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In the present paper, we consider the existence of solutions with a prescribed l 2 -norm for the following discrete Schrödinger equations, { − Δ 2 u k − 1 − f (u k) = λ u k k ∈ Z , ∑ k ∈ Z | u k | 2 = α 2 , where Δ 2 u k − 1 = u k + 1 + u k − 1 − 2 u k , f ∈ C (R) , α is a fixed constant, and λ ∈ R arises as a Lagrange multiplier. To get the solutions, we investigate the corresponding minimizing problem with the l 2 -norm constraint: E α = inf { 1 2 ∑ | Δ u k − 1 | 2 − ∑ F (u k) : ∑ | u k | 2 = α 2 }. An elaborative analysis on a minimizing sequence with respect to E α is obtained. We prove that there is a constant α 0 ≥ 0 such that there exists a global minimizer if α > α 0 , and there exists no global minimizer if α < α 0 . It seems that it is the first time to consider the solution with a prescribed l 2 -norm of the discrete Schrödinger equations. [ABSTRACT FROM AUTHOR]

In the present paper, we study a class of discrete Schrödinger equations with concave–convex nonlinear terms via the variational method. Under certain conditions on the nonlinearities, two nontrivial solutions of the equations have been obtained by finding the minimizers on Nehari manifolds, and one of them is the ground state solution with negative energy. As we all know, there are few results on discrete systems involving concave–convex nonlinearities. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of multiple solutions for discrete boundary value problems involving the mean curvature operator by means of Clark's Theorem, where the nonlinear terms do not need any asymptotic and superlinear conditions at 0 or at infinity. Further, the existence of a positive solution has been considered by the strong comparison principle. As an application, some examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this present paper, we consider the following critical Kirchhoff problem - (a + λ ∫ R N | ∇ u | 2 d x) Δ u + m u = μ | u | p - 2 u + | u | 2 ∗ - 2 u in R N , where a , λ ∈ R and m , μ ∈ R + ∪ { 0 } , N ≥ 3 and 2 < p < 2 ∗ . In this first part, a pure critical Kirchhoff problem ( m = μ = 0 ) has been considered for both a > 0 and a ≤ 0 . We obtain a series of fairly complete existence and multiplicity results and have a clear understand the solutions of this pure critical Kirchhoff problem. In particular, if N ≥ 5 , a > 0 and λ > 0 is suitable small, we obtain two positive solutions, in which one is a mountain pass solution and another one is a global (local) minimum solution. In the second part, the original perturbation problem with m , μ > 0 has been considered and two positive solutions also have been obtained for N ≥ 5 , which is rather different compared with the case that λ = 0 . [ABSTRACT FROM AUTHOR]

