LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS

We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.

Exact solutions of the Schrodinger equation for a class of hyperbolic potential well

We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.

PERIODIC SOLUTIONS FOR HAMILTONIANSYSTEMS IN A NONCONVEX POTENTIAL WELL

Recently there has been a considerable amount of work on the existence of Tperiodic solutions for Hamiltonian systems with singular potentials, (see [1]—[7],[10], [11], [13], [14]). In this paper we will study the existence of T-periodic solutions for nonconservative second-order dynamical systems

Geochemical fingerprints and hydrocarbon potential of Paleocene mudrocks in the Tano Basin, Ghana: insights from biomarkers and stable carbon isotopes

The Paleocene mudrocks in Ghana’s Tano Basin have received limited attention despite ongoing efforts to explore hydrocarbon resources.A thorough geochemical analysis is imperative to assess these mudrocks’petroleum generation potential and formulate effective exploration strategies.In this study,a comprehensive geochemical analysis was carried out on ten Paleocene rock cuttings extracted from TP-1,a discovery well within the Tano Basin.Various analytical techniques,including total organic carbon(TOC)analysis,Rock–Eval pyrolysis,gas chromatography-mass spectrometry,and isotope ratio-mass spectrometry,were employed to elucidate their hydrocar-bon potential and organic facies.Thefindings in this study were subsequently compared to existing geochemical data on Paleocene source rocks in the South Atlantic marginal basins.The results indicated that the Paleocene samples have TOC content ranging from 0.68 to 2.93 wt%.The prevalent kerogen types identified in these samples were Type Ⅱ and Type Ⅲ.Molecular and isotope data suggest that the organic matter found in the Paleocene mudrocks can be traced back to land plants and lower aquatic organisms.These mudrocks were deposited in a transi-tional environment withfluctuating water salinity,charac-terized by sub-oxic redox conditions.Maturity indices,both bulk and molecular,indicated a spectrum of maturity levels within the Paleocene mudrocks,spanning from immature to marginally mature,with increasing maturity observed with greater depth.In comparison,the organic composition and depositional environments of Paleocene source rocks in the Tano Basin closely resemble those found in the Niger Delta Basin,Douala,and Kribi-Campo Basins,the Kwanza Formation in Angola,and certain Brazilian marginal basins.However,it is worth noting that Paleocene source rocks in some of the basins,such as the Niger Delta and Brazilian marginal basins,exhibit rela-tively higher thermal maturity levels compared to those observed in the current Paleocene samples from the Tano Basin.In conclusion,the comprehensive geochemical analysis of Paleocene mudrocks within Ghana’s Tano Basin has unveiled their marginal hydrocarbon generation potential.The shared geochemical characteristics between the Paleocene mudrocks in the Tano Basin and those in the nearby South Atlantic marginal basins offer valuable insights into source rock quality,which is crucial for shaping future strategies in petroleum exploration in this region.

Quantitative effect of kerogen type on the hydrocarbon generation potential of Paleogene lacustrine source rocks,Liaohe Western Depression,China

Kerogen types exert a decisive effect on the onset and capacity of hydrocarbon generation of source rocks.Lacustrine source rocks in the Liaohe Western Depression are characterized by thick deposition,high total organic carbon(TOC)content,various kerogen types,and a wide range of thermal maturity.Consequently,their hydrocarbon generation potential and resource estimation can be misinterpreted.In this study,geochemical tests,numerical analysis,hydrocarbon generation kinetics,and basin modeling were integrated to investigate the differential effects of kerogen types on the hydrocarbon generation potential of lacustrine source rocks.Optimized hydrocarbon generation and expulsion(HGE)models of different kerogen types were established quantitatively upon abundant Rock-Eval/TOC/vitrinite reflectance(R_(o))datasets.Three sets of good-excellent source rocks deposited in the fourth(Es4),third(Es3),and first(Es1)members of Paleogene Shahejie Formation,are predominantly types I-II_(1),II_(1)-II_(2),and II-III,respectively.The activation energy of types I-II_(2)kerogen is concentrated(180-230 kcal/mol),whereas that of type III kerogen is widely distributed(150-280 kcal/mol).The original hydrocarbon generation potentials of types I,II_(1),II_(2),and III kerogens are 790,510,270,and 85 mg/g TOC,respectively.The Ro values of the hydrocarbon generation threshold for type I-III source rocks gradually increase from 0.42%to 0.74%,and Ro values of the hydrocarbon expulsion threshold increase from 0.49%to 0.87%.Types I and II_(1)source rocks are characterized by earlier hydrocarbon generation,more rapid hydrocarbon expulsion,and narrower hydrocarbon generation windows than types II_(2)and III source rocks.The kerogen types also affect the HGE history and resource potential.Three types(conventional,tight,and shale oil/gas)and three levels(realistic,expected,and prospective)of hydrocarbon resources of different members in the Liaohe Western Depression are evaluated.Findings suggest that the Es3 member has considerable conventional and unconventional hydrocarbon resources.This study can quantitatively characterize the hydrocarbon generation potential of source rocks with different kerogen types,and facilitate a quick and accurate assessment of hydrocarbon resources,providing strategies for future oil and gas exploration.

