Sharp Energy Research Articles

Two-dimensional gravity waves at low regularity I: Energy estimates

This article represents the first installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on sharp cubic energy estimates. Precisely, we introduce and develop the techniques to prove a new class of energy estimates, which we call balanced cubic estimates . This yields a key improvement over the earlier cubic estimates of Hunter–Ifrim–Tataru (2016), while preserving their scale-invariant character and their position-velocity potential holomorphic coordinate formulation. Even without using any Strichartz estimates, these results allow us to significantly lower the Sobolev regularity threshold for local well-posedness, drastically improving earlier results obtained by Alazard–Burq–Zuily (2014, 2018), Hunter–Ifrim–Tataru (2016) and Ai (2019).

Sintering of Copper Nanoparticles using Intense Pulsed Light for screen-printed films on flexible substrate

Abstract Rapid growth in applications involving large area flexible electronics has led to wide adoption of the technique of sintering printed films using intense pulsed light (IPL) due to its pulse mode operation and ability to reach high sintering temperatures without affecting the underlying substrate significantly. We study sintering mechanisms of screen-printed thin films of copper nanoparticles on polyethylene terephthalate (PET) plastic substrate by varying irradiance energy over a wide range to monitor conductivity and associated microstructure changes. We obtain optimized parameters which indicate existence of a sharp threshold irradiance energy to kickstart sintering, and two distinct regimes beyond that. The low temperature regime has a high energy barrier while the high temperature regime has a substantially reduced energy barrier with change of phase due to local melting.

Robust Effective Ground State in a Nonintegrable Floquet Quantum Circuit.

An external periodic (Floquet) drive is believed to bring any initial state to the featureless infinite temperature state in generic nonintegrable isolated quantum many-body systems in the thermodynamic limit, irrespective of the driving frequency Ω. However, numerical or analytical evidence either proving or disproving this hypothesis is very limited and the issue has remained unsettled. Here, we study the initial state dependence of Floquet heating in a nonintegrable kicked Ising chain of length up to L=30 with an efficient quantum circuit simulator, showing a possible counterexample: the ground state of the effective Floquet Hamiltonian is exceptionally robust against heating, and could stay at finite energy density even after infinitely many Floquet cycles, if the driving period is shorter than a threshold value. This sharp energy localization transition or crossover does not happen for generic excited states. The exceptional robustness of the ground state is interpreted by (i)its isolation in the energy spectrum and (ii)the fact that those states with L-independent ℏΩ energy above the ground state energy of any generic local Hamiltonian, like the approximate Floquet Hamiltonian, are atypical and viewed as a collection of noninteracting quasiparticles. Our finding paves the way for engineering Floquet protocols with finite driving periods realizing long-lived, or possibly even perpetual, Floquet phases by initial state design.

Feasibility assessment of next-generation smart district heating networks by intelligent energy management strategies

Increasing flexibility of energy demand in a district heating network (DHN) results in both more possibility of interactions between the heating network and renewable resources and managing peak loads by shaving and shifting. This paper summarizes a series of tests performed in a large building complex that may drive future operational strategies for DHN. These novel strategies aim to impact selected customers with a specific range of heat consumption intensity to assess achievable flexibilities in heating demand without additional cost. The results show that a reduction in DHN supplied temperature by 6 °C does not significantly influence the heat consumption of customers equipped with radiators and thermostatic valves. However, its reduction by 10 °C, and 20 °C can impact users with higher consumed heat rates of approximately 0.2 and 0.1 [Unit/10min], respectively. Moreover, prolonging test periods until midday, when there is the highest probable outdoor temperature and solar irradiation may avoid sharp energy variations after tests.

Characteristics of household energy consumption in the shadow of the Russia-Ukraine war - a case study from Hungary

This study aims to identify the factors affecting household energy consumption by applying spatial econometric models. Our findings suggest that sharp energy price growth is followed by significant reductions in household energy consumption, but it is difficult to distinguish specific consumer groups. Weather conditions are of particular importance (compared to the EU average). The results highlight two things: a) the problem of obsolete housing stock and the need for energy efficiency improvements and b) low energy awareness of households, especially before the energy crisis. Furthermore, hotspots with higher per capita gas consumption are also identified in Hungary. The geographical dimension is crucial, and it is not possible to make general decisions on energy efficiency issues. Effective results can be achieved through spatially concentrated interventions.

