ON A CLASS OF INHOMOGENEOUS,ENERGY-CRITICAL,FOCUSING,NONLINEAR SCHRDINGER EQUATIONS

In this paper, we study the Cauchy problem of the inhomogeneous energy-critical Schrōdinger equation： iаtu=-△u-k（x）｜u｜4/N-2u,N≥3. Using the potential well method, we establish some new sharp criteria for blow-up of solutions in tile nonradial case. In particular, our conclusion in some sense improves on the results in [Kenig and Merle, invent. Math. 166, 645-675 （2006）], where only the radial case is considered in dimensions 3. 4. 5.

Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.

Near-zero-adhesion-enabled intact wafer-scale resist-transfer printing for high-fidelity nanofabrication on arbitrary substrates

There is an urgent need for novel processes that can integrate different functional nanostructures onto specific substrates,so as to meet the fast-growing need for broad applications in nanoelectronics,nanophotonics,and fexible optoelectronics.Existing direct-lithography methods are difficult to use on fexible,nonplanar,and biocompatible surfaces.Therefore,this fabrication is usually accomplished by nanotransfer printing.However,large-scale integration of multiscale nanostructures with unconventional substrates remains challenging because fabrication yields and quality are often limited by the resolution,uniformity,adhesivity,and integrity of the nanostructures formed by direct transfer.Here,we proposed a resist-based transfer strategy enabled by near-zero adhesion,which was achieved by molecular modification to attain a critical surface energy interval.This approach enabled the intact transfer of wafer-scale,ultrathin-resist nanofilms onto arbitrary substrates with mitigated cracking and wrinkling,thereby facilitating the in situ fabrication of nanostructures for functional devices.Applying this approach,fabrication of three-dimensional-stacked multilayer structures with enhanced functionalities,nanoplasmonic structures with~10 nm resolution,and MoS2-based devices with excellent performance was demonstrated on specific substrates.These results collectively demonstrated the high stability,reliability,and throughput of our strategy for optical and electronic device applications.

Optimization of Maturation of Radio-Cephalic Arteriovenous Fistula Using a Model Relating Energy Loss Rate and Vascular Geometric Parameters

The main reason for the early failure of radio-cephalic arteriovenous fistula (RCAVF) is non-maturity, which means that the blood flow rate in the fistula cannot increase to the expected value for dialysis. From a mechanical perspective, the vascular resistance at the artificially designed anastomosis causes an energy loss that affects blood flow rate growth and leads to early failure. This research studied how to maximize the RCAVF maturity and primary patency by controlling the energy loss rate. We theoretically analyzed and derived a model that evaluates the energy loss rate Eavf in RCAVF as a function of its blood vessel geometric parameters (GPs) for given flow rates. There was an aggregate of five controllable GPs in RCAVF: radial artery diameter (Dra), cephalic vein diameter (Dcv), blood vessel distance between artery and vein (h), anastomotic diameter (Da), and anastomotic angle (θ). Through this analysis, it was found that Eavf was inversely proportional to Dra, Dcv, Da, and θ, whereas proportional to h. Therefore, we recommended surgeons choose the vessels with large diameters, close distance, and increase the diameter and angle of the anastomosis to decrease the early failure of RCAVF. Simultaneously, we could explain the results of many clinical empiricisms with our formula. We found that increasing Dcv and θ was more significant in reducing Eavf than increasing Dra and Da. Based on our model, we could define two critical energy loss rates (CELa, CELb) to help surgeons evaluate the blood vessels and choose the ideal range of θ, and help them design the preoperative RCAVF plan for each patient to increase the maturity and the primary patency of RCAVF.

Effects of temperature, particle size, and air humidity on sensibility of typical high-energetic explosives

