Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

An ultrasound-guided percutaneous electrical nerve stimulation regimen devised using finite element modeling promotes functional recovery after median nerve transection

Percutaneous electrical nerve stimulation of an injured nerve can promote and accelerate peripheral nerve regeneration and improve function.When performing acupuncture and moxibustion,locating the injured nerve using ultrasound before percutaneous nerve stimulation can help prevent further injury to an already injured nerve.However,stimulation parameters have not been standardized.In this study,we constructed a multi-layer human forearm model using finite element modeling.Taking current density and activated function as optimization indicators,the optimal percutaneous nerve stimulation parameters were established.The optimal parameters were parallel placement located 3 cm apart with the injury site at the midpoint between the needles.To validate the efficacy of this regimen,we performed a randomized controlled trial in 23 patients with median nerve transection who underwent neurorrhaphy.Patients who received conventional rehabilitation combined with percutaneous electrical nerve stimulation experienced greater improvement in sensory function,motor function,and grip strength than those who received conventional rehabilitation combined with transcutaneous electrical nerve stimulation.These findings suggest that the percutaneous electrical nerve stimulation regimen established in this study can improve global median nerve function in patients with median nerve transection.

Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory(KSDFT),the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures.However,stochastic density functional theory(SDFT)can overcome this limitation.Recently,SDFT and the related mixed stochastic–deterministic density functional theory,based on a plane-wave basis set,have been implemented in the first-principles electronic structure software ABACUS[Q.Liu and M.Chen,Phys.Rev.B 106,125132(2022)].In this study,we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV.Importantly,we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories.Subsequently,we compute and analyze the structural properties,dynamic properties,and transport coefficients of warm dense matter.

Functional hyperconnectivity related to brain disease:maladaptive process or element of resilience?

Neuroimaging techniques such as magnetic resonance imaging(MRI)and positron emission tomography provide unique in vivo data to analyze structural and functional connectivity of the whole brain.Recent advances in small animal neuroimaging have opened new opportunities for the study of structure-function interactions in healthy and diseased brain networks,which are essential to develop therapies targeting network reorganization associated with functional improvement.

The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation

The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.

Genesis of the Nuri Cu-W-Mo Deposit,Tibet,China:Constraints from in situ Trace Elements and Sr Isotopic Analysis of Scheelite

The Nuri deposit is the only Cu-W-Mo polymetallic deposit with large-scale WO3 resources in the eastern section of the Gangdese metallogenic belt,Tibet,China.However,the genetic type of this deposit has been controversial since its discovery.Based on a study of the geological characteristics of the deposit,this study presents mineralization stages,focusing on the oxide stage and the quartz-sulfide stage where scheelite is mainly formed,referred to as Sch-A and Sch-B,respectively.Through LA-ICP-MS trace element and Sr isotope analyses,the origin,evolutionary process of the oreforming fluid and genesis of the ore deposit are investigated.Scanning Electron Microscope-Cathodoluminescence(SEMCL)observations reveal that Sch-A consists of three generations,with dark gray homogenous Sch-A1 being replaced by relatively lighter and homogeneous Sch-A2 and Sch-A3,with Sch-A2 displaying a gray CL image color with vague and uneven growth bands and Sch-A3 has a light gray CL image color with hardly any growth band.In contrast,Sch-B exhibits a‘core-rim’structure,with the core part(Sch-B1)being dark gray and displaying a uniform growth band,while the rim part(Sch-B2)is light gray and homogeneous.The normalized distribution pattern of rare earth elements in scheelite and Sr isotope data suggest that the early ore-forming fluid in the Nuri deposit originated from granodiorite porphyry and,later on,some country rock material was mixed in,due to strong water-rock interaction.Combining the O-H isotope data further indicates that the ore-forming fluid in the Nuri deposit originated from magmatic-hydrothermal sources,with contributions from metamorphic water caused by water-rock interaction during the mineralization process,as well as later meteoric water.The intense water-rock interaction likely played a crucial role in the precipitation of scheelite,leading to varying Eu anomalies in different generations of scheelite from the oxide stage to the quartz-sulfide stage,while also causing a gradual decrease in oxygen fugacity(fO2)and a slow rise in pH value.Additionally,the high Mo and low Sr contents in the scheelite are consistent with typical characteristics of magmatic-hydrothermal scheelite.Therefore,considering the geological features of the deposit,the geochemical characteristics of scheelite and the O-H isotope data published previously,it can be concluded that the genesis of the Nuri deposit belongs to porphyry-skarn deposit.