Weak Solutions of Mullins–Sekerka Flow as a Hilbert Space Gradient Flow

We propose a novel weak solution theory for the Mullins–Sekerka equation in dimensions d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document} and 3, primarily motivated from a gradient flow perspective. Previous existence results on weak solutions due to Luckhaus and Sturzenhecker (Calc. Var. PDE 3, 1995) or Röger (SIAM J. Math. Anal. 37, 2005) left open the inclusion of both a sharp energy dissipation principle and a weak formulation of the contact angle at the intersection of the interface and the domain boundary. To incorporate these, we introduce a functional framework encoding a weak solution concept for Mullins–Sekerka flow essentially relying only on (i) a single sharp energy dissipation inequality in the spirit of De Giorgi, and (ii) a weak formulation for an arbitrary fixed contact angle through a distributional representation of the first variation of the underlying capillary energy. Both ingredients are intrinsic to the interface of the evolving phase indicator and an explicit distributional PDE formulation with potentials can be derived from them. The existence of weak solutions is established via subsequential limit points of the naturally associated minimizing movements scheme. Smooth solutions are consistent with the classical Mullins–Sekerka flow, and even further, we expect our solution concept to be amenable, at least in principle, to the recently developed relative entropy approach for curvature driven interface evolution.

On the convergence of the Willmore flow with Dirichlet boundary conditions

Very little is yet known regarding the Willmore flow of surfaces with Dirichlet boundary conditions. We consider surfaces with a rotational symmetry as initial data and prove a global existence and convergence result for solutions of the Willmore flow with initial data below an explicit, sharp energy threshold. Strikingly, this threshold depends on the prescribed boundary conditions — it can even be made to be 0. We show sharpness for some critical boundary data by constructing surfaces above this energy threshold so that the corresponding Willmore flow develops a singularity. Finally, a Li–Yau inequality for open curves in H2 is proved.

Thermodynamics and evaporation of perfect fluid dark matter black hole in phantom background

We present a novel interpretation of the thermodynamics of perfect fluid dark matter (PFDM) black hole based on Misner–Sharp energy and then investigate its evaporation behavior. We find that the ratio between dark sector initial density and black hole horizon radius significantly influences black hole evaporation behaviors. We demonstrate that the presence of the dark sector can significantly extend the lifetime of a black hole which is similar to the Reissner–Nordström case. Our work reformulates the thermodynamics of PFDM black holes and points out the existence of long-lived black holes in the presence of the dark sector.

Recent progresses on BSM and dark matter searches with CUORE

The Cryogenic Underground Observatory for Rare Events (CUORE) is the first bolometric 0\nu\beta\beta0νββ experiment to reach the one-tonne mass scale. The detector, located underground at the Laboratori Nazionali del Gran Sasso in Italy, consists of 988 TeO_22 crystals arranged in a compact cylindrical structure of 19 towers, operating at a base temperature of about 10 mK. After beginning its first physics data run in 2017, CUORE has since collected the largest amount of data ever acquired with a solid state detector and provided the most sensitive measurement of 0\nu\beta\beta0νββ decay in ^{130}130Te ever conducted. The large exposure, sharp energy resolution, segmented structure and radio-pure environment make CUORE an ideal instrument for a wide array of searches for rare events and symmetry violations. New searches for low mass dark matter, solar axions, CPT and Lorenz violations, and refined measurements of the 2\nu\beta\beta2νββ spectrum in CUORE have the potential to provide new insight and constraints on extensions to the standard model complementary to other particle physics searches. In this contribution, the recent progress on BSM and dark matter searches in CUORE are discussed.

Energy criteria of global existence for a class of Hartree equations with Coulomb potential

This paper studies a class of Hartree equations with Coulomb potential. Combined with the conservation of mass and energy, we analyze the variational characteristics of the corresponding nonlinear elliptic equation. According to the range of parameters, we construct the evolution invariant flows of the equation in different cases. Then the sharp energy thresholds for global existence and blow-up of solutions are discussed in detail.

Low Energy Structures in Nuclear Reactions with 4n in the Final State

We investigate a reaction model that describes a fast removal of the α particle from the ^{8}He nucleus with eventual emission of four neutrons. The obtained four neutron energy distribution allows one to explain the sharp low energy peak observed by studying the missing mass spectra of four neutrons in Duer etal. [Nature (London) 606, 678 (2022)NATUAS0028-083610.1038/s41586-022-04827-6], as a consequence of dineutron-dineutron correlations. The phenomenon of the emergence of a sharp low-energy peak in the four-neutron energy distribution should be more general and is expected in the decay of other systems containing a four-neutron halo.

