Exact Analytical and Numerical Solutions to the Time-Dependent Schrödinger Equation for a One-Dimensional Potential Exhibiting Non-Exponential Decay at All Times

The departure at large times from exponential decay in the case of resonance wavefunctions is mathematically demonstrated. Then, exact, analytical solutions to the time-dependent Schr?dinger equation in one dimension are developed for a time-independent potential consisting of an infinite wall and a repulsive delta function. The exact solutions are obtained by means of a superposition of time-independent solutions spanning the given Hilbert space with appropriately chosen spectral functions for which the resulting integrals can be evaluated exactly. Square-integrability and the boundary conditions are satisfied. The simplest of the obtained solutions is presented and the probability for the particle to be found inside the potential well as a function of time is calculated. The system exhibits non-exponential decay for all times;the probability decreases at large times as . Other exact solutions found exhibit power law behavior at large times. The results are generalized to all normalizable solutions to this problem. Additionally, numerical solutions are obtained using the staggered leap-frog algorithm for select potentials exhibiting the prevalence of non-exponential decay at short times.

INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.

αDecay in extreme laser fields within a deformed Gamow-like model

In this study, the effect of extreme laser fields on the α decay process of ground-state even–even nuclei was investigated.Using the deformed Gamow-like model, we found that state-of-the-art lasers can cause a slight change in the α decay penetration probability of most nuclei. In addition, we studied the correlation between the rate of change of the α decay penetration probability and angle between the directions of the laser electric field and α particle emission for different nuclei. Based on this correlation, the average effect of extreme laser fields on the half-life of many nuclei with arbitrary α particle emission angles was calculated. The calculations show that the laser suppression and promotion effects on the α decay penetration probability of the nuclei population with completely random α particle-emission directions are not completely canceled.The remainder led to a change in the average penetration probability of the nuclei. Furthermore, the possibility of achieving a higher average rate of change by altering the spatial shape of the laser is explored. We conclude that circularly polarized lasers may be helpful in future experiments to achieve a more significant average rate of change of the α decay half-life of the nuclei population.

Microbial Growth and Decay: A Commented Review of the Model

The paper reviews previous publications and reports some comments about a semi empirical model of the growth and decay process of a planktonic microbial culture. After summarizing and reshaping some fundamental mathematical expressions, the paper highlights the reasons for the choice of a suitable time origin that makes the parameters of the model self-consistent. Besides the potential applications to predictive microbiology studies and to effects of bactericidal drugs, the model allows a suitable proxy of the fitness of the microbial culture, which can be of interest for the studies on the evolution across some thousand generations of a Long Term Evolution Experiment.

Calculation of Particle Decay Times in the Standard Model

We present here a two-step method of classification and calculation for decay rates in the Standard Model. The first step is a phenomenological classification method, which is an extended and improved schematic experimental formula for decay width originally introduced by Chang. This schematic formula separates decays into seven classes. Furthermore, from it is derived a process-specific interaction energy mX. The second step is a numerical calculation method, which calculates this interaction energy mX numerically by minimization of action from the Lagrangian of the process, from which follows the decay width via the phenomenological formula. The Lagrangian is based on an extension of the Standard Model, the extended SU(4)-preon-model. A comparison of numerically calculated and observed decay widths for a large selection of decays shows a good agreement.

Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

Effects of sequential decay on collective flows and nuclear stopping power in heavy-ion collisions at intermediate energies

In this study, the rapidity distribution, collective flows, and nuclear stopping power in ^(197)Au+^(197)Au collisions at intermediate energies were investigated using the ultrarelativistic quantum molecular dynamics(UrQMD) model with GEMINI++ code. The UrQMD model was adopted to simulate the dynamic evolution of heavy-ion collisions, whereas the GEMINI++ code was used to simulate the decay of primary fragments produced by UrQMD. The calculated results were compared with the INDRA and FOPI experimental data. It was found that the rapidity distribution, collective flows, and nuclear stopping power were affected to a certain extent by the decay of primary fragments, especially at lower beam energies. Furthermore, the experimental data of the collective flows and nuclear stopping power at the investigated beam energies were better reproduced when the sequential decay effect was included.

GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN R^(3)

In this paper, we consider the initial value problem for the incompressible generalized Phan-Thien-Tanner(GPTT) model. This model pertains to the dynamic properties of polymeric fluids. Under appropriate assumptions on smooth function f, we find a particular solution to the GPTT model. In dimension three, we establish the global existence and the optimal time decay rates of strong solutions provided that the initial data is close to the particular solution. The results which are presented here are generalizations of the network viscoelastic models.

Random forest-based prediction of decay modes and half-lives of superheavy nuclei

Information on the decay process of nuclides in the superheavy region is critical in investigating new elements beyond oganesson and the island of stability.This paper presents the application of a random forest algorithm to examine the competition among different decay modes in the superheavy region,includingα decay,β^(-)decay,β^(+)decay,electron capture and spontaneous fission.The observed half-lives and dominant decay mode are well reproduced.The dominant decay mode of 96.9%of the nuclei beyond ^(212) Po is correctly obtained.Further,α decay is predicted to be the dominant decay mode for isotopes in new elements Z=119-122,except for spontaneous fission in certain even–even elements owing to the increased Coulomb repulsion and odd–even effect.The predicted half-lives demonstrate the existence of a long-lived spontaneous fission island southwest of ^(298) Fl caused by the competition between the fission barrier and Coulomb repulsion.A better understanding of spontaneous fission,particularly beyond ^(286)Fl,is crucial in the search for new elements and the island of stability.

Gamma-,neutron-,and muon-induced environmental background simulations for 100Mo-based bolometric double-beta decay experiment at Jinping Underground Laboratory

The sensitivity of an experiment to detect the Majorana neutrino mass via neutrinoless double-beta decay(0νββ) strongly depends on the rate of background events that can mimic this decay. One major source of this background is the radioactive emissions from the laboratory environment. In our study, we focused on assessing the background contributions from environmental gamma rays, neutrons, and underground muons to the Jinping bolometric demonstration experiment. This experiment uses an array of lithium molybdate crystal bolometers to probe the potential 0νββ decay of the100Mo isotope at the China Jinping Underground Laboratory. We also evaluated the shielding effectiveness of the experimental setup through an attenuation study. Our simulations indicate that the combined background from environmental gamma rays, neutrons, and muons in the relevant100Mo 0νββ Q-value region can be reduced to approximately 0.003 cts/kg/keV/yr.

Molecular Nature of X(3872)in B^(0)→K^(0)X(3872)and B^(+)→K^(+)X(3872)Decays

We investigate the decays of B^(0)→K^(0)X(3872)and B^(+)→K^(+)X(3872)based on the picture where the X(3872)resonance is strongly coupled to the DD*+c.c.channel.In addition to the decay mechanism where the X(3872)resonance is formed from the DD*pair hadronization with the short-distance interaction,we have also considered the DD*rescattering diagrams in the long-distance scale,where D andD*are formed from c andDD*separately.Because of the difference of the mass thresholds of charged and neutralDD*channels,and the rather narrow width of the X(3872)resonance,at the X(3872)mass,the loop functions ofD^(0)D*^(0)andD^(+)D*^(-)are much different.Taking this difference into account,the ratio of B[B^(0)→K^(0)X(3872)]/B[B+→K+X(3872)]■0.5 can be naturally obtained.Based on this result,we also evaluate the decay widths of B_s^(0)→η(η′)X(3872).It is expected that future experimental measurements of these decays can be used to elucidate the nature of the X(3872)resonance.

