), (where x= 0, 0.1, 0.5, 1.0, 1.5 and 2mol%) were fabricated using the melt-quenching method. Obtain X-ray diffraction (XRD), energy-dispersive X-ray (EDAX), and Fourier transform infrared (FTIR) spectra were used to characterize the structure of the prepared PBNSEu glass. The J-O (Judd-Ofelt) intensity parameters (Ω2 , Ω4 ) were estimated using photoluminescence emission spectra. When excited with a xenon lamp at λexc = 394 nm, the most intense red-emission transition occurred at ~612 nm (5 D0 →7 F2 ). J-O intensity parameters were used to calculate radiative properties, whereas the radiative branching ratio (βR ), radiative transition probability (AR ), radiative lifetime (τR ), and total radiative transition rate (Aτ ) were calculated for the transitions 5 D0 →7 FJ (where J = 0-4) and were obtained in the emission spectra for europium ion-doped in the current glass. Using the CIE1931 chromaticity coordinates axes, the colours of various concentrations of Eu3+ ion-doped PBNS glass were evaluated using the emission spectra. Temperature-dependent luminescence spectra were recorded for the optimized PBNSEu20 glass to calculate the activation energy. These results strongly suggested red components in w-LEDs and visible display laser applications.

Rare event asymptotics for exploration processes for random graphs

Large deviations for random graph models has been a topic of significant recent research activity. Much work in this area is focused on the class of dense random graph models (number of edges in the graph scale as n2, where n is the number of vertices) where the theory of graphons has emerged as a principal tool in the study of large deviation properties. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. The aim of this paper is to study an approach for large deviation problems in this regime by establishing large deviation principles (LDP) on suitable path spaces for certain exploration processes of the associated random graph sequence. Exploration processes are an important tool in the study of sparse random graph models and have been used to understand detailed asymptotics of many functionals of sparse random graphs, such as component sizes, surplus, deviations from trees, etc. In the context of rare event asymptotics of interest here, the point of view of exploration process transforms a large deviation analysis of a static random combinatorial structure to the study of a small noise LDP for certain stochastic dynamical systems with jumps. Our work focuses on one particular class of random graph models, namely the configuration model; however, the general approach of using exploration processes for studying large deviation properties of sparse random graph models has broader applicability. The goal is to study asymptotics of probabilities of nontypical behavior in the large network limit. The first key step for this is to establish a LDP for an exploration process associated with the configuration model. A suitable exploration process here turns out to be an infinite-dimensional Markov process with transition probability rates that diminish to zero in certain parts of the state space. Large deviation properties of such Markovian models is challenging due to poor regularity behavior of the associated local rate functions. Our proof of the LDP relies on a representation of the exploration process in terms of a system of stochastic differential equations driven by Poisson random measures and variational formulas for moments of nonnegative functionals of Poisson random measures. Uniqueness results for certain controlled systems of deterministic equations play a key role in the analysis. Next, using the rate function in the LDP for the exploration process we formulate a calculus of variations problem associated with the asymptotics of component degree distributions. The second key ingredient in our study is a careful analysis of the infinite-dimensional Euler–Lagrange equations associated with this calculus of variations problem. Exact solutions of these systems of nonlinear differential equations are identified which then provide explicit formulas for decay rates of probabilities of nontypical component degree distributions and related quantities.

Anti‐disturbance resilient tracking control for semi‐Markov jumping systems

AbstractThis article investigates the output tracking problem of semi‐Markov jump systems with exogenous disturbance and generally uncertain transition probability rates. In particular, the elements in the transition rates are allowed to be known, uncertain or completely unknown. In specific, a state‐space of the modified repetitive controller is considered for tracking the given reference signals. Then, a generalized extended state observer is constructed to estimate the external disturbances and these estimates are incorporated in the control law to reject the disturbances effectively. Moreover, additive gain fluctuations are considered in the control design to tolerate gain fluctuations. First, a continuous‐discrete two‐dimensional (2D) delayed system is developed based on the lifting technique to characterize the repetitive control system's control and learning behavior. Then a sufficient condition for the bounded stability of the 2D hybrid system is obtained by choosing a suitable Lyapunov–Krasovskii functional. In addition, the control and observer gains are evaluated by solving a set of linear matrix inequalities and using the pole placement technique. At last, a robot arm model is presented to show the applicability of the proposed control scheme and a comparison study is made over some existing literature.