Stability of hopfions in bulk magnets with competing exchange interactions

Magnetic hopfions are string-like three-dimensional topological solitons, characterised by the Hopf number. They serve as a fundamental prototype for three-dimensional magnetic quasiparticles and are an inspiration for novel device concepts in the field of spintronics. Based on a micromagnetic model and without considering temperature, the existence of such hopfions has been predicted in certain magnets with competing exchange interactions. However, physical realisation of freely moving hopfions in bulk magnets have so far been elusive. Here, we consider an effective Heisenberg model with competing exchange interactions and study the stability of small toroidal hopfions with Hopf number ${Q}_{\text{H}}=1$ by finding first-order saddle points on the energy surface representing the transition state for the decay of hopfions via the formation of two coupled Bloch points. We combine the geodesic nudged elastic band method and an adapted implementation of the dimer method to resolve the sharp energy profile of the reaction path near the saddle point. Our analysis reveals that the energy barrier can reach substantial height and is largely determined by the size of the hopfion relative to the lattice constant.

Ab-initio study of the optical properties of 2D Yn+1Cn (n = 1, 2, and 3) MXenes and bulk of YC

Calculations are accomplished in the framework of density functional theory and pseudopotential method with local density approximation (LDA) and QUANTUM-ESPRESSO/PWSCF computational code. Large negative values of ε1ω represent that materials exhibit Drude-like behavior while at higher energies, interband transitions occur. According to the results of the imaginary part of the dielectric functionε2ω, it can be stated that the absorption starts from small energies, which indicates that the bulk of YC and Yn+1Cn (n = 1, 2, and 3) monolayers have no energy bandgap and show a metallic nature. The sharp plasmonic energy peak for the YC structure in the x-direction can be seen at 18.61 eV; also the values of sharp plasmonic energy peaks for the Y2C, Y3C2, and Y4C3 in the x-direction are 13.40 eV, 11.98 eV, and 10.14 eV respectively. The results of the reflection spectrum show that the bulk of YC and 2D Yn+1Cn (n = 1, 2, and 3) MXenes have large values due to the presence of free electrons and plasma fluctuations, and confirm the metallic nature of the mentioned compounds. For the bulk of YC, the refractive index prominent peaks approach zero within the photon energy range of 13 eV up to 16 eV, while the corresponding range for the 2D Yn+1Cn MXenes is narrower and equal to 6 eV up to 7 eV. Also, the absorption spectrum in the bulk structure of YC and Yn+1Cn MXenes starts from zero photon energy which verifies the metallic behavior of the studied structures.

Statistically optimized sequential hydrothermal route for FeTiO3 surface modification: evaluation of hazardous cationic dyes adsorptive removal.

In the present study, the performance of facile hybrid sequential chemical treatments of titanomagnetite concentrate (TC), alkaline leaching, and sodium dodecyl sulfate (SDS) modification has been evaluated for the removal of crystal violet (CV), malachite green (MG), and methylene blue (MB) cationic dyes. The physical and chemical properties of samples were characterized using scanning electron microscopy (SEM), energy dispersive X-ray (EDX), N2 adsorption-desorption, X-ray diffraction (XRD), X-ray fluorescence spectroscopy (XRF), and Fourier transform infrared spectroscopy (FTIR) analyses. Moreover, dye removal in the batch system was investigated by evaluating adsorbent dosage, contact time, initial dye concentration, pH of the solution, temperature, electrolyte concentration, adsorption isotherm, kinetic, and thermodynamic. The results showed that the maximum adsorption capacity was obtained at SDS concentration of 6mM, NaOH concentration of 9M, the temperature of 160°C, solid/liquid ratio of 4g/100mL, and the process duration of 24h. In the alkaline leaching process, forming the Na2TiO3 phase with sharp and high energy points can be improved the adsorption properties. Accordingly, the adsorption capacity and removal efficiency attained 19.84, 18.64, and 19.66mg/g and 99.21, 93.24, and 98.31% for CV, MG, and MB, respectively. Furthermore, the dye removal followed pseudo-second-order (R2 = 0.9990) and Freundlich (R2 = 0.9970) models. The evaluation of thermodynamic parameters indicated the endothermic (∆H° = 110.91J/mol) and spontaneous nature (ΔG˚ < 0) of the adsorption process. This study concluded that the modified TC had a potential ability for application in textile wastewater treatment.