Nonstructural protein 1 (nsp1) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a 180-residue protein that blocks translation of host mRNAs in SARS-CoV-2-infected cells. Although it is known that SARS-CoV-2's own RNA evades nsp1's host translation shutoff, the molecular mechanism underlying the evasion was poorly understood. We performed an extended ensemble molecular dynamics simulation to investigate the mechanism of the viral RNA evasion. Simulation results suggested that the stem loop structure of the SARS-CoV-2 RNA 5'-untranslated region (SL1) binds to both nsp1's N-terminal globular region and intrinsically disordered region. The consistency of the results was assessed by modeling nsp1-40S ribosome structure based on reported nsp1 experiments, including the X-ray crystallographic structure analysis, the cryo-EM electron density map, and cross-linking experiments. The SL1 binding region predicted from the simulation was open to the solvent, yet the ribosome could interact with SL1. Cluster analysis of the binding mode and detailed analysis of the binding poses suggest residues Arg124, Lys47, Arg43, and Asn126 may be involved in the SL1 recognition mechanism, consistent with the existing mutational analysis. Author summary: The pandemic of COVID-19 is still rampant all over the world as of 2021 June. SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), the causative pathogen of COVID-19, encodes a protein called nsp1 (nonstructural protein 1), which modulates and hijacks the ribosome of the infected host cells. With nsp1, infected human cells selectively translate SARS-CoV-2's RNA, which increases the virus reproduction efficiency while evading the host immunity. Though it has been known that nsp1 recognizes characteristic stem-loop structure at 5'-end of SARS-CoV-2's RNA (called SL1), the molecular mechanism underlying the recognition has been poorly understood. We investigated the mechanism of selective translation using the all-atom molecular dynamics simulation of nsp1-SL1 complex. Our simulation results suggest that the binding between nsp1 and SL1 is multi-modal. The results also imply that both the N-terminal globular part and the C-terminal flexible tail of nsp1 are involved in the binding. The residues involved in nsp1-SL1 binding coincides with the known mutant analyses of SARS-CoV-1 and SARS-CoV-2, as well as experimental evidence about nsp1-ribosome interactions. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the following discrete Schrödinger equations − (a + b ∑ k ∈ Z | Δ u k − 1 | 2) Δ 2 u k − 1 + V k u k = f k (u k) k ∈ Z , where a, b are two positive constants and V = { V k } is a positive potential. Δ u k − 1 = u k − u k − 1 and Δ 2 = Δ (Δ) is the one-dimensional discrete Laplacian operator. Infinitely many high-energy solutions are obtained by the Symmetric Mountain Pass Theorem when the nonlinearities { f k } satisfy 4-superlinear growth conditions. Moreover, if the nonlinearities are sublinear at infinity, we obtain infinitely many small solutions by the new version of the Symmetric Mountain Pass Theorem of Kajikiya. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the following degenerate Kirchhoff type problem { − (b ∫ R N | ∇ u | 2 d x) Δ u + V (x) u = | u | 2 ⁎ − 2 u in R N , u ∈ D 1 , 2 (R N) , where b is a positive constant, V ∈ L N 2 (R N) is a given nonnegative function and 2 ⁎ is the critical exponent. Quite a few papers have been published about the degenerate Kirchhoff type problem with a critical exponent; moreover, this degenerate problem in R N (N ≥ 5) has never been considered so far. We obtain some sufficient conditions on the existence of bounded state solution for this degenerate problem. As to the cases where N ≥ 5 , it is the first time to consider the degenerate problem. [ABSTRACT FROM AUTHOR]

Abstract In the present paper, we consider the discrete nonlinear Schrödinger equation − Δ u n + v n u n − ω u n = γ g n (u n) + h n , n ∈ Z , where v n , h n are real valued sequences, ω ∈ R , γ = ± 1 , and g n is a function sequence. We study this non-periodic discrete nonlinear Schrödinger equation with infinitely growing potential. Under some suitable conditions, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. It is the first time to investigate the nonhomogeneous discrete nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the following Kirchhoff type problem with critical exponent { − ( ε 2 a + ε b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u = f ( u ) , in R 3 , u ∈ H 1 ( R 3 ) . By variational methods, we show the existence of the positive solutions concentrating around global minima of the potential V ( x ) , as ε → 0 . We do not need the monotonicity of the function ξ → f ( ξ ) ξ 3 . [ABSTRACT FROM AUTHOR]

In the present paper, we consider the following Kirchhoff type problems { − ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u = u 5 , in R 3 , u ∈ D 1 , 2 ( R 3 ) , where a > 0 , b > 0 and V ∈ L 3 2 ( R 3 ) is a given nonnegative function. If | V | 3 2 is suitable small, we prove that this problem has at least one bound state solution. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the following Kirchhoff problem ( K ) { − ( 1 + b ∫ R 3 | ∇ u | 2 d x ) Δ u + a ( x ) u = | u | p − 2 u , in R 3 , u ∈ H 1 ( R 3 ) , where b > 0 and p ∈ ( 4 , 6 ) . Under some suitable decay assumptions but without any symmetry property on a ( x ) , we obtain infinitely many bound state solutions of this problem. [ABSTRACT FROM AUTHOR]

The existence and concentration of positive solutions for a class of Kirchhoff-type problems with a nonnegative steep well potential in R 3 are obtained via variational methods. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the following discrete Schrödinger equations m (∑ k ∈ Z (| Δ u k − 1 | 2 + V k | u k | 2)) (− Δ 2 u k − 1 + V k u k) − ω u k = f k (u k) k ∈ Z , where m is a continuous function and V = { V k } is a positive potential, ω ∈ R , Δ u k − 1 = u k − u k − 1 and Δ 2 = Δ (Δ) is the one dimensional discrete Laplacian operator. Under some suitable assumptions on f k , we prove the existence of nontrivial solutions for this nonlocal problems by variation methods. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the following Kirchhoff type problem − (a + b ∫ R 3 | ∇ u | 2 d x) Δ u + V (x) u = f (u) in R 3 , where a , b > 0 and the potential V has double potential well. With an asymptotically 4-linear nonlinearity f , we prove that the Kirchhoff type problem has one least energy nodal solution by variational methods. [ABSTRACT FROM AUTHOR]