Greatly enhanced corrosion/wear resistances of epoxy coating for Mg alloy through a synergistic effect between functionalized graphene and insulated blocking layer

The poor corrosion and wear resistances of Mg alloys seriously limit their potential applications in various industries.The conventional epoxy coating easily forms many intrinsic defects during the solidification process,which cannot provide sufficient protection.In the current study,we design a double-layer epoxy composite coating on Mg alloy with enhanced anti-corrosion/wear properties,via the spin-assisted assembly technique.The outer layer is functionalized graphene(FG)in waterborne epoxy resin(WEP)and the inner layer is Ce-based conversion(Ce)film.The FG sheets can be homogeneously dispersed within the epoxy matrix to fill the intrinsic defects and improve the barrier capability.The Ce film connects the outer layer with the substrate,showing the transition effect.The corrosion rate of Ce/WEP/FG composite coating is 2131 times lower than that of bare Mg alloy,and the wear rate is decreased by~90%.The improved corrosion resistance is attributed to the labyrinth effect(hindering the penetration of corrosive medium)and the obstruction of galvanic coupling behavior.The synergistic effect derived from the FG sheet and blocking layer exhibits great potential in realizing the improvement of multi-functional integration,which will open up a new avenue for the development of novel composite protection coatings of Mg alloys.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Impact of stage-specific limb function exercises guided by a selfmanagement education model on arteriovenous fistula maturation status

BACKGROUND The exercise of limb function is the most economical and safe method to promote the maturation of arteriovenous fistula(AVF).However,due to the lack of a uni-fied exercise standard in China,many patients have insufficient awareness of the importance of AVF,leading to poor effectiveness of limb function exercise.The self-management education model can effectively promote patients to take pro-active health-related actions.This study focuses on the characteristics of patients during the peri-AVF period and conducts a phased limb function exercise under the guidance of the self-management education model to observe changes in fac-tors such as the maturity of AVF.AIM To assess the impact of stage-specific limb function exercises,directed by a self-management education model,on the maturation status of AVFs.METHODS This study is a randomized controlled trial involving 74 patients with forearm AVFs from the Nephrology Department of a tertiary hospital in Sichuan Province,China.Patients were randomly divided into an observation group and a control group using a random number table method.The observation group underwent tailored stage-specific limb func-tion exercises,informed by a self-management education model which took into account the unique features of AVF at various stages,in conjunction with routine care.Conversely,the control group was given standard limb function exercises along with routine care.The assessment involves the maturity of AVFs post-intervention,post-operative complications,and the self-management level of the fistula in both groups patients.Analyses were conducted using SPSS version 23.0.Count data were represented by frequency and percentage and subjected to chi-square test comparisons.Measurement data adhering to a normal distribution were presented as mean±SD.The independent samples t-test was utilized for inter-group comparisons,while the paired t-test was used for intra-group comparisons.For measurement data not fitting a normal distribution,the median and interquartile range were presented and analyzed using the Wilcoxon rank sum test.RESULTS At the 8-wk postoperative mark,the observation group demonstrated significantly higher scores in AVF symptom recognition,symptom prevention,and self-management compared to the control group(P<0.05).However,the variance in symptom management scores between the observation and control groups lacked statistical signi-ficance(P>0.05).At 4 wk after the operation,the observation group displayed a superior vessel diameter and depth from the skin of the drainage vessels in comparison to the control group(P<0.05).While the observation group did manifest elevated blood flow rates in the drainage vessels relative to the control group,this distinction was not statistically significant(P>0.05).By the 8-wk postoperative interval,the observation group outperformed the control group with notable enhancements in blood flow rates,vessel diameter,and depth from the skin of drainage vessels(P<0.01).Seven days following the procedure,the observation group manifested significantly diminished limb swelling and an overall reduced complication rate in contrast to the control group(P<0.05).The evaluation of infection,thrombosis,embolism,arterial aneurysm stenosis,and incision bleeding showed no notable differences between the two groups(P>0.05).By the 4-wk postoperative juncture,complications between the observation and control groups were statistically indistinguishable(P>0.05).CONCLUSION Stage-specific limb function exercises,under the guidance of a self-management education model,amplify the capacity of AVF patients to discern and prevent symptoms.Additionally,they expedite AVF maturation and miti-gate postoperative limb edema,underscoring their efficacy as a valuable method for the care and upkeep of AVF in hemodialysis patients.

