How to estimate isotope fractionations of a Rayleigh-like but diffusion-limited disequilibrium process?

The Rayleigh distillation isotope fractionation(RDIF) model is one of the most popular methods used in isotope geochemistry. Numerous isotope signals observed in geologic processes have been interpreted with this model. The RDIF model provides a simple mathematic solution for the reservoir-limited equilibrium isotope fractionation effect. Due to the reservoir effect, tremendously large isotope fractionations will always be produced if the reservoir is close to being depleted. However, in real situations, many prerequisites assumed in the RDIF model are often difficult to meet. For instance, it requires the relocated materials, which are removed step by step from one reservoir to another with different isotope compositions(i.e., with isotope fractionation), to be isotopically equilibrated with materials in the first reservoir simultaneously. This ‘‘quick equilibrium requirement’’ is indeed hard to meet if the first reservoir is sufficiently large or the removal step is fast. The whole first reservoir will often fail to re-attain equilibrium in time before the next removal starts.This problem led the RDIF model to fail to interpret isotope signals of many real situations. Here a diffusion-coupled and Rayleigh-like(i.e., reservoir-effect included) separation process is chosen to investigate this problem. We find that the final isotope fractionations are controlled by both the diffusion process and the reservoir effects via the disequilibrium separation process. Due to its complexity, we choose to use a numerical simulation method to solve this problem by developing specific computing codes for the working model.According to our simulation results, the classical RDIF model only governs isotope fractionations correctly at the final stages of separation when the reservoir scale(or thickness of the system) is reduced to the order of magnitude of the quotient of the diffusivity and the separation rate. The RDIF model fails in other situations and the isotope fractionations will be diffusion-limited when the reservoir is relatively large, or the separation rate is fast. We find that the effect of internal isotope distribution inhomogeneity caused by diffusion on the Rayleigh-like separation process is significant and cannot be ignored. This method can be applied to study numerous geologic and planetary processes involving diffusion-limited disequilibrium separation processes including partial melting,evaporation, mineral precipitation, core segregation, etc.Importantly, we find that far more information can be extracted through analyzing isotopic signals of such ‘‘disequilibrium’’processes than those of fully equilibrated ones, e.g., reservoir size and the separation rate. Such information may provide a key to correctly interpreting many isotope signals observed from geochemical and cosmochemical processes.

A review of fractionations of rare earth elements in plants

Studies were carried out on several aspects of rare earth elements （REEs）, such as the theory and practice of their applications in agriculture, their geochemical behaviors in natural and agricultural ecosystems, the mechanisms for the increase of crop yield using REE fertilizer, and their toxicology. However, limited knowledge was available for the transfer processes and the features and mechanisms of distribution and fractionations of REEs inside plants. The characteristics of REE fractionations in plants can be used to ＂trace＂ the pathway of REE transportation from soils （solution） to plants. A better understanding of the mechanisms of REE fractionations was helpful to investigate the controlling factors, including both the internal and the external ones. The characteristics and mechanisms of REE fractionations in plants and their significance were reviewed. Furthermore, the prospect for these fields was discussed, in hope of providing a new way in studying the bioavailability of REEs and heavy metals.

Changes in soil organic carbon contents and fractionations of forests along a climatic gradient in China