Using gamma rays as a probe has garnered increasing attention in dynamic measurement as the potential of obtaining an earlier fitting starting point and less diffusion time. We developed a single-particle measurement system based on the randomly pulsed source method. And we presented a comprehensive validation process by measuring the leakage ray decay curve of borated polyethylene samples. The system primarily comprised an organic liquid scintillator detector and a waveform digitizer. We carefully selected source intensity and detector efficiency to meet the single-particle condition. Additionally, we implemented energy and time calibration, pulse shape discrimination, and time-dependent coincidence to enhance signal quality by reducing noise. The experimental gamma-ray decay curves closely match the Monte Carlo simulation results, demonstrating the system's feasibility and reliability. The complete verification process provides convenience for more accurate measurement with subcritical assemblies in future research. • Measuring gamma-ray signals using the RPS method in the single-particle condition. • The gamma-ray probe shows application potential in the subcritical parameter measurement. • Comprehensive validation process of the single-particle system is presented. [ABSTRACT FROM AUTHOR]

Highlights • A 3D FEM code is developed to calculate dynamic behavior of burst in Godiva I reactor. • Fission rate in plateau vibrates with displacement for medium and fast bursts. • Point kinetic and adiabatic approximations are applicable for the three selected bursts. • Stress concentration in core center occurs at time of displacement wave crest. Abstract In this paper, the neutronic and thermoelastic behaviors of prompt supercritical bursts in the fast burst reactor are numerically studied by developing a 3D coupled multiphysics FEM (finite element method) code FBR-MPC based on the neutron transport theory for neutronics, thermal conduction equation for temperature and thermoelastic equations for displacement/stress. Because the feedback effect of core expansion on the neutronics can be accurately modeled by reforming the discretized element and changing the material density, the developed code is expected to be applicable for simulating the dynamic behaviors of all the bursts under controlled condition. To validate the developed code and obtain precise pictures of the dynamic behaviors, the slow, medium and fast bursts in the Godiva I reactor are investigated. The results show that the developed code can provide accurate results for all the three selected bursts. For the medium and fast bursts where the inertia effect is generated, the fission rate oscillation caused by the core vibration, which cannot be reproduced with the simplified models in early works, is first observed by using the developed FBR-MPC code. Due to the small core expansion and short burst time, the point kinetic and adiabatic approximations are suitable for the neutronic and temperature calculations for all the three selected bursts. At the time of displacement wave crest, the stress concentration in the core central regions becomes more significant for faster bursts. [ABSTRACT FROM AUTHOR]

• A neutron time sequence acquisition system was developed. • Both neutron & gamma was used to analyze the prompt neutron decay constant. • The A/C ratio in the measurement was explored. • The timing precision brought by TOF of neutrons was discussed. Aiming at measuring the prompt neutron decay constant α of fast critical assemblies, Rossi-α method was improved by means of the acquisition of neutron and gamma time sequence. The application of the time sequence method in delayed critical & subcritical experiments at a fast critical assembly was here in described, focus in particular on the gamma analysis and the exploration of A/C ratio which directly affects the measurement precision of α. The reliability of the time sequence method is proved by the agreement of the α values obtained based on neutron and gamma. The A/C ratio based on neutron and gamma shows an obvious difference and the corresponding conclusion guides to a larger A/C ratio. The time sequence method shows advantages of higher experimental efficiency and flexible data analysis which contribute to more accurate experimental result. [ABSTRACT FROM AUTHOR]