Transient receptor potential channels as predictive marker and potential indicator of chemoresistance in colon cancer

Transient receptor potential(TRP)channels are strongly associated with colon cancer development and progression.This study leveraged a multivariate Cox regression model on publicly available datasets to construct a TRP channels-associated gene signature,with further validation of signature in real world samples from our hospital treated patient samples.Kaplan-Meier(K-M)survival analysis and receiver operating characteristic(ROC)curves were employed to evaluate this gene signature’s predictive accuracy and robustness in both training and testing cohorts,respectively.Additionally,the study utilized the CIBERSORT algorithm and single-sample gene set enrichment analysis to explore the signature’s immune infiltration landscape and underlying functional implications.The support vector machine algorithm was applied to evaluate the signature’s potential in predicting chemotherapy outcomes.The findings unveiled a novel three TRP channels-related gene signature(MCOLN1,TRPM5,and TRPV4)in colon adenocarcinoma(COAD).The ROC and K-M survival curves in the training dataset(AUC=0.761;p=1.58e-05)and testing dataset(AUC=0.699;p=0.004)showed the signature’s robust predictive capability for the overall survival of COAD patients.Analysis of the immune infiltration landscape associated with the signature revealed higher immune infiltration,especially an increased presence of M2 macrophages,in high-risk group patients compared to their low-risk counterparts.High-risk score patients also exhibited potential responsiveness to immune checkpoint inhibitor therapy,evident through increased CD86 and PD-1 expression profiles.Moreover,the TRPM5 gene within the signature was highly expressed in the chemoresistance group(p=0.00095)and associated with poor prognosis(p=0.036)in COAD patients,highlighting its role as a hub gene of chemoresistance.Ultimately,this signature emerged as an independent prognosis factor for COAD patients(p=6.48e-06)and expression of model gene are validated by public data and real-world patients.Overall,this bioinformatics study provides valuable insights into the prognostic implications and potential chemotherapy resistance mechanisms associated with TRPs-related genes in colon cancer.

Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system

There exists an optimal range of intensity of a chaotic force in which the behavior of a chaos-driven bistable system with two weak inputs can be consistently mapped to a specific logic output. This phenomenon is called logical chaotic resonance(LCR). However, realization of a reliable exclusive disjunction(XOR) through LCR has not been reported.Here, we explore the possibility of using chaos to enhance the reliability of XOR logic operation in a triple-well potential system via LCR. The success probability P of obtaining XOR logic operation can take the maximum value of 1 in an optimal window of intensity D of a chaotic force. Namely, success probability P displays characteristic bell-shaped behavior by altering the intensity of the chaotic driving force, indicating the occurrence of LCR. Further, the effects of periodic force on LCR have been investigated. For a subthreshold chaotic force, a periodic force with appropriate amplitude and frequency can help enhance the reliability of XOR logic operation. Thus, LCR can be effectively regulated by changing the amplitude and frequency of the periodic force.

Probing the electric double layer structure at nitrogen-doped graphite electrodes by constant-potential molecular dynamics simulations

Electric double layer(EDL)is a critical topic in electrochemistry and largely determines the working performance of lithium batteries.However,atomic insights into the EDL structures on heteroatom-modified graphite anodes and EDL evolution with electrode potential are very lacking.Herein,a constant-potential molecular dynamics(CPMD)method is proposed to probe the EDL structure under working conditions,taking N-doped graphite electrodes and carbonate electrolytes as an example.An interface model was developed,incorporating the electrode potential and atom electronegativities.As a result,an insightful atomic scenario for the EDL structure under varied electrode potentials has been established,which unveils the important role of doping sites in regulating both the EDL structures and the following electrochemical reactions at the atomic level.Specifically,the negatively charged N atoms repel the anions and adsorb Li~+at high and low potentials,respectively.Such preferential adsorption suggests that Ndoped graphite can promote Li~+desolvation and regulate the location of Li~+deposition.This CPMD method not only unveils the mysterious function of N-doping from the viewpoint of EDL at the atomic level but also applies to probe the interfacial structure on other complicated electrodes.

