Application of Monte Carlo method to calculate the effective delayed neutron fraction in molten salt reactor

Delayed neutron loss is an important parameter in the safety analysis of molten salt reactors. In this study,to obtain the effective delayed neutron fraction under flow condition, a delayed neutron precursor transport was implemented in the Monte Carlo code MCNP. The moltensalt reactor experiment(MSRE) model was used to analyze the reliability of this method. The obtained flow losses of reactivity for 235 U and 233 U fuels in the MSRE are223 pcm and 100.8 pcm, respectively, which are in good agreement with the experimental values(212 pcm and100.5 pcm, respectively). Then, six groups of effective delayed neutron fractions in a small molten salt reactor were calculated under different mass flow rates. The flow loss of reactivity at full power operation is approximately105.6 pcm, which is significantly lower than that of the MSRE due to the longer residence time inside the active core. The sensitivity of the reactivity loss to other factors,such as the residence time inside or outside the core and flow distribution, was evaluated as well. As a conclusion,the sensitivity of the reactivity loss to the residence time inside the core is greater than to other parameters.

Nuclear volume effects in kinetic isotope fractionation:A case study of mercury oxidation by chlorine species

It is well-known that the equilibrium isotope fractionation of mercury(Hg)includes classical massdependent fractionations(MDFs)and nuclear volume effect(NVE)induced mass-independent fractionations(MIFs).However,the effect of the NVE on these kinetic processes is not known.The total fractionations(MDFs+NVEinduced MIFs)of several representative Hg-incorporated substances were selected and calculated with ab initio calculations in this work for both equilibrium and kinetic processes.NVE-induced MIFs were calculated with scaled contact electron densities at the nucleus through systematic evaluations of their accuracy and errors using the Gaussian09 and DIRAC19 packages(named the electron density scaling method).Additionally,the NVE-induced kinetic isotope effect(KIE)of Hg isotopes are also calculated with this method for several representative Hg oxidation reactions by chlorine species.Total KIEs for 202 Hg/^(198)Hg ranging from−2.27‰to 0.96‰are obtained.Three anomalous^(202)Hg-enriched KIEs(δ^(202)Hg/^(198)Hg=0.83‰,0.94‰,and 0.96‰,)caused by the NVE are observed,which are quite different from the classical view(i.e.,light isotopes react faster than the heavy ones).The electron density scaling method we developed in this study can provide an easier way to calculate the NVE-induced KIEs for heavy isotopes and serve to better understand the fractionation mechanisms of mercury isotope systems.

Memory effect in time fractional Schrödinger equation

A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.

Nuclear ?eld shift effects on stable isotope fractionation: a review

An anomalous isotope effect exists in many heavy element isotope systems （e.g., Sr, Gd, Zn, U）. This effect used to be called the ＂odd--even isotope effect＂ because the odd mass number isotopes behave differently from the even mass number isotopes. This mass-indepen- dent isotope fractionation driving force, which originates from the difference in the ground-state electronic energies caused by differences in nuclear size and shape, is cur- rently denoted as the nuclear field shift effect （NFSE）. It is found that the NFSE can drive isotope fractionation of some heavy elements （e.g., Hg, T1, U） to an astonishing degree, far more than the magnitude caused by the con- ventional mass-dependent effect （MDE）. For light ele- ments, the MDE is the dominant factor in isotope fractionation, while the NFSE is neglectable. Furthermore, the MDE and the NFSE both decrease as temperatures increase, though at different rates. The MDE decreases rapidly with a factor of 1/T2, while the NFSE decreases slowly with a factor of 1/T. As a result, even at high temperatures, the NFSE is still significant for many heavy element isotope systems. In this review paper, we begin with an introduction of the basic concept of the NSFE, including its history and recent progress, and follow with the potential implications of the inclusion of the NFSE into the kinetic isotope fractionation effect （KIE） and heavy isotope geochronology.