Transplantation of fibrin-thrombin encapsulated human induced neural stem cells promotes functional recovery of spinal cord injury rats through modulation of the microenvironment

Recent studies have mostly focused on engraftment of cells at the lesioned spinal cord,with the expectation that differentiated neurons facilitate recovery.Only a few studies have attempted to use transplanted cells and/or biomaterials as major modulators of the spinal cord injury microenvironment.Here,we aimed to investigate the role of microenvironment modulation by cell graft on functional recovery after spinal cord injury.Induced neural stem cells reprogrammed from human peripheral blood mononuclear cells,and/or thrombin plus fibrinogen,were transplanted into the lesion site of an immunosuppressed rat spinal cord injury model.Basso,Beattie and Bresnahan score,electrophysiological function,and immunofluorescence/histological analyses showed that transplantation facilitates motor and electrophysiological function,reduces lesion volume,and promotes axonal neurofilament expression at the lesion core.Examination of the graft and niche components revealed that although the graft only survived for a relatively short period(up to 15 days),it still had a crucial impact on the microenvironment.Altogether,induced neural stem cells and human fibrin reduced the number of infiltrated immune cells,biased microglia towards a regenerative M2 phenotype,and changed the cytokine expression profile at the lesion site.Graft-induced changes of the microenvironment during the acute and subacute stages might have disrupted the inflammatory cascade chain reactions,which may have exerted a long-term impact on the functional recovery of spinal cord injury rats.

Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.

Small but big leaps towards neuroglycomics:exploring N-glycome in the brain to advance the understanding of brain development and function

Glycosylation is a process that involves the addition of sugar moieties or glycans to different types of molecules,including proteins,lipids,and nucleic acids.Among these,protein glycosylation is one of the most prevalent forms of post-translational modification,playing a crucial role in biological complexity.With more than ten monosaccharides identified within mammalian brain cells and more than 1×1012 possible combinations,the heterogeneity of glycosylation is extensive(Conroy et al.,2021).The diversity of glycans and the complexity of their structures allow for a wide range of protein functions.N-glycans are one of the most abundant forms of glycans and are involved in various cellular functions.N-glycans can be added to proteins at specific sequons,Asn-X-Ser/Thr,and are classified into three main types in mature glycoproteins:high mannose,complex,and hybrid.High mannose N-glycans consist of 5-9 mannose residues linked to a chitobiose core and undergo processing into complex or hybrid forms in the Golgi apparatus(Varki et al.,2017).Complex N-glycans are more diverse and contain various branched structures such as antennae with fucose,galactose,and sialic acid residues.Hybrid N-glycans contain one or more complex branches in conjunction with an oligomannose branch(Fisher and Ungar,2016).Understanding the specific functions of these different types of N-glycans in protein regulation,folding,and function is an active area of research in the life sciences,including glycobiology.

Emerging insights into the function of very long chain fatty acids at cerebellar synapses

Very long chain-saturated and-polyunsaturated fatty acids(VLC-SFA and VLC-PUFA, respectively) are a functionally important class of fatty acids containing 28 carbons or more in their acyl chain. They are synthesized by the elongation of very long fatty acids-4(ELOVL4) enzyme, expressed mainly in the brain, retina, skin, testes, and meibomian gland, where these fatty acids are found(Agbaga et al., 2008). Further, these organs exhibit tissuespecific VLC-PUFA and VLC-SFA biosynthesis and incorporation into complex lipids for specific functions. In the brain, skin, and Meibomian glands, the ELOVL4 mainly makes VLC-SFA, which are incorporated into complex sphingolipids. In the retina, the ELOVL4 makes VLC-PUFA that are incorporated into phosphatidylcholine, that are critical for visual function, while in testes and sperm, the VLC-PUFA are incorporated into sphingolipids that are critical for fertility(Yeboah et al., 2021).