Vertical plane depth-resolved surface potential and carrier separation characteristics in flexible CZTSSe solar cells with over 12% efficiency

Cu2ZnSn(S,Se)4(CZTSSe)solar cells have resource distribution and economic advantages.The main cause of their low efficiency is carrier loss resulting from recombination of photo-generated electron and hole.To overcome this,it is important to understand their electron-hole behavior characteristics.To determine the carrier separation characteristics,we measured the surface potential and the local current in terms of the absorber depth.The elemental variation in the intragrains(IGs)and at the grain boundaries(GBs)caused a band edge shift and bandgap(Eg)change.At the absorber surface and subsurface,an upward Ec and Ev band bending structure was observed at the GBs,and the carrier separation was improved.At the absorber center,both upward Ec and Ev and downward Ec-upward Ev band bending structures were observed at the GBs,and the carrier separation was degraded.To improve the carrier separation and suppress carrier recombination,an upward Ec and Ev band bending structure at the GBs is desirable.

Modelling analysis embodies drastic transition among global potential natural vegetations in face of changing climate

Potential natural vegetation(PNV)is a valuable reference for ecosystem renovation and has garnered increasing attention worldwide.However,there is limited knowledge on the spatio-temporal distributions,transitional processes,and underlying mechanisms of global natural vegetation,particularly in the case of ongoing climate warming.In this study,we visualize the spatio-temporal pattern and inter-transition procedure of global PNV,analyse the shifting distances and directions of global PNV under the influence of climatic disturbance,and explore the mechanisms of global PNV in response to temperature and precipitation fluctuations.To achieve this,we utilize meteorological data,mainly temperature and precipitation,from six phases:the Last Inter-Glacial(LIG),the Last Glacial Maximum(LGM),the Mid Holocene(MH),the Present Day(PD),2030(20212040)and 2090(2081–2100),and employ a widely-accepted comprehensive and sequential classification sy–stem(CSCS)for global PNV classification.We find that the spatial patterns of five PNV groups(forest,shrubland,savanna,grassland and tundra)generally align with their respective ecotopes,although their distributions have shifted due to fluctuating temperature and precipitation.Notably,we observe an unexpected transition between tundra and savanna despite their geographical distance.The shifts in distance and direction of five PNV groups are mainly driven by temperature and precipitation,although there is heterogeneity among these shifts for each group.Indeed,the heterogeneity observed among different global PNV groups suggests that they may possess varying capacities to adjust to and withstand the impacts of changing climate.The spatio-temporal distributions,mutual transitions and shift tendencies of global PNV and its underlying mechanism in face of changing climate,as revealed in this study,can significantly contribute to the development of strategies for mitigating warming and promoting re-vegetation in degraded regions worldwide.

Seedling potential of trees species along the elevational gradient in temperate hill forest of central Nepal

Regeneration status of tree species along elevation gradient in temperate hill forest was not understood greatly.Present research examined the tree diversity and its regeneration patterns along an elevation gradient in temperate hill forest,central Nepal.Data were collected from 300 sample plots within vertical elevation bands of 10,ranging from 1365 to 2450 m asl.A random sampling method was used for data collection in three seasons,winter,pre-monsoon and post monsoon seasons.Diameter at breast height(DBH)was used to broadly categorize the plant individual into trees,saplings and seedlings.The tree species richness ranged from 12 to 25 with density of 350 to 1200 individuals per hectare.Species richness of tree and sapling showed statistically significant unimodal pattern,which peaked at mid-elevation.Elevation showed a strong and positive linear correlation with the seedling density(Deviance=0.99,p<0.001)and a significant hump-shaped relationship with sapling density(Deviance=0.95,p<0.001).Similarly,elevations showed a statistically significant negative hump-shaped relationship with all trees,saplings and seedling stages(Deviances=0.89,0.87 and 0.57).The highest values of the Shannon-Wiener index and the lowest value of the Simpson index were found at mid-elevation for all growth forms.Nearly 92%of tree species were found at regenerating stage;49%in a good renewal regeneration status,32%in fair renewal regeneration,and 11%at a poor regenerating condition.Nevertheless,4%of tree species were reported as non-regenerating stages and 4%were newly introduced species.Hence,the regeneration status of the study area was considered fairly well since sapling(78.5%)>seedling(10.6%)≤mature(10.9%).Among tested environmental variables,elevation and annual mean rainfall were the most influential factors in the regeneration of tree species.