Vital effects of K isotope fractionation in organisms： observations and a hypothesis

Compared with the measureable but limited K isotope variation in geological samples,biological samples have much larger variations in δ^41 values：from-1.3‰ to＋1.1‰ relative to the international K standard NIST SRM 3141a.Notably,higher plants generally have δ^41 values that are lower than igneous rocks,whereas sea plants（algae）have δ^41 values that are higher than seawater;the range in δ^41K values of plants encompasses the δ^41 values of both igneous rocks and seawater.Plant cells utilize different K uptake mechanisms in response to highand low-K conditions.In a low-K environment,plant cells use energy-consuming ion pumps for active uptake of K;plant cells in high-K environments use non-energy-consuming ion channels.Based on these facts and on K isotope data from sea and land plants,it is hypothesized that the different K uptake mechanisms are accompanied by distinct K isotope fractionation behaviors or vital effects.The enrichment of light K isotopes in terrestrial plants could be attributed to preferential transport of isotopically light K in the energy-consuming active uptake process by K ion pumps in the membranes of plant root cells.On the other hand,the enrichment of heavy K isotopes in algae may be caused by a combination of the lack of K isotope fractionation during K uptake from seawater via ion channels and the preferential efflux of light K isotopes across the cell membrane back to the seawater.The large variation of K isotope compositions in biological samples therefore may reflect the diversity of isotopic vital effects for K in organisms,which implies the great potential of K isotopes in biogeochemical studies.

First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios(10^3 lnb)and103lna of 44 Ca/40 Ca in forsterite(Fo)are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca+Mg)varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/(Ca+Mg)is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 10^3 lnb is negatively correlated with Ca–O bond length,the 10^3lnb significantly increases with decreasing Ca/(Ca+Mg)when 1/64<Ca/(Ca+Mg)<2/16.As a consequence,the 10^3lna between forsterite and other minerals also strongly depend on the Ca content in forsterite.Combining previous studies with our results,the heavier Ca isotopes enrichment sequence in minerals is:forsterite[orthopyroxene[clinopyroxene[calcite & diopside[dolomite[aragonite.Olivineand pyroxenes are enriched in heavier Ca isotope compared to carbonates.The 10^3lna between forsterite with a Ca/(Ca+Mg)of 1/64 and clinopyroxene(Ca/Mg=1/1,i.e.,diopside)is up to^0.64%at 1200 K.The large 103lnaFodiopsiderelative to the current analytical precision for Ca isotope measurements suggests that the dependence of10^3 lnaFo-diopsideon temperature can be used as a thermometer,similar to the one based on the 103lna of 44 Ca/40 Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.

Secondary decay effects of the isospin fractionation in the projectile fragmentation at GeV/nucleon

The isospin fractionations in 124Sn,107Sn+120Sn at 600 MeV/nucleon,and 136Xe,124Xe+208Pb at 1000 MeV/nucleon are investigated by the isospin-dependent quantum molecular dynamics model coupled with the statistical code GEMINI.The yield ratio as a function of the binding energy difference for light mirror nuclei 3H/3He,7Li/7Be,11B/11C,and 15N/15O is applied to estimate the ratio between neutrons and protons in the gas of the fragmenting system.By comparing the estimated values resulting from the simulations with and without the GEMINI code,it was found that the secondary decay distorts the signal of the isospin fractionation.To minimize the secondary decay effects,the yield ratio of the light mirror nuclei 3H/3He as well as its double ratio between two systems with different isospin asymmetries of the projectiles is recommended as robust isospin observables.

CLOUD RADIATIVE AND MICROPHYSICAL EFFECTS ON THE RELATION BETWEEN SPATIAL MEAN RAIN RATE, RAIN INTENSITY AND FRACTIONAL RAINFALL COVERAGE