Paleoenvironmental Characteristics of Paleogene Lacustrine Source Rocks in the Western Bozhong Sag,Bohai Bay Basin,China:Evidence from Biomarkers,Major and Trace Elements

The organic matter(OM)enrichment mechanisms and depositional environment characteristics of lacustrine source rocks in the western Bozhong Sag,Bohai Bay Basin in Northeast China remain controversial.To address these issues,based on Rock-Eval pyrolysis,kerogen macerals,H/C and O/C ratios,GC-MS,major and trace elements,the Dongying Formation Member(Mbr)3(E_(3)d_(3)),the Shahejie Formation mbrs 1 and 2(E_(2)s_(1+2)),and the Shahejie Mbr 3(E_(2)s_(3))source rocks in the western Bozhong Sag were studied.The above methods were used to reveal their geochemical properties,OM origins and depositional environments,all of which indicate that E_(2)s_(1+2)and E_(2)s_(3)are excellent source rocks,and that E_(3)d_(3)is of the second good quality.E_(3)d_(3)source rocks were formed under a warm and humid climate,mainly belong to fluvial/delta facies,the E_(3)d_(3)sediments formed under weakly oxidizing and freshwater conditions.Comparatively,the depositional environments of E_(2)s_(1+2)source rocks were arid and cold climate,representing saline or freshwater lacustrine facies,and the sediments of E_(2)s_(1+2)belong to anoxic or suboxic settings with large evaporation and salinity.During the period of E_(2)s_(3),the climate became warm and humid,indicating the freshwater lacustrine facies,and E_(2)s_(3)was characterized by freshwater and abundant algae.Moreover,compared with other intervals,the OM origin of E_(3)d_(3)source rocks has noticeable terrestrial input.The OM origin of the E_(2)s_(1+2)and E_(2)s_(3)are mainly plankton and bacteria.Tectonic subsidence and climate change have affected the changes of the depositional environment in the western Bozhong Sag,thus controlling the distribution of the source rocks,the geochemical characteristics in the three intervals of lacustrine source rocks have distinct differences.Overall,these factors are effective to evaluate the paleoenvironmental characteristics of source rocks by biomarkers,major and trace elements.The established models may have positive implications for research of lacustrine source rocks in offshore areas with few drillings.

Elevated brain temperature under severe heat exposure impairs cortical motor activity and executive function

Background:Excessive heat exposure can lead to hyperthermia in humans,which impairs physical performance and disrupts cognitive function.While heat is a known physiological stressor,it is unclear how severe heat stress affects brain physiology and function.Methods:Eleven healthy participants were subjected to heat stress from prolonged exercise or warm water immersion until their rectal temperatures(T_(re))attained 39.5℃,inducing exertional or passive hyperthermia,respectively.In a separate trial,blended ice was ingested before and during exercise as a cooling strategy.Data were compared to a control condition with seated rest(normothermic).Brain temperature(T_(br)),cerebral perfusion,and task-based brain activity were assessed using magnetic resonance imaging techniques.Results:T_(br)in motor cortex was found to be tightly regulated at rest(37.3℃±0.4℃(mean±SD))despite fluctuations in T_(re).With the development of hyperthermia,T_(br)increases and dovetails with the rising T_(re).Bilateral motor cortical activity was suppressed during high-intensity plantarflexion tasks,implying a reduced central motor drive in hyperthermic participants(T_(re)=38.5℃±0.1℃).Global gray matter perfusion and regional perfusion in sensorimotor cortex were reduced with passive hyperthermia.Executive function was poorer under a passive hyperthermic state,and this could relate to compromised visual processing as indicated by the reduced activation of left lateral-occipital cortex.Conversely,ingestion of blended ice before and during exercise alleviated the rise in both T_(re)and T_(bc)and mitigated heat-related neural perturbations.Conclusion:Severe heat exposure elevates T_(br),disrupts motor cortical activity and executive function,and this can lead to impairment of physical and cognitive performance.

Functional microfluidics:theory,microfabrication,and applications

Microfluidic devices are composed of microchannels with a diameter ranging from ten to a few hundred micrometers.Thus,quite a small(10-9–10-18l)amount of liquid can be manipulated by such a precise system.In the past three decades,significant progress in materials science,microfabrication,and various applications has boosted the development of promising functional microfluidic devices.In this review,the recent progress on novel microfluidic devices with various functions and applications is presented.First,the theory and numerical methods for studying the performance of microfluidic devices are briefly introduced.Then,materials and fabrication methods of functional microfluidic devices are summarized.Next,the recent significant advances in applications of microfluidic devices are highlighted,including heat sinks,clean water production,chemical reactions,sensors,biomedicine,capillaric circuits,wearable electronic devices,and microrobotics.Finally,perspectives on the challenges and future developments of functional microfluidic devices are presented.This review aims to inspire researchers from various fields engineering,materials,chemistry,mathematics,physics,and more—to collaborate and drive forward the development and applications of functional microfluidic devices,specifically for achieving carbon neutrality.