Modification of Wood by Tannin-Furfuryl Alcohol Resins-Effect on Dimensional Stability,Mechanical Properties and Decay Durability

Furfurylation is a well-known wood modification technology.This paper studied the effect of tannin addition on the wood furfurylation.Three kinds of dicarboxylic acids,adipic acid,succinic acid,and tartaric acid,as well as glyoxal as a comparing agent,were used to catalyse the polymerisation of furanic or tannin-furanic solutions during wood modification.Impregnation of furanic or tannin-furanic solution at a certain concentration into the wood followed with curing at 103℃for a specific duration was performed for the wood modification.Different properties of the modified woods like dimensional stability,resistance of treatment to leaching,mechanical properties,decay durability against white-rot(Coriolus versicolor,Pycnoporus sanguineus)and brown-rot(Coniophora puteana)as well as their chemical and anatomical characteristics were evaluated.Results revealed that the partial substitution of FA by the tannins improved the fixation of the chemicals impregnated in wood.Further,dimensional stability,leaching resistance,Brinell hardness,modulus of elasticity/modulus of rupture,and decay durability properties of the furfurylated wood were also improved in the presence of tannins.Scanning electron microscopy revealed the deposition of the polymer in the wood lumen cells and in the wood cell walls.

Theoretical analyses on the one-dimensional charged particle transport in a decaying plasma under an electrostatic field

The spatiotemporal evolutions of a one-dimensional collisionless decaying plasma bounded by two electrodes with an externally applied electrostatic field are studied by theoretical analyses and particle-in-cell(PIC)simulations with the ion extraction process in a laser-induced plasma as the major research background.Based on the theoretical analyses,the transport process of the charged particles including electrons and ions can be divided into three stages:electron oscillation and ion matrix sheath extraction stage,sheath expansion and ion rarefaction wave propagation stage and the plasma collapse stage,and the corresponding criterion for each stage is also presented.Consequently,a complete analytical model is established for describing the ion extraction flux at each stage during the decaying of the laser-induced plasmas under an electrostatic field,which is also validated by the PIC modeling results.Based on this analytical model,influences of the key physical parameters,including the initial electron temperature and number density,plasma width and the externally applied electric voltage,on the ratio of the extracted ions are predicted.The calculated results show that a higher applied electric potential,smaller initial plasma number density and plasma width lead to a higher ratio of the extracted ions during the first stage;while in this stage,the initial electron temperature shows little effect on it.Meanwhile,more ions will be extracted before the plasma collapse once a higher electric potential is applied.The theoretical model presented in this paper is helpful not only for a deep understanding to the charged particle transport mechanisms for a bounded decaying plasma under an applied electrostatic field,but also for an optimization of the ion extraction process in practical applications.

Long-term decay of the water pressure in the osmotic tensiometer

Matric suction is an important state variable required for the assessment of unsaturated soil properties.Tensiometers are commonly used for direct matric suction measurement but have a limited measuring range up to 90 kPa due to the cavitation problem.Osmotic tensiometer(OT)can improve the measuring range of tensiometers by increasing the osmotic pressure of water to avoid the cavitation.However,the long-term water pressure decay that appeared in OTs caused a gradual decrease in their measuring range.In this study,crosslinked poly(acrylamide-co-acrylic acid)potassium salt(PAM-co-PAAK)was used for the preparation of OTs(five in total)to explore the mechanism of water pressure decay of OTs.The maximum water pressure in the OT versus the volume fraction of polymer filled in the OT was described based on the Flory-Huggins polymer theories and validated using WP4C dewpoint hygrometer.The long-term pressure decay of OT-1,OT-2,and OT-3 was observed for 130 d and constant pressures were found for OT-1 and OT-2,indicating that the pressure decay of OT was mainly caused by the stress relaxation of the polymer hydrogels,and standard linear solid(SLS)rheological model was appropriate to fit the decay data.For OT-1,OT-2 and OT-3,the theoretical osmotic pressure that was calculated based on the mass of retrieved polymer from OTs after 130-d pressure observation was higher than the actual osmotic pressure as observed,indicating that polymer leakage cannot explain the pressure decay of the OT.The ultravioletevisible(UVevisible)spectrophotometry examined the change in polymer concentrations in the water containers of OT-4 and OT-5 and demonstrated that there was no increase in polymer leakage during the period of pressure decay of OT-4 and OT-5.As a result,the pressure decay of OT was not caused by polymer leakage.The results of this research suggested that the viscoelastic properties of polymers should be taken into consideration in further OT development.