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

Hepatic perivascular epithelioid cell tumors:Benign,malignant,and uncertain malignant potential

In 2013,the World Health Organization defined perivascular epithelioid cell tumor(PEComa)as“a mesenchymal tumor which shows a local association with vessel walls and usually expresses melanocyte and smooth muscle markers.”This generic definition seems to better fit the PEComa family,which includes angiomyolipoma,clear cell sugar tumor of the lung,lymphangioleiomyomatosis,and a group of histologically and immunophenotypically similar tumors that include primary extrapulmonary sugar tumor and clear cell myomelanocytic tumor.Clear cell tumors with this immunophenotypic pattern have also had their malignant variants described.When localizing to the liver,preoperative radiological diagnosis has proven to be very difficult,and most patients have been diagnosed with hepatocellular carcinoma,focal nodular hyperplasia,hemangioma,or hepatic adenoma based on imaging findings.Examples of a malignant variant of the liver have been described.Finally,reports of malignant variants of these lesions have increased in recent years.Therefore,we support the use of the Folpe criteria,which in 2005 established the criteria for categorizing a PEComa as benign,malignant,or of uncertain malignant potential.Although they are not considered ideal,they currently seem to be the best approach and could be used for the categorization of liver tumors.

Ab initio potential energy surface and anharmonic vibration spectrum of NF_(3)^(+)

Potential energy surfaces(PESs), vibrational frequencies, and infrared spectra are calculated for NF_(3)^(+) using ab initio calculations, based on UCCSD(T)/cc-p VTZ combined with vibrational configuration interaction(VCI). Based on an iterative algorithm, the surfaces(SURF) program adds automatic points to the lattice representation of the potential function, the one-dimensional and two-dimensional PESs are calculated after reaching a convergence threshold, finally the smooth image of the potential energy surface is fitted. The PESs accurately account for the interaction between the different modes, with the mode q_(6) symmetrical stretching vibrations having the greatest effect on the potential energy change of the whole system throughout the potential energy surface shift. The anharmonic frequencies are obtained when the VCI matrix is diagonalized. Fundamental frequencies, overtones, and combination bands of NF_(3)^(+) are calculated, which generate the degenerate phenomenon between their frequencies. Finally, the calculated anharmonic frequency is used to plot the infrared spectra.Modal antisymmetric stretching ν_(5) and symmetric stretching ν_(6) exhibit a phenomenon of large-intensity borrowing. This study can provide data to support the characterization in the laboratory.

Tetrathiafulvalene esters with high redox potentials and improved solubilities for non-aqueous redox flow battery applications

The exploitation of high performance redox-active substances is critically important for the development of non-aqueous redoxflow batteries.Herein,three tetrathiofulvalene(TTF)derivatives with different substitution groups,namely TTF diethyl ester(TTFDE),TTF tetramethyl ester(TTFTM),and TTF tetraethyl ester(TTFTE),are prepared and their energy storage properties are evaluated.It has been found that the redox potential and solubility of these TTF derivatives in conventional carbonate electrolytes increases with the number of ester groups.The battery with a catholyte of 0.2 mol L^(-1) of TTFTE delivers a specific capacity of more than 10 Ah L^(-1) at the current density of 0.5 C with two discharge voltage platforms locating at as high as 3.85 and 3.60 V vs.Li/Liþ.Its capacity retention can be improved from 2.34 Ah L^(-1) to 3.60 Ah L^(-1) after 100 cycles by the use of an anion exchange membrane to block the crossover of TTF species.The excellent cycling stability of the TIF esters is supported by their well-delocalized electrons,as revealed by the density function theory calculations.Therefore,the introduction of more and larger electron-withdrawing groups is a promising strategy to simultaneously increase the redox-potential and solubility of redox-active ma-terials for non-aqueous redoxflow batteries.

Plasma potential measurements using an emissive probe made of oxide cathode

A novel emissive probe consisting of an oxide cathode coating is developed to achieve a low operating temperature and long service life.The properties of the novel emissive probe are investigated in detail,in comparison with a traditional tungsten emissive probe,including the operating temperature,the electron emission capability and the plasma potential measurement.Studies of the operating temperature and electron emission capability show that the tungsten emissive probe usually works at a temperature of 1800 K-2200 K while the oxide cathode emissive probe can function at about 1200 K-1400 K.In addition,plasma potential measurements using the oxide cathode emissive probe with different techniques have been accomplished in microwave electron cyclotron resonance plasmas with different discharge powers.It is found that a reliable plasma potential can be obtained using the improved inflection point method and the hot probe with zero emission limit method,while the floating point method is invalid for the oxide cathode emissive probe.