1,1,4,4-tetraphenyl-1,3-butadiene (TPB) is an organic wavelength-shifting (WLS) material, which can down-convert wavelength from extreme ultraviolet (EUV) region to blue-visible region. When it is used in noble element detectors, TPB will be applied in strong radiation fields, so the radiation-resistance behavior of TPB is of crucial importance. The radiation effects of α and γ irradiation on TPB were studied by using 241Am α source and 60Co γ source. The results show that the peak intensity of fluorescence decreases linearly for α irradiation, while demonstrate an obvious turning point for γ irradiation when the accumulated dose is over 100 kGy. Experimental results confirmed that TPB is a promising WLS material in strong radiation environment. • The α and γ radiation experiments on tetraphenyl butadiene were conducted. • The peak of tetraphenyl butadiene fluorescence decreases with α cumulative flux. • Fluorescent intensity declines sharply when γ irradiation dose is over 100 kGy. • TPB is a promising wavelength conversion material for radiation environment. [ABSTRACT FROM AUTHOR]

• Criteria on feasible working-state spaces of heat pipes(HPs) were established. • Heat transfer limit(HTL) and isothermality(ISO) are analyzed in an integrated way. • ISO and HTL criteria compete to found lower but no upper bound of alkali metal HPs. • Both upper bound (by HTL) and lower bound (by ISO) exist for water HPs. • Once HPs are designed not to exceed HTL, ISO can naturally be guaranteed. Heat pipes (HPs) are promising in advanced energy and power systems, featured by capability to transfer large heat flow over long distances with small temperature drops. However, the feasibility verification of such isothermality is usually ignored while only heat transfer limits (HTLs) are checked when HPs are to be designed and applied. In this work, criteria on feasible working-state spaces of HPs have been established, integrating the classical HTL and the pseudo-wick-thermal-conductivity-based isothermality theories. Calculations and comparisons have been done in wide ranges of working medium species, lengths, temperature and cooling condition. Isothermality is found to improve with increasing temperature and decreasing length as well as cooling coefficient, thus could always be achieved as long as temperature is sufficiently high. With regard to HTLs, differences exist between water HPs and alkali metal HPs. The isothermality and the HTL criteria compete to found the lower bounds of temperature but no upper bound exists for alkali metal HPs, while both upper bounds (determined by the HTL criterion) and lower bounds (determined by the isothermality criterion) exist for water HPs. The ranges of feasible working-state spaces of HPs with different working mediums are primarily determined by the HTL criterion. Once HPs are designed to operate not exceeding HTLs, isothermality can generally be guaranteed. [ABSTRACT FROM AUTHOR]

• A pseudo wick thermal conductivity (PWTC) for heat pipes was defined and derived. • A vapor transfer factor complementary to the classical Figure of Merit was defined. • A PWTC -based pure-conduction heat pipe transient model was developed and verified. • A criterion for heat pipe isothermality was developed and verified. • The new criterion proved to be more rigorous and accurate than the traditional one. Heat pipes (HPs) are promising in advanced energy and power systems, and simulating their transient performances is of great importance. However, the existing elaborate transient models are too complex for engineering simulations, and there is a lack of comprehensive and accurate criteria for HP isothermality on which various simplified models depend. Based on an analogy between the pressure drop formula of vapor flow and the Fourier's law, a pseudo wick thermal conductivity (PWTC) of HPs was novelly defined and derived. A novel pure-conduction transient model and a novel criterion of isothermality for HPs were developed and verified by experimental results. PWTC was found to depend on both the physical properties of working mediums as well as the HP dimensions, and proportional to a vapor transfer factor (VTF). VTF characterizes the coupled heat transfer effect of the vapor flow and the phase-change, thus complementary to the classical Figure of Merit (FOM) in HP theory. VTF increases with increasing temperature, and so does PWTC. The startup of a sodium HP was accurately simulated with the pure-conduction model. The effect of free-molecular flow proves to be negligible in the transient model. The PWTC -based criterion of isothermality proved to be more rigorous and accurate than the traditional transition-temperature-based criterion. The isothermal characteristics of room-temperature HPs differ from that of high-temperature HPs. FOM s of water always counts, while FOM s of the alkali-metals are significant only when temperature exceeds certain thresholds determined by PWTC and the boundary conditions.The modeling and analyzing methods are of certain generality, and can be extended to evaluate the applicability of simplified models, to judge the isothermality, and to construct three-dimensional transient models of complex systems. [ABSTRACT FROM AUTHOR]