The production and utilization of high-energetic explosives often pose a range of safety hazards,with sensitivity being a key factor in evaluating these risks.To investigate how temperature,particle size,and air humidity affect the responsiveness of commonly used high-energetic explosives,a series of BAM(Bundesanstalt für Materialforschung und-prüfung)impact and friction sensitivity tests were carried out to determine the critical impact energy and critical load pressure of four representative high-energetic explosives(RDX,HMX,PETN and CL-20)under different temperatures,particle sizes,and air humidity conditions.The experimental findings facilitated an examination of temperature and particle size affecting the sensitivity of high-energetic explosives,along with an assessment of the influence of air humidity on sensitivity testing.The results clearly indicate that high-energetic explosives display a substantial decline in critical reaction energy when subjected to micrometre-sized particles and an air humidity level of 45%at a temperature of 90℃.Furthermore,it was noted that the critical reaction energy of high-energetic explosives diminishes with an increase in temperature within 25℃−90℃.In the same vein,as the particle sizes of high-energetic explosives increase,so does the critical reaction energy for micrometre-sized particles.High air humidity significantly affects the sensitivity testing of high-energetic explosives,emphasizing the importance of refraining from conducting sensitivity tests in such conditions.

Anisotropy in shear-sliding fracture behavior of layered shale under different normal stress conditions

Shear-sliding mode(mode Ⅱ)fracture of rocks is a vital failure form in deep underground engineering.To gain deep insight into the anisotropic shear fracture behaviors of a typical shale under high normal stress conditions,a series of direct shear tests were conducted on double-notched specimens in three typical bedding orientations(i.e.,the arrester,divider,short-transverse orientations)and under five normal stresses.The modeⅡfracture toughness(K_(Ⅱc))is found to exhibit a significant 3D anisotropy.The maximum K_(Ⅱc)is obtained in the divider orientation,followed by those in the arrester and short-transverse orientations.In contrast,the 3D anisotropy in the critical modeⅡenergy release rate(G_(Ⅱc))is not as significant as that in K_(Ⅱc),and G_(Ⅱc)in the arrester orientation is quite close to that in the divider orientation.The anisotropy in the prepeak input energy accumulated during shearing is found to be exactly consistent with that in G_(Ⅱc),which has not been noted before.Furthermore,the anisotropies in the modeⅡfracture resistances will,unexpectedly,not be weakened by the high normal stress.Owing to the layered structures,tensile cracks are involved during the modeⅡfracture process,resulting in the formation of rough fracture surfaces.

The temperature-dependent fracture strength model for ultra-high temperature ceramics

Breaking down the entire structure of a material implies severing all the bonds between its atoms either by applying work or by heat transfer. Because bond-breaking is indifferent to either means, there is a kind of equivalence between heat energy and strain energy. Based on this equivalence, we assume the existence of a constant maximum storage of energy that includes both the strain energy and the corresponding equivalent heat energy. A temperaturedependent fracture strength model is then developed for ultrahigh temperature ceramics （UHTCs）. Model predictions for UHTCs, HfB2, TiC and ZrB2, are presented and compared with the experimental results. These predictions are found to be largely consistent with experimental results.

Investigation on the Dielectric Properties of CO2 and CO2-Based Gases Based on the Boltzmann Equation Analysis

In this paper, the dielectric properties of CO2, CO2/air, CO2/O2, CO2/N2, CO2/CF4, CO2/CH4, CO2/He, C02/H2, CO2/NH3 and CO2/CO were investigated based on the Boltzmann equation analysis, in which the reduced critical electric field strength （E/N）cr of the gases was derived from the calculated electron energy distribution function （EEDF） by solv- ing the Boltzmann transport equation. In this work, it should be noted that the fundamental data were carefully selected by the published experimental results and calculations to ensure the validity of the calculation. The results indicate that if He, H2, N2 and CH4, in which there axe high ionization coefficients or a lack of attachment reactions, are added into CO2, the dielectric properties will decrease. On the other hand, air, O2, NH3 and CFa （ranked in terms of （E/N）cr value in increasing order） have the potential to improve the dielectric property of CO2 at room temperature.

The Study of Chamber Rockburst by the CUSP Model of Catastrophe Theory

By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .

Experimental study on detonation parameters and cellular structures of fuel cloud

In this paper, detonation parameters of fuel cloud, such as propylene oxide （PO）, isopropyl nitrate （IPN）, hex- ane, 90# oil and decane were measured in a self-designed and constructed vertical shock tube. Results show that the deto- nation pressure and velocity of PO increase to a peak value and then decrease smoothly with increasing equivalence ra- tio. Several nitrate sensitizers were added into PO to make fuel mixtures, and test results indicated that the additives can efficiently enhance detonation velocity and pressure of fuel cloud and one type of additive n-propyl nitrate （NPN） played the best in the improvement. The critical initiation energy that directly initiated detonation of all the test liquid fuel clouds showed a U-shape curve relationship with equiva- lence ratios. The optimum concentration lies on the rich-fuel side （;b 〉 1）. The critical initiation energy is closely related to molecular structure and volatility of fuels. IPN and PO have similar critical values while that of alkanes are larger. Detonation cell sizes of PO were respectively investigated at 25;C, 35;C and 50;C with smoked foil technique. The cell width shows a U-shape curve relationship with equivalence ratios at all temperatures. The minimal cell width also lies on the rich-fuel side （;b 〉 1）. The cell width of PO vapor is slightly larger than that of PO cloud. Therefore, the deto- nation reaction of PO at normal temperature is controlled by gas phase reaction.

Temperature-Dependent Tearing Behavior of Rubber Materials:Characterization and Modeling

With the increasingly widespread application of rubber in many fields,there is a growing demand for quantitative characterization of temperature-dependent mechanical properties in high-temperature service environments.The critical tearing energy is an important criterion for determining whether rubber materials will experience tearing instability,while tear strength is a key parameter for rubber materials to resist tearing.It is necessary to quantitatively characterize their evolution with temperature.Current theoretical research mainly relies on fitting a large amount of experimental data,which is not convenient for engineering applications.Therefore,in this work,a temperature-dependent critical tearing energy model is firstly developed based on the force-heat equivalence energy density principle.This model considers the equivalent relationship between the critical tearing energy required for crack instability propagation and the thermal energy stored in the rubber material.It is demonstrated that our model has higher prediction accuracy when compared to other models.Furthermore,combining with the Griffith fracture theory,temperature-dependent tear strength models applicable to three different crack modes are separately established.These models are validated using experimental data for Mode I opening cracks and ModeⅢtearing cracks,and good consistency is achieved.Additionally,a quantitative analysis of the influence of elastic modulus on tear strength at different temperatures is conducted.This work provides a reliable way for predicting temperature-dependent tearing instability behavior and offers beneficial suggestions for improving the tear strength of rubber materials at different temperatures.

Effect of interface debonding on matrix multicracking evolution of fiber-reinfroced ceramic-matrix composites

An analytical methodology was developed to investigate the effect of fiber/matrix interface debonding on matrix multicracking evolution of fiber-reinforced CMCs(ceramic-matrix composites).The Budiansky-Hutchinson-Evans shear-lag model was adopted to analyse the micro-stress field of the damaged composites.The critical matrix strain energy criterion,which presupposes the existence of an ultimate or critical matrix strain energy with matrix,was obtained to simulate the matrix multicracking evolution of CMCs.With the increase of the applied stress,the matrix multicracking and fiber/matrix interface debonding occurred to dissipate the additional energy entered into the composites.The fiber/matrix interface debonded length under matrix multicracking evolution was obtained by treating the interface debonding as a particular crack propagation problem.The conditions for no-debonding and debonding during the evolution of matrix multicracking were discussed in terms of two interfacial properties,i.e.,the interface shear stress and interface debonded toughness.When the fiber/matrix interface was bonded,the matrix multicracking evolution was much more intense compared with the interface debonding;when the fiber/matrix interface was debonded,the matrix crack density increased with the increasing of interface shear stress and interface debonded energy.The theoretical results were compared with experimental data of unidirectional SiC/CAS(calcium alumina silicate),SiC/CAS-Ⅱand SiC/borosilicate composites.

On the Cahn-Hilliard-Brinkman Equations in R^(4):Global Well-Posedness

We study the global well-posedness of large-data solutions to the Cauchy problem of the energy critical Cahn-Hilliard-Brinkman equations in R^(4).By developing delicate energy estimates,we show that for any given initial datum in H^(5)(R^(4)),there exists a unique global-in-time classical solution to the Cauchy problem.As a special consequence of the result,the global well-posedness of large-data solutions to the energy critical Cahn-Hilliard equation in R^(4) follows,which has not been established since the model was first developed over 60 years ago.The proof is constructed based on extensive applications of Gagliardo-Nirenberg type interpolation inequalities,which provides a unified approach for establishing the global well-posedness of large-data solutions to the energy critical Cahn-Hilliard and Cahn-Hilliard-Brinkman equations for spatial dimension up to four.