Background: Soil organic carbon(SOC) is a large reservoir of terrestrial carbon(C); it consists of different fractions of varying complexity and stability. Partitioning SOC into different pools of decomposability help better predict the trend of changes in SOC dynamics under climate change. Information on how physical fractions and chemical structures of SOC are related to climate and vegetation types is essential for spatial model ing of SOC processes and responses to global change factors.Method: Soil samples were col ected from multiple representative forest sites of three contrasting climatic zones(i.e. cool temperate, warm temperate, and subtropical) in eastern China. Measurements were made on SOC contents and physical fractions of the 0–20 cm soil layer, and the chemical composition of SOC of the 0–5 cm soil layer, along with measurements and compilation of the basic site and forest stand variables. The long-term effects of temperature, litter inputs, soil characteristics and vegetation type on the SOC contents and factions were examined by means of "space for time substitution" approach and statistical analysis.Result: Mean annual temperature(MAT) varied from 2.1 °C at the cool temperate sites to 20.8 °C at the subtropical sites. Total SOC of the 0–20 cm soil layer decreased with increasing MAT, ranging from 89.2 g·kg^(-1) in cool temperate forests to 57.7 g·kg^(-1) in subtropical forests, at an average rate of 1.87% reduction in SOC with a 1 °C increase in MAT.With increasing MAT, the proportions of aromatic C and phenolic C displayed a tendency of decreases, whereas the proportion of alkyl C and A/O-A value(the ratio of alkyl C to the sum of O-alkyl C and acetal C) displayed a tendency of increases. Overall, there were no significant changes with MAT and forest type in either the physical fractions or the chemical composition. Based on the relationship between the SOC content and MAT, we estimate that SOC in the top 20 soil layer of forests potentially contribute 6.58–26.3 Pg C globally to the atmosphere if global MAT increases by 1 °C–4 °C by the end of the twenty-first century, with nearly half of which(cf. 2.87–11.5 Pg C) occurring in the 0–5 cm mineral soils.Conclusion: Forest topsoil SOC content decreased and became chemical y more recalcitrant with increasing MAT,without apparent changes in the physical fractions of SOC.

First-principles Study on Equilibrium Sn Isotope Fractionations in Hydrothermal Fluids

Tin(Sn)isotope geochemistry has great potential in tracing geological processes.However,lack of equilibrium Sn isotope fractionation factors of various Sn species limits the development of Sn isotope geochemistry.Equilibrium Sn isotope fractionation factors(124Sn/116Sn and 122Sn/116Sn)among various Sn(II,IV)complexes in aqueous solution were calculated using first-principles calculations.The results show that the oxidation states and the change of Sn(II,IV)species in hydrothermal fluids are the main factors leading to tin isotope fractionation in hydrothermal systems.For the Sn(IV)complexes,Sn isotope fractionation factors depend on the number of H2O molecules.For the Sn(II)complexes,the Sn isotope fractionation between Sn(II)−F,Sn(II)−Cl and Sn(II)−OH complexes is mainly affected by the bond length and the coordination number of anion,whereas the difference in 1000lnβvalues of Sn(II)−SO4 and Sn(II)−CO_(3) complexes is insignificant with the change of anion coordination number.By comparing the 1000lnβvalues of all Sn(II,IV)complexes,the enrichment trend in heavy Sn isotopes is Sn(IV)complexes>Sn(II)complexes.The equilibrium Sn isotopic fractionation factors enhance our understanding of the tin transportation and enrichment processes in hydrothermal systems.

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials.The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass,as well as the local volume fraction of all phases.The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function,avoiding the parameter dependence in the conventional aggregation process.Furthermore,the local volume percentage can be precisely satisfied.The effects including the globalmass bound,the influence radius and local volume percentage on final designs are exploited through numerical examples.The numerical results also reveal that porous structures keep a balance between the bulk design and periodic design in terms of the resulting compliance.All results,including those for irregular structures andmultiple volume fraction constraints,demonstrate that the proposedmethod can provide an efficient solution for multiple material infill structures.

Damage evolution of rock-encased-backfill structure under stepwise cyclic triaxial loading

Rock-encased-backfill(RB)structures are common in underground mining,for example in the cut-andfill and stoping methods.To understand the effects of cyclic excavation and blasting activities on the damage of these RB structures,a series of triaxial stepwise-increasing-amplitude cyclic loading experiments was conducted with cylindrical RB specimens(rock on outside,backfill on inside)with different volume fractions of rock(VF=0.48,0.61,0.73,and 0.84),confining pressures(0,6,9,and 12 MPa),and cyclic loading rates(200,300,400,and 500 N/s).The damage evolution and meso-crack formation during the cyclic tests were analyzed with results from stress-strain hysteresis loops,acoustic emission events,and post-failure X-ray 3D fracture morphology.The results showed significant differences between cyclic and monotonic loadings of RB specimens,particularly with regard to the generation of shear microcracks,the development of stress memory and strain hardening,and the contact forces and associated friction that develops along the rock-backfill interface.One important finding is that as a function of the number of cycles,the elastic strain increases linearly and the dissipated energy increases exponentially.Also,compared with monotonic loading,the cyclic strain hardening characteristics are more sensitive to rising confining pressures during the initial compaction stage.Another finding is that compared with monotonic loading,more shear microcracks are generated during every reloading stage,but these microcracks tend to be dispersed and lessen the likelihood of large shear fracture formation.The transition from elastic to plastic behavior varies depending on the parameters of each test(confinement,volume fraction,and cyclic rate),and an interesting finding was that the transformation to plastic behavior is significantly lower under the conditions of 0.73 rock volume fraction,400 N/s cyclic loading rate,and 9 MPa confinement.All the findings have important practical implications on the ability of backfill to support underground excavations.

Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.

Left bundle branch pacing vs biventricular pacing in heart failure patients with left bundle branch block:A systematic review and meta-analysis

BACKGROUND Left bundle branch pacing(LBBP)is a novel pacing modality of cardiac resynchronization therapy(CRT)that achieves more physiologic native ventricular activation than biventricular pacing(BiVP).AIM To explore the validity of electromechanical resynchronization,clinical and echocardiographic response of LBBP-CRT.METHODS Systematic review and Meta-analysis were conducted in accordance with the standard guidelines as mentioned in detail in the methodology section.RESULTS In our analysis,the success rate of LBBP-CRT was determined to be 91.1%.LBBP CRT significantly shortened QRS duration,with significant improvement in echocardiographic parameters,including left ventricular ejection fraction,left ventricular end-diastolic diameter and left ventricular end-systolic diameter in comparison with BiVP-CRT.CONCLUSION A significant reduction in New York Heart Association class and B-type natriuretic peptide levels was also observed in the LBBP-CRT group vs BiVP-CRT group.Lastly,the LBBP-CRT cohort had a reduced pacing threshold at follow-up as compared to BiVP-CRT.

Chromatin condensation but not DNA integrity of pig sperm is greater in the sperm-rich fraction

Background Protamination and condensation of sperm chromatin as well as DNA integrity play an essential role during fertilization and embryo development.In some mammals,like pigs,ejaculates are emitted in three separate fractions:pre-sperm,sperm-rich(SRF)and post sperm-rich(PSRF).These fractions are known to vary in volume,sperm concentration and quality,as well as in the origin and composition of seminal plasma(SP),with differences being also observed within the SRF one.Yet,whether disparities in the DNA integrity and chromatin condensation and pro-tamination of their sperm exist has not been interrogated.Results This study determined chromatin protamination(Chromomycin A3 test,CMA_(3)),condensation(Dibromobi-mane test,DBB),and DNA integrity(Comet assay)in the pig sperm contained in the first 10 m L of the SRF(SRF-P1),the remaining portion of the sperm-rich fraction(SRF-P2),and the post sperm-rich fraction(PSRF).While chromatin protamination was found to be similar between the different ejaculate fractions(P>0.05),chromatin condensation was seen to be greater in SRF-P1 and SRF-P2 than in the PSRF(P=0.018 and P=0.004,respectively).Regarding DNA integrity,no differences between fractions were observed(P>0.05).As the SRF-P1 has the highest sperm concentra-tion and ejaculate fractions are known to differ in antioxidant composition,the oxidative stress index(OSi)in SP,calcu-lated as total oxidant activity divided by total antioxidant capacity,was tested and confirmed to be higher in the SRF-P1 than in SRF-P2 and PSRF(0.42±0.06 vs.0.23±0.09 and 0.08±0.00,respectively;P<0.01);this index,in addition,was observed to be correlated to the sperm concentration of each fraction(Rs=0.973;P<0.001).Conclusion While sperm DNA integrity was not found to differ between ejaculate fractions,SRF-P1 and SRF-P2 were observed to exhibit greater chromatin condensation than the PSRF.This could be related to the OSi of each fraction.

A novel variable-order fractional chaotic map and its dynamics

In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.

Dynamics of the Fractional-Order Lorenz System Based on Adomian Decomposition Method and Its DSP Implementation

Dear Editor,Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method(ADM).Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents(LEs),bifurcation diagram.