Na^(+)/K^(+)-ATPase:ion pump,signal transducer,or cytoprotective protein,and novel biological functions

Na^(+)/K^(+)-ATPase is a transmembrane protein that has important roles in the maintenance of electrochemical gradients across cell membranes by transporting three Na^(+)out of and two K^(+)into cells.Additionally,Na^(+)/K^(+)-ATPase participates in Ca^(2+)-signaling transduction and neurotransmitter release by coordinating the ion concentration gradient across the cell membrane.Na^(+)/K^(+)-ATPase works synergistically with multiple ion channels in the cell membrane to form a dynamic network of ion homeostatic regulation and affects cellular communication by regulating chemical signals and the ion balance among different types of cells.Therefo re,it is not surprising that Na^(+)/K^(+)-ATPase dysfunction has emerged as a risk factor for a variety of neurological diseases.However,published studies have so far only elucidated the important roles of Na^(+)/K^(+)-ATPase dysfunction in disease development,and we are lacking detailed mechanisms to clarify how Na^(+)/K^(+)-ATPase affects cell function.Our recent studies revealed that membrane loss of Na^(+)/K^(+)-ATPase is a key mechanism in many neurological disorders,particularly stroke and Parkinson's disease.Stabilization of plasma membrane Na^(+)/K^(+)-ATPase with an antibody is a novel strategy to treat these diseases.For this reason,Na^(+)/K^(+)-ATPase acts not only as a simple ion pump but also as a sensor/regulator or cytoprotective protein,participating in signal transduction such as neuronal autophagy and apoptosis,and glial cell migration.Thus,the present review attempts to summarize the novel biological functions of Na^(+)/K^(+)-ATPase and Na^(+)/K^(+)-ATPase-related pathogenesis.The potential for novel strategies to treat Na^(+)/K^(+)-ATPase-related brain diseases will also be discussed.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.

Effect of Rare-Earth Element Substitution in Superconducting R_(3)Ni_(2)O_(7) under Pressure

Recently,high temperature(T_(c)≈80 K)superconductivity(SC)has been discovered in La_(3)Ni_(2)O_(7)(LNO)under pressure.This raises the question of whether the superconducting transition temperature T_(c) could be further enhanced under suitable conditions.One possible route for achieving higher T_(c) is element substitution.Similar SC could appear in the Fmmm phase of rare-earth(RE)R_(3)Ni_(2)O_(7)(RNO,R=RE element)material series under suitable pressure.The electronic properties in the RNO materials are dominated by the Ni 3d orbitals in the bilayer NiO_(2) plane.In the strong coupling limit,the SC could be fully characterized by a bilayer single 3d_(x^(2)−y^(2))-orbital t–J‖–J⊥ model.With RE element substitution from La to other RE element,the lattice constant of the Fmmm RNO material decreases,and the resultant electronic hopping integral increases,leading to stronger superexchanges between the 3d_(x^(2)−y^(2)) orbitals.Based on the slave-boson mean-field theory,we explore the pairing nature and the evolution of T_(c) in RNO materials under pressure.Consequently,it is found that the element substitution does not alter the pairing nature,i.e.,the inter-layer s-wave pairing is always favored in the superconducting RNO under pressure.However,the T_(c) increases from La to Sm,and a nearly doubled T_(c) could be realized in SmNO under pressure.This work provides evidence for possible higher T_(c) R_(3)Ni_(2)O_(7) materials,which may be realized in further experiments.

The Extended Non-Elementary Amplitude Functions as Solutions to the Damped Pendulum Equation, the Van der Pol Equation, the Damped Duffing Equation, the Lienard Equation and the Lorenz Equations

In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a name, a symbol and putting them into a group of functions and into the context of other functions. These solutions are equal to the amplitude, or upper limit of integration in a non-elementary integral that can be arbitrary. In order to define solutions to some short second-order nonlinear ODEs, we will make an extension to the general amplitude function. The only disadvantage is that the first derivative to these solutions contains an integral that disappear at the second derivation. We will also do a second extension: the two-integral amplitude function. With this extension we have the solution to a system of ODEs having a very strange behavior. Using the extended amplitude functions, we can define solutions to many short second-order nonlinear ODEs.