First-principles investigation on narrow bandgap InSb1−xBix dilute bismide alloys for highly efficient long-wavelength infrared optoelectronics

The electronic structure, optical properties and crystal structure of the dilute bismide InSb1−xBix alloys with (0 ≤ x ≤ 0.125) have been studied using the DFT FP − LAPW method within the novel TB-mBJ and WC-GGA models. The lattice constant increases quasi-linearly in InSb1−xBix for small Bi contents. Based on calculations of the formation energy, we demonstrated the thermodynamic stability of the alloys. The small content of Bi into InSb1−xBix results in a large bandgap narrowing by ∼ 264 meV up to a composition of 0.125 covering the mid- and long wavelength IR ∼ 3.4–12.5 μm spectral range. From DOS analysis, a bandgap reduction in the InSb1-xBix can be explained by both upward movement of the valence band (VB) induced by the resonance interaction of Bi-6p states at the top of VB and the downward moves of In-s and Sb/Bi-p states at the conduction band (CB). A semiconductor-semimetal transition in InSb1−xBix at × ∼ 0.137 was expected. The optical properties in terms of dielectric functions (ε1, ε2), refractive index n, extinction coefficient k, reflectivity R and the absorption coefficient α were calculated for photon energies of 0–8 eV and compared to experimental data. The sharp energy structures appear in various optical spectra associated with interband transitions from occupied In-s, Sb-p and Bi-p orbitals located at VBmax to unoccupied In-s/p, Sb-p and Bi-p states located at CBmin. Good absorbance in the ultraviolet range was observed, which is useful for solar cells design. InSb1−xBix/InSb bismide alloy is an attractive candidate for realizing highly efficient light-emitting sources and photodetectors operating in the long-wavelength infrared spectral range (λLWIR ≥ 8 μm).

Three-dimensional sharp V-notch stress intensity factor and strain energy rate density under creeping conditions

Fracture evaluation of three dimensional (3D) notches in creeping solids have drawn considerable attention due to their potential application in structural integrity assessment. In this paper, the notch stress intensity factor (NSIF) and the strain energy rate density (SERD) rule are extended to 3D sharp V-notch tip under creeping conditions. In particular, the out-of-plane factor Tz is introduced to describe the 3D NSIF of creeping sharp V-notch tip field. The out-of-plane effect on the SERD is also studied based on the KN(t)-Tz solution. A method to evaluate the 3D sharp V-notch NSIF was proposed based on the concept of SERD. The link between the NISF and SERD of 3D sharp V-notch is established and discussed. It is found that the SERD is obviously influenced by the out-of-plane factor. The variations of NSIF along the thickness direction of 3D sharp V-notch front and the effect of creep time are also discussed. The accuracy of the presented evaluation form is also validated. The solution given in this paper could provide a new perspective and theoretical foundation on understanding the NSIF and SERD for sharp V-notch.

One‐dimensional periodic fractional Schrödinger equations with exponential critical growth

In the present paper, we study the existence of nontrivial solutions of the following one‐dimensional fractional Schrödinger equation where stands for the 1/2‐Laplacian, , and is a continuous function with an exponential critical growth. Comparing with the existing works in the field of exponential‐critical‐growth fractional Schrödinger equations, we encounter some new challenges due to the weaker assumptions on the reaction term . By using some sharp energy estimates, we present a detailed analysis of the energy level, which allows us to establish the existence of nontrivial solutions for a wider class of nonlinear terms. Furthermore, we use the non‐Nehari manifold method to establish the existence of Nehari‐type ground state solutions of the one‐dimensional fractional Schrödinger equations.

Dynamics of the nonlinear Hartree equation with a focusing and defocusing perturbation

In this paper, we identify the sharp energy threshold for the global existence and blow-up to the Hartree equation with a focusing and defocusing perturbation, respectively, by utilizing comprehensive potential-well structures generated by the combined nonlinearities. Then, by adopting the refined compactness lemma, we detect the dynamical properties of blow-up solutions near the sharp threshold mass, including blow