Many-server asymptotics for join-the-shortest-queue: Large deviations and rare events

The join-the-shortest-queue routing policy is studied in an asymptotic regime where the number of processors n scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as n→∞, in a suitable infinite-dimensional path space. Model features that present technical challenges include, Markovian dynamics with discontinuous statistics, a diminishing rate property of the transition probability rates, and an infinite-dimensional state space. The difficulty is in the proof of the Laplace lower bound which requires establishing the uniqueness of solutions of certain infinite-dimensional systems of controlled ordinary differential equations. The LDP gives information on the rate of decay of probabilities of various types of rare events associated with the system. We illustrate this by establishing explicit exponential decay rates for probabilities of long queues. In particular, denoting by Ejn(T) the event that there is at least one queue with j or more jobs at some time instant over [0,T], we show that, in the critical case, for large n and T, P(Ejn(T))≈exp[−n(j−2)24T].

Uniformly accelerated quantum counting detector in Minkowski and Fulling vacuum states

In this work we discuss the process of measurements by a detector in an uniformly accelerated rectilinear motion, interacting linearly with a massive scalar field. The detector model for field quanta is a point-like system with a ground state and a continuum of unbounded states. We employ the Glauber theory of photodetection. In an uniformly accelerated reference frame, the detector, interacting with the field prepared in an arbitrary state of the Rindler Fock space, is excited only by absorption processes. For the uniformly accelerated detector prepared in the ground state, we evaluate the transition probability rate in three important situations. In the first one the field is prepared in an arbitrary state of $n$-Rindler quanta, then we consider a thermal Rindler state at a given temperature $\beta^{-1}$, and finally the case in which the state of the field is taken to be the Minkowski vacuum. The well-known result that the latter excitation rates are equal is recovered. Accelerated or inertial observer interpretations of the measurements performed by the accelerated detector is presented. Finally, we investigate the behaviour of the detector in a frame which is inertial in the remote past but in the far future becomes uniformly accelerated. For the massless case, we obtain that the transition probability rate of the detector in the far future is tantamount to the analogous quantity for the detector at rest in a non-inertial reference frame interacting with the field prepared in an usual thermal state.

Dynamic sleep stage transition process analysis in patients with Parkinson's disease having sleep apnea syndrome

Early detection of non-motor symptoms, such as sleep disorder, is recommended for those with Parkinson's disease (PD). It is important to understand the sleep patterns of patients with PD having concomitant sleep apnea syndrome (SAS). The effect of PD on static sleep variables has been investigated, but its effect on the dynamic transition process of sleep stage has not been fully clarified. The aim of this study was to analyze the dynamic transition process of sleep stages between patients with PD with concomitant SAS and non-PD patients with SAS and to clarify one aspect of the difference in sleep disorder pathology in both patient groups. Sleep stage data of 31 patients with PD and concomitant SAS and 31 propensity score matched non-PD patients with SAS were analyzed, and (i) normalized transition probability and transition rate between each sleep stage as well as (ii) cumulative probability density function of the duration of each sleep stage were calculated. It was found that normalized transition probability and transition rate from rapid eye movement (REM) to Wake and from Wake to REM in PD patients with concomitant SAS were significantly lower than those in the non-PD patients with SAS. In addition, the cumulative probability density function of the duration of sleep stages was compared, and Wake and REM of PD patients with concomitant SAS were significantly more likely to continue than those of the non-PD patients with SAS. These results suggest that both REM-to-Wake transition and Wake-to-REM transition are less likely to occur in PD patients with SAS and that the stage is more likely to continue once Wake and REM sleep occur.