Cloud radiative and microphysical effects on the relation between spatial mean rain rate, rain intensity and fractional rainfall coverage are investigated in this study by conducting and analyzing a series of two-dimensional cloud resolving model sensitivity experiments of pre-summer torrential rainfall in June 2008. The analysis of time-mean data shows that the exclusion of radiative effects of liquid clouds reduces domain mean rain rate by decreasing convective rain rate mainly through the reduced convective-rainfall area associated with the strengthened hydrometeor gain in the presence of radiative effects of ice clouds, whereas it increases domain mean rain rate by enhancing convective rain rate mainly via the intensified convective rain intensity associated with the enhanced net condensation in the absence of radiative effects of ice clouds. The removal of radiative effects of ice clouds decreases domain mean rain rate by reducing stratiform rain rate through the suppressed stratiform rain intensity related to the suppressed net condensation in the presence of radiative effects of liquid clouds, whereas it increases domain mean rain rate by strengthening convective rain rate mainly via the enhanced convective rain intensity in response to the enhanced net condensation in the absence of radiative effects of liquid clouds. The elimination of microphysical effects of ice clouds suppresses domain mean rain rate by reducing stratiform rain rate through the reduced stratiform-rainfall area associated with severely reduced hydrometeor loss.

Intermittent disturbance mechanical behavior and fractional deterioration mechanical model of rock under complex true triaxial stress paths

Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.

Weight losing, antihyperlipidemic and cardioprotective effects of the alkaloid fraction of Hunteria umbellata seed extract on normal and triton-induced hyperlipidemic rats

Objective: To investigate the weight losing, antihyperlipidemic and cardioprotective effects of the alkaloid fraction of Hunteria umbellata(H. umbellata) seed.Methods: Adult female Wistar rats(weight range: 120-150 g) were randomly divided into 4 and 5 treatment groups in the normal and triton-induced hyperlipidemic models, respectively. and were daily treated for 14 d before they were humanely sacrificed under inhaled diethyl ether anesthesia. About 5 mL of whole blood was obtained by cardiac puncture from each treated rat, from which serum for lipids assay was subsequently separated. Tissue samples of livers of treated rats were harvested and processed for histopathological analysis.Results: Repeated daily oral treatments of normal rats with 25 and 50 mg/kg/day of alkaloid fraction of H. umbellata resulted in significant(P<0.05 and P<0.001) and dose-dependent weight loss, and decreases in the serum triglyceride, total cholesterol and low density lipoprotein cholesterol, while significantly(P<0.001) increased the serum levels of high density lipoprotein cholesterol fraction. Similarly, oral pre-treatments with 25 and 50 mg/kg/day of alkaloid fraction of H. umbellata for 14 d before induction of hyperlipidemia with triton WR-1339 significantly(P<0.01, P<0.001) and dose-dependently attenuated increases in the average body weights, serum levels of triglyceride, total cholesterol and low density lipoprotein cholesterol while also significantly(P<0.01, P<0.001) and dose-dependently attenuated significant(P<0.001) decrease in the serum high-density lipoproteincholesterol levels when compared to the untreated control values. However, the results obtained for 50 mg/kg of alkaloid fraction of H. umbellata in both normal and triton WR-1339-induced hyperlipidemic rats were comparable to that recorded for 20 mg/kg of simvastatin. Similarly, oral pretreatments with 25 and 50 mg/kg/day of alkaloid fraction of H. umbellata significantly improved the histological lesions of fatty hepatic degeneration induced by triton WR-1339 treatment.Conclusions: Overall, results of this study showed that repeated oral treatments with 25 and 50 mg/kg/day of alkaloid fraction of H. umbellata elicited weight losing, antihyperlipidemic and cardioprotective effects in triton WR-1339 induced hyperlipidemic rats that were mediated via de novo cholesterol biosynthesis inhibition.

PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.

Production of Infant Formula Analogs by Membrane Fractionation of Caprine Milk: Effect of Temperature Treatment on Membrane Performance

A two-step-cascade membrane separation by ultrafiltration was performed on caprine milk prepared under different temperature conditions to eliminate beta-lactoglobulin (β-Lg) from the whey fraction. Effects of temperature treatment and membrane pore size on the elimination of β-Lg and retention of alpha-lactalbumin (α-La) were examined to determine the optimum permeate fraction for production of infant formula analogues from caprine milk. The frozen raw caprine milk, with and without prior pasteurization, showed the best membrane separation performance. The permeates obtained from the 800/30kDa membrane combination showed the optimal results. The infant formula analog produced using the casein and 800/30kDa-permeate fractions of the treated caprine milk had the closest similarity to human milk with respect to the total protein content (1.3g 100g-1), beta-lactoglobulin content (1% - 2%), and casein- α-lactalbumin ratio (0.6 - 0.7). Membrane performance during ultrafiltration of caprine milk was affected by temperature treatment of the milk prior to membrane separation.