Identification of transient receptor potential channel genes and functional characterization of TRPA1 in Spodoptera frugiperda

Spodoptera frugiperda is a highly destructive pest that has become a global problem due to its robust reproductive and migratory capabilities.Transient receptor potential(TRP)channels,which constitute a vast ion channel family,play pivotal roles in sensing the external environment and maintaining internal homeostasis in insects.TRP channels have been widely investigated for their critical roles in regulating various insect behaviors in recent years.In this study,we identified 15 TRP gene loci encoding 26 transcripts in the genome of S.frugiperda and analyzed their expression profiles at different developmental stages.The results revealed that S.frugiperda possesses four TRPC genes,six TRPA genes,one TRPM gene,two TRPV genes,one TRPN gene,and one TRPML gene,while a canonical TRPP is absent.Moreover,the SfruTRPA1 was functionally characterized using the Xenopus oocyte expression system.The results showed that SfruTRPA1 is activated by temperature increases from 20 to 45℃,and there is no significant desensitization after repeated stimuli within the same temperature range.Additionally,SfruTRPA1 is activated by certain natural chemicals,including allyl isothiocyanate(AITC)and cinnamaldehyde(CA).These findings provide valuable insights to the TRP genes in S.frugiperda.

Properties of radiation defects and threshold energy of displacement in zirconium hydride obtained by new deep-learning potential

Zirconium hydride(ZrH_(2)) is an ideal neutron moderator material. However, radiation effect significantly changes its properties, which affect its behavior and the lifespan of the reactor. The threshold energy of displacement is an important quantity of the number of radiation defects produced, which helps us to predict the evolution of radiation defects in ZrH_(2).Molecular dynamics(MD) and ab initio molecular dynamics(AIMD) are two main methods of calculating the threshold energy of displacement. The MD simulations with empirical potentials often cannot accurately depict the transitional states that lattice atoms must surpass to reach an interstitial state. Additionally, the AIMD method is unable to perform largescale calculation, which poses a computational challenge beyond the simulation range of density functional theory. Machine learning potentials are renowned for their high accuracy and efficiency, making them an increasingly preferred choice for molecular dynamics simulations. In this work, we develop an accurate potential energy model for the ZrH_(2) system by using the deep-potential(DP) method. The DP model has a high degree of agreement with first-principles calculations for the typical defect energy and mechanical properties of the ZrH_(2) system, including the basic bulk properties, formation energy of point defects, as well as diffusion behavior of hydrogen and zirconium. By integrating the DP model with Ziegler–Biersack–Littmark(ZBL) potential, we can predict the threshold energy of displacement of zirconium and hydrogen in ε-ZrH_(2).

A study of the soil water potential threshold values to trigger irrigation of ‘Shimizu Hakuto’ peach at pivotal fruit developmental stages

Water management is an important practice that affects fruit size and quality.Effective implementation of irrigation scheduling requires knowledge of the appropriate indicators and thresholds,which are established manly based on the effects of water deficits on final fruit quality.Few studies have focused on the real-time effects of water status on fruit and shoot growth.To establish soil water potential (ψ_(soil)) thresholds to trigger irrigation of peach at pivotal fruit developmental stages,photogrammetry,^(13)C labelling,and other techniques were used in this study to investigate real-time changes in stem diameter,fruit projected area,net leaf photosynthetic rate (P_(n)),and allocation of photoassimilates to fruit under soil water potential conditions ranging from saturation to stress in 6-year-old Shimizu hakuto’peach.Stem growth,fruit growth,and P_n exhibited gradually decreasing sensitivity to water deficits during fruit developmental stages I,II,and III.Stem diameter growth was significantly inhibited whenψ_(soil)dropped to-8.5,-7.6,and-5.4 k Pa,respectively.Fruit growth rate was low,reaching zero when theψ_(soil)was-9.0 to-23.1,-14.9 to-21.4,and-16.5 to-23.3 k Pa,respectively,and P_ndecreased significantly when theψ_(soil)reached-24.2,-22.7,and-20.4 kPa,respectively.In addition,more photoassimilates were allocated to fruit under moderateψ_(soil)conditions (-10.1 to-17.0 k Pa) than under otherψ_(soil)values.Our results revealed threeψ_(soil)thresholds,-10.0,-15.0,and-15.0 kPa,suitable for triggering irrigation during stages I,II,and III,respectively.These thresholds can be helpful for controlling excessive tree vigor,maintaining rapid fruit growth and leaf photosynthesis,and promoting the allocation of more photoassimilates to fruit.