Electric Monopole Transitions in Nd Nuclei within IBM-2

The monopole transitions of 144-154Nd isotopes have been investigated in this work within the interacting boson model-2 (IBM-2) framework. The low-lying energy levels, electric quadrupole transition probability rates B(E2), electric quadrupole moments for first excited states monopole transition matrix elements and the intensity ratio were calculated in this work. The results of IBM-2 have been compared with the available experimental data; we have obtained a reasonable agreement. Unfortunately, the experimental data available on E0 transitions are very rare.The electric transition probability rates of beta and gamma bands to ground state band were calculated are fairly good agreement with available experimental values. Concerning the electric transition rates properties in IBM-2, we find that all calculations trends is reproduced well reasonably. The effective charges for neutron bosons and proton bosons calculated within IBM-2 are depending on the IBM-2 symmetries, we get suitable values for which is a constant for all 144-154Nd isotopes because the number of proton bosons is constant. The effective charge for neutron bosons varies from isotope to another

Age-Related Changes in Cortical Connectivity During Surgical Anesthesia.

An advanced understanding of the neurophysiologic changes that occur with aging may help improve care for older, vulnerable surgical patients. The objective of this study was to determine age-related changes in cortical connectivity patterns during surgical anesthesia. This was a substudy analysis of a prospective, observational study characterizing cortical connectivity during surgical anesthesia in adult patients (n = 45) via whole-scalp (16-channel) electroencephalography. Functional connectivity was estimated using a weighted phase lag index (wPLI), which was classified into a discrete set of states through k-means analysis. Temporal dynamics were quantified by occurrence rate and state transition probabilities. The mean global connectivity state transition probability [13.4% (±8.1)] was not correlated with age (ρ = 0.100, p = 0.513). Increasing age was inversely correlated with prefrontal-frontal alpha-beta connectivity (ρ = −0.446, p = 0.002) and positively correlated with frontal-parietal theta connectivity (ρ = 0.414, p = 0.005). After adjusting for anesthetic-related confounders, prefrontal-frontal alpha-beta connectivity remained significantly associated with age (β = −0.625, 95% CI −0.99 to −0.26; p = 0.001), while frontal-parietal theta connectivity was no longer significant (β = 0.436, 95% CI −0.03 to 0.90; p = 0.066). Specific transition states were also examined. Between frontal-parietal connectivity states, transitioning from theta-alpha to theta-dominated connectivity positively correlated with age (ρ = 0.545, p = 0.001). Dynamic connectivity states during surgical anesthesia, particularly involving alpha and theta bandwidths, maybe an informative measure to assess neurophysiologic changes that occur with aging.

On Existence and Uniqueness to Homogeneous Boltzmann Flows of Monatomic Gas Mixtures

We solve the Cauchy problem for the full non-linear homogeneous Boltzmann system of equations describing multi-component monatomic gas mixtures for binary interactions in three dimensions. More precisely, we show existence and uniqueness of the vector value solution by means of an existence theorem for ODE systems in Banach spaces under the transition probability rates assumption corresponding to hard potentials rates in the interval $(0,1]$, with an angular section modeled by an integrable function of the angular transition rates modeling binary scattering effects. The initial data for the vector valued solutions needs to be a vector of non-negative measures with finite total number density, momentum and strictly positive energy, as well as to have a finite $L^1_{k_*}(\mathbb{R}^3)$-integrability property corresponding to a sum across each species of $k_*$-polynomial weighted norms depending on the corresponding mass fraction parameter for each species as much as on the intermolecular potential rates, referred as to the scalar polynomial moment of order $k_*$. The existence and uniqueness rigorous results rely on a new angular averaging lemma adjusted to vector values solution that yield a Povzner estimate with constants that decay with the order of the corresponding dimensionless scalar polynomial moment. In addition, such initial data yields global generation of such scalar polynomial moments at any order as well as their summability of moments to obtain estimates for corresponding scalar exponentially decaying high energy tails, referred as to scalar exponential moments associated to the system solution. Such scalar polynomial and exponential moments propagate as well.