Examining Knowledge Decay in the Anesthesia Provider—An Integrative Review

Background: Knowledge decay can be present in a lot of different careers but it is especially important when affecting the anesthesia provider. Knowledge decay can lead to skill decay. Therefore, it leads to worse patient outcomes. It is important to know how knowledge decay occurs and to know how to prevent it. Purpose: The purpose of this review was to explore the contributing factors of knowledge decay while also examining how different learning activities can be used to prevent it from occurring. Methods: A systematic literature search was performed in PubMed, Cochrane databases, and Embase. The American Association of Nurse Anesthesiology website was also examined. Findings: Knowledge decay usually occurs when either the anesthesia provider is in a new area of practice or when the provider has had a significant amount of time pass since the latest implementation of an anesthesia skill. The type of activity shown to best combat knowledge decay is the use of a simulation-based learning activity. Classroom learning can also help combat knowledge decay, but not to the same extent. Conclusions: The most significant way to prevent knowledge decay in the anesthesia provider is to implement simulation-based learning activities, as well as keep anesthesia providers comfortable with the skills that they practice.

Differential Calculus the Study of the Growth and Decay of an Entity’s Population

Population Growth and Decay study of the growth or the decrease of a population of a given entity, is carried out according to the environment. In an infinite environment, i.e. when the resources are unlimited, a population P believes according to the following differential equation P’ = KP, with the application of the differential calculus we obtasin an exponential function of the variable time (t). The function of which we can predict approximately a population according to the signs of k and time (t). If k > 0, we speak of the Malthusian croissant. On the other hand, in a finite environment i.e. when resources are limited, the population cannot exceed a certain value. and it satisfies the logistic equation proposed by the economist Francois Verhulst: P’ = P(1-P).

Efficiency of a Modular Cleanroom for Space Applications

A prototype cleanroom for hazardous testing and handling of satellites prior to launcher encapsulation,satisfying the ISO8 standard has been designed and analyzed in terms of performances.Unsteady Reynolds Averaged Navier-Stokes(URANS)models have been used to study the related flow field and particulate matter(PM)dispersion.The outcomes of the URANS models have been validated through comparison with equivalent large-eddy simulations.Special attention has been paid to the location and shape of the air intakes and their orientation in space,in order to balance the PM convection and diffusion inside the cleanroom.Forming a cyclone-type flow pattern inside the cleanroom is a key to maintaining a high ventilation efficiency.

Overshoot phenomena:Observation and simulation

High-power O-mode radio waves can excite artificial instabilities in the F region,according to experiments conducted at the European Incoherent Scatter Science Association(EISCAT)heating facility.The main instabilities include the parametric decay instability(PDI),oscillating two-stream instability(OTSI),and thermal parametric instability(TPI).The PDI and OTSI not only compete with each other,but also compete with the TPI,leading to a two-stage overshoot phenomenon:a miniovershoot occurs on a millisecond time scale after pump-on,followed by the main overshoot.We gain insight into the miniovershoot via a generalized Zakharov model,whereas the main overshoot can be observed as an enhanced plasma line overshoot phenomenon in incoherent scatter radar spectra.We can also observe that the zero-frequency ion line exists only in the initial heating period after a cold start and that the upshifted and downshifted ion lines behave irregularly in the spectra.The simulation results show that competition between the PDI and OTSI leads to an initial peak,which we named the pre-miniovershoot.The following processes,namely ion density caviton generation,and collapse and cascade in the development of the PDI,contribute to the miniovershoot phenomenon.

GLOBAL CLASSICAL SOLUTIONS OF SEMILINEAR WAVE EQUATIONS ON R^(3)×T WITH CUBIC NONLINEARITIES

In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.