RELATION BETWEEN THE EFFECTS OF FINITE THICKNESS AND TILTED MAGNETIC FIELDS IN THE FRACTIONAL QUANTUM HALL EFFECT

We present an approximate mathematical relation between the finite thickness and the tilted magnetic fields' effects in the fractional quantum Hall effect.We show that the experimental results for the 2/3 filling can be explained qualitatively by the existing theoretical results,and the Monte Carlo results for ground state energy vs finite thickness of two-dimensional layer at 1/3 filling can be rewritten in the form of ground state energy vs tilt angle.

Solutions and memory effect of fractional-order chaotic system:A review

Fractional calculus is a 300 years topic,which has been introduced to real physics systems modeling and engineering applications.In the last few decades,fractional-order nonlinear chaotic systems have been widely investigated.Firstly,the most used methods to solve fractional-order chaotic systems are reviewed.Characteristics and memory effect in those method are summarized.Then we discuss the memory effect in the fractional-order chaotic systems through the fractionalorder calculus and numerical solution algorithms.It shows that the integer-order derivative has full memory effect,while the fractional-order derivative has nonideal memory effect due to the kernel function.Memory loss and short memory are discussed.Finally,applications of the fractional-order chaotic systems regarding the memory effects are investigated.The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.

Fractional Langevin Equation in Quantum Systems with Memory Effect

In this paper, we introduce the fractional generalized Langevin equation (FGLE) in quantum systems with memory effect. For a particular form of memory kernel that characterizes the quantum system, we obtain the analytical solution of the FGLE in terms of the two-parameter Mittag-Leffler function. Based on this solution, we study the time evolution of this system including the qubit excited-state energy, polarization and von Neumann entropy. Memory effect of this system is observed directly through the trapping states of these dynamics.

Inhibitory effect induced by fractional Gaussian noise in neuronal system

We discover a phenomenon of inhibition effect induced by fractional Gaussian noise in a neuronal system. Firstly,essential properties of fractional Brownian motion(fBm) and generation of fractional Gaussian noise(fGn) are presented,and representative sample paths of fBm and corresponding spectral density of fGn are discussed at different Hurst indexes.Next, we consider the effect of fGn on neuronal firing, and observe that neuronal firing decreases first and then increases with increasing noise intensity and Hurst index of fGn by studying the time series evolution. To further quantify the inhibitory effect of fGn, by introducing the average discharge rate, we investigate the effects of noise and external current on neuronal firing, and find the occurrence of inhibitory effect about noise intensity and Hurst index of f Gn at a certain level of current. Moreover, the inhibition effect is not easy to occur when the noise intensity and Hurst index are too large or too small. In view of opposite action mechanism compared with stochastic resonance, this suppression phenomenon is called inverse stochastic resonance(ISR). Finally, the inhibitory effect induced by fGn is further verified based on the inter-spike intervals(ISIs) in the neuronal system. Our work lays a solid foundation for future study of non-Gaussian-type noise on neuronal systems.

Adaptive Neuro-Fuzzy Inference System for Prediction of Effective Thermal Conductivity of Polymer-Matrix Composites

In the present study, the adaptive neuro-fuzzy inference system (ANFIS) is developed for the prediction of effective thermal conductivity (ETC) of different fillers filled in polymer matrixes. The ANFIS uses a hybrid learning algorithm. The ANFIS is a class of adaptive networks that is functionally equivalent to fuzzy inference systems (FIS). The ANFIS is based on neuro-fuzzy model, trained with data collected from various sources of literature. ETC is predicted using ANFIS with volume fraction and thermal conductivities of fillers and matrixes as input parameters, respectively. The predicted results by ANFIS are in good agreements with experimental values. The predicted results also show the supremacy of ANFIS in comparison with other earlier developed models.

Fractional derivative statistical damage model of unsaturated expansive soil based on unified hydraulic effect

Unsaturated expansive soil is widely distributed in China and has complex engineering properties.This paper proposes the unified hydraulic effect shear strength theory of unsaturated expansive soil based on the effective stress principle,swelling force principle,and soil–water characteristics.Considering the viscoelasticity and structural damage of unsaturated expansive soil during loading,a fractional hardening–damage model of unsaturated expansive soil was established.The model parameters were established on the basis of the proposed calculation method of shear strength and the triaxial shear experiment on unsaturated expansive soil.The proposed model was verified by the experimental data and a traditional damage model.The proposed model can satisfactorily describe the entire process of the strain-hardening law of unsaturated expansive soil.Finally,by investigating the damage variables of the proposed model,it was found that:(a)when the values of confining pressure and matric suction are close,the coupling of confining pressure and matric suction contributes more to the shear strength;(b)there is a damage threshold for unsaturated expansive soil,and is mainly reflected by strength criterion of infinitesimal body;(c)the strain hardening law of unsaturated expansive soil is mainly reflected by fractional derivative operator.

Radiobiological effect of abdominal X-ray hypo-fraction irradiation on Wistar rats liver

Objective: The aim of our study was to investigate the impact of abdominal hypo-fraction irradiation on liver damage in rats so as to provide a reference for its clinical application. Methods: A total of 100 Wistar rats were equally randomized to five groups as control, 4 Gy, 6 Gy, 8 Gy and 12 Gy group, and the corresponding fractionated doses were offered. Liver functions were examined at the 2nd, 4th, 6th, 8th and 10th week after irradiation. Morphological changes were observed by HE staining. Expressions of Bcl-2 and Bax were examined by immunohistochemical technique. Results: In all irradiation groups, hepatocellular swell, degeneration, necrosis and even hepatic fibrosis could be seen. The differences of the liver coefficient, Glutamyl pyruvic transaminase (GPT), Glutamyl oxaloacetic transaminase (GOT) were significant among the groups and different time points (F = 11.833-781.972, F = 20.857-264.692, P < 0.001). Expressions of Bcl-2 and Bax were significantly different between each group (F = 211.607, 116.577; P < 0. 001), and between each time point (F = 54.083, 68.749; P < 0. 001). Conclusion: Compare with conventional fraction, abdominal hypo-fraction irradiation may cause radiation damage to rat liver, being dose-and-time dependent. Up-regulation of activating apoptosis protein Bax and down-regulation of inhibiting apoptosis protein Bcl-2 may involve in the process.

Observation on clinical effect of botulinum toxin type A injection combined with low-energy CO2 fractional laser periocular rejuvenation treatment

Objective To investigate the clinical effect of botulinum toxin type A injection combined with low-energy CO2 fractional laser periocular rejuvenation treatment.Methods The clinical effect of botulinum type A injection alone and botulinum type A injection combined with low-energy CO2 fractional laser was compared in 96 patients who needed to receive periocular rejuvenation treatment from April 2018 to April 2019.Results After the combined low-energy CO2 fractional laser treatment was given on the basis of botulinum toxin type A injection,the follow-up global aesthetic improvement scale(GAIS)scores of the observation group were 86.78±4.67,80.31±3.66,76.94±4.03 and 40.59±4.78.The global aesthetic improvement of the dynamic and static wrinkles was obvious.The total effective rate was 93.7%.The total satisfaction rate of the patients was 95.8%,which was higher than that of the control group(P<0.05).The clinical efficacy was significant.Conclusion The application of the combined periocular rejuvenation treatment can improve the dynamic and static wrinkles simultaneously with remarkable rejuvenation effect,increase the effective rate of treatment and enhance the patients'satisfaction.