An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities

This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method is general enough to cover a wide spectrum of systems from those with completely known transition probability rates to those with completely unknown transition probability rates. Based on some mode-dependent Lyapunov-Krasovski functionals and making use of the free-connection weighting matrices, new delay-dependent conditions guaranteeing the existence of linear switching surfaces and the stochastic stability of sliding mode dynamics are derived in terms of linear matrix inequalities (LMIs). Then, a sliding mode controller is designed such that the resulted closed-loop system's trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. This paper also proposes an adaptive sliding mode controller design method which applies to cases in which mode-dependent time-varying delays are unknown. All the conditions obtained in this paper are in terms of LMI feasibility problems. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Luminescence properties of Dy3+ doped lithium zinc borosilicate glasses for photonic applications

Different concentrations of Dy3+ ions doped lithium zinc borosilicate glasses of chemical composition (30-x) B2O3 - 25 SiO2 -10 Al2O3 -30 LiF - 5 ZnO - x Dy2O3 (x = 0, 0.1, 0.5, 1.0 and 2.0 mol%) were prepared by the melt quenching technique. The prepared glasses were investigated through X-ray diffraction, optical absorption, photoluminescence and decay measurements. Intensities of absorption bands expressed in terms of oscillator strengths (f) were used to determine the Judd-Ofelt (J-O) intensity parameters Ωλ (λ = 2, 4 and 6). The evaluated J-O parameters were used to determine the radiative parameters such as transition probabilities (AR), total transition probability rate (AT), radiative lifetime (τR) and branching ratios (βR) for the excited 4F9/2 level of Dy3+ ions. The chromaticity coordinates determined from the emission spectra were found to be located in the white light region of CIE chromaticity diagram.

Axion mediated photon to dark photon mixing

The interaction between the dark/mirror sector and the ordinary sector is considered, where the two sectors interact with each other by sharing the same QCD axion field. This feature makes the mixing between ordinary and dark/mirror photons in ordinary and dark electromagnetic fields possible. Perturbative solutions of the equations of motion describing the evolution of fields in ordinary and dark external magnetic fields are found. User-friendly quantities such as transition probability rates and Stokes parameters are derived. Possible astrophysical and cosmological applications of this model are suggested.

White light generation in Dy2O3 -doped NBSAZB glasses

The NBSAZBDy glasses containing different concentrations (0 ≤ x ≤ 2.0 mol%) of Dy2O3 were prepared by conventional melt quenching method. The concentration effect of Dy2O3 on optical absorption, photoluminescence excitation, emission and luminescence decay was investigated. The Dy2O3 concentration was optimized as 1.0 mol% for proficient luminescence in NBSAZBDy glasses. The optical characterization was carried out using the Judd-Ofelt theory. For NBSAZBDy10 glass, the Judd-Ofelt intensity parameters were determined as Ω2 = 6.15 × 10−20; Ω4 = 2.42 × 10−20 and Ω6 = 1.98 × 10−20 cm2 by least square fit method. These intensity parameters were used to evaluate the radiative parameters such as transition probability rates, branching ratios, radiative lifetimes and stimulated emission cross-sections. The chromaticity coordinates calculated from the emission spectra were located in the white region of CIE diagram. The NBSAZBDy10 glass has potential to generate white light under 378 nm excitation.

Response of a rotating detector coupled to a polymer quantized field

Assuming that high energy effects may alter the standard dispersion relations governing quantized fields, the influence of such modifications on various phenomena has been studied extensively in the literature. In different contexts, it has generally been found that, while super-luminal dispersion relations hardly affect the standard results, sub-luminal relations can lead to (even substantial) modifications to the conventional results. A polymer quantized scalar field is characterized by a series of modified dispersion relations along with suitable changes to the standard measure of the density of modes. Amongst the modified dispersion relations, one finds that the lowest in the series can behave sub-luminally over a small domain in wavenumbers. In this work, we study the response of a uniformly rotating Unruh-DeWitt detector that is coupled to a polymer quantized scalar field. While certain sub-luminal dispersion relations can alter the response of the rotating detector considerably, in the case of polymer quantization, due to the specific nature of the dispersion relations, the modification to the transition probability rate of the detector does not prove to be substantial. We discuss the wider implications of the result.