Fractional-order heterogeneous memristive Rulkov neuronal network and its medical image watermarking application

This article proposes a novel fractional heterogeneous neural network by coupling a Rulkov neuron with a Hopfield neural network(FRHNN),utilizing memristors for emulating neural synapses.The study firstly demonstrates the coexistence of multiple firing patterns through phase diagrams,Lyapunov exponents(LEs),and bifurcation diagrams.Secondly,the parameter related firing behaviors are described through two-parameter bifurcation diagrams.Subsequently,local attraction basins reveal multi-stability phenomena related to initial values.Moreover,the proposed model is implemented on a microcomputer-based ARM platform,and the experimental results correspond to the numerical simulations.Finally,the article explores the application of digital watermarking for medical images,illustrating its features of excellent imperceptibility,extensive key space,and robustness against attacks including noise and cropping.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

A sustainable process to 100%bio-based nylons integrated chemical and biological conversion of lignocellulose

Considerable progress has been made in recent years to the development of sustainable polymers from bio-based feedstocks.In this study,100%bio-based nylons were prepared via an integrated chemical and biological process from lignocellulose.These novel nylons were obtained by the melt polymerization of 3-propyladipic acid derived from lignin and 1,5-pentenediamine/1,4-butanediamine derived from carbohydrate sugar.Central to the concept is a three-step noble metal free catalytic chemical funnelling sequence(Raney Ni mediated reductive catalytic fractionation-reductive funnelling-oxidative funnelling),which allowed for obtaining a single component 3-propyladipic acid from lignin with high efficiency.The structural and thermodynamic properties of the obtained nylons have been systematically investigated,and thus obtained transparent bio-based nylons exhibited higher Mw(>32,000)and excellent thermal stability(Td5%>265℃).Considering their moderate Tg and good melt strength,these transparent bio-based nylons could serve as promising functional additives or temperature-responsive materials.

Diagnostic performance of intravascular ultrasound-based fractional flow reserve in evaluating of intermediate left main stenosis

BACKGROUND The recently introduced ultrasonic flow ratio(UFR),is a novel fast computational method to derive fractional flow reserve(FFR)from intravascular ultrasound(IVUS)images.In the present study,we evaluate the diagnostic performance of UFR in patients with intermediate left main(LM)stenosis.METHODS This is a prospective,single center study enrolling consecutive patients with presence of intermediated LM lesions(diameter stenosis of 30%-80%by visual estimation)underwent IVUS and FFR measurement.An independent core laboratory assessed offline UFR and IVUS-derived minimal lumen area(MLA)in a blinded fashion.RESULTS Both UFR and FFR were successfully achieved in 41 LM patients(mean age,62.0±9.9 years,46.3%diabetes).An acceptable correlation between UFR and FFR was identified(r=0.688,P<0.0001),with an absolute numerical difference of 0.03(standard difference:0.01).The area under the curve(AUC)in diagnosis of physiologically significant coronary stenosis for UFR was 0.94(95%CI:0.87-1.01),which was significantly higher than angiographic identified stenosis>50%(AUC=0.66,P<0.001)and numerically higher than IVUS-derived MLA(AUC=0.82;P=0.09).Patient level diagnostic accuracy,sensitivity and specificity for UFR to identify FFR≤0.80 was 82.9%(95%CI:70.2-95.7),93.1%(95%CI:82.2-100.0),58.3%(95%CI:26.3-90.4),respectively.CONCLUSION In patients with intermediate LM diseases,UFR was proved to be associated with acceptable correlation and high accuracy with pressure wire-based FFR as standard reference.The present study supports the use of UFR for functional evaluation of intermediate LM stenosis.

Interaction between systemic iron parameters and left ventricular structure and function in the preserved ejection fraction population:a two-sample bidirectional Mendelian randomization study

BACKGROUND Left ventricular(LV)remodeling and diastolic function in people with heart failure(HF)are correlated with iron status;however,the causality is uncertain.This Mendelian randomization(MR)study investigated the bidirectional causal relationship between systemic iron parameters and LV structure and function in a preserved ejection fraction population.METHODS Transferrin saturation(TSAT),total iron binding capacity(TIBC),and serum iron and ferritin levels were extracted as instrumental variables for iron parameters from meta-analyses of public genome-wide association studies.Individuals without myocardial infarction history,HF,or LV ejection fraction(LVEF)<50%(n=16,923)in the UK Biobank Cardiovascular Magnetic Resonance Imaging Study constituted the outcome dataset.The dataset included LV end-diastolic volume,LV endsystolic volume,LV mass(LVM),and LVM-to-end-diastolic volume ratio(LVMVR).We used a two-sample bidirectional MR study with inverse variance weighting(IVW)as the primary analysis method and estimation methods using different algorithms to improve the robustness of the results.RESULTS In the IVW analysis,one standard deviation(SD)increased in TSAT significantly correlated with decreased LVMVR(β=-0.1365;95%confidence interval[CI]:-0.2092 to-0.0638;P=0.0002)after Bonferroni adjustment.Conversely,no significant relationships were observed between other iron and LV parameters.After Bonferroni correction,reverse MR analysis showed that one SD increase in LVEF significantly correlated with decreased TSAT(β=-0.0699;95%CI:-0.1087 to-0.0311;P=0.0004).No heterogeneity or pleiotropic effects evidence was observed in the analysis.CONCLUSIONS We demonstrated a causal relationship between TSAT and LV remodeling and function in a preserved ejection fraction population.

Three anti-inflammatory polysaccharides from Lonicera japonica Thunb.:insights into the structure-function relationships

This study demonstrates the feasibility of producing three polysaccharides(neutral LJP-1,acidic LJP-2 and acidic LJP-3)with significant in vitro and in vivo anti-inflammatory activities from the flowers of Lonicera japonica.The three polysaccharides differed in chemical composition,molecular weight(Mw)distribution,glycosidic linkage pattern,functional groups and morphology.They exhibited excellent protective effects(in a dose-dependent manner)in lipopolysaccharide-injured RAW264.7 macrophages and Cu SO4-damaged zebrafish via reducing NO production and inhibiting the overexpressions of inflammation-related transcription factors,inflammatory proteins and cytokines in the NF-κB/MAPK signaling pathways.Their antiinflammatory effects varied owing to their different molecular characteristics and chemical compositions.Overall,LJP-2 at 400μg/m L was the most effective.LJP-2 consisted mainly of→5)-α-L-Araf(1→,→4)-α-LGalp A(1→and→2)-α-L-Rhap(1→residues with terminal T-β-D-Glcp.Thus,honeysuckle flowers are good sources of anti-inflammatory polysaccharides,and precise fractionation enables the production of potent antiinflammatory agents for the development of functional foods and healthcare products.

Allotetraploidization event of Coptis chinensis shared by all Ranunculales

Coptis chinensis Franch.,also named Chinese goldthread is a member of Ranunculaceae in the order Ranunculales and represents an important lineage of early eudicots with traditional medicinal value.In our study,by using syntenic analysis combined with phylogenomic analysis of C.chinensis and four other representative genomes from basal and core eudicots,we confirmed that the WGD event in C.chinensis was shared by Aquilegia coerulea and Papaver somniferum L.and quickly occurred after Ranunculales diverged from other eudicots,likely a Ranunculales common tetraploidization(RCT).The synonymous nucleotide substitutions at synonymous sites distribution of syntenic blocks across these genomes showed that the evolutionary rate of the P.somniferum genome is faster than that of the C.chinensis genome by approximately 13.7%,possibly due to Papaveraceaes having an additional special tetraploidization event(PST).After Ks correction,the RCT dated to 115—130 million years ago(MYA),which was close to the divergence of Ranunculaceaes and Papaveraceaes approximately115.45—130.51 MYA.Moreover,we identified homologous genes related to polyploidization and speciation and constructed multiple sequence alignments with different reference genomes.Notably,the event-related subgenomes in the basal genomes all showed genomic fractionation bias,suggesting a likely allopolyploid nature of the RCT,PST and T-Alpha and T-Beta events in Tetracentron sinense.In addition,we detected that the sixteen P450 subfamilies were markedly expanded in the genomes of Ranunculales,and most of them were related to the RCT and PST events.We constructed a new platform for Early Eudicot Comparative Genomic Research(http://www.cgrpoee.top/index.html)to store more information.In summary,our findings support the WGD of C.chinensis shared by Ranunculales,which is likely an allotetraploidization event.This present effort offered new insights into the evolution of key polyploidization events and the genes related to secondary metabolites during the diversification of early eudicots.

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.

THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT

Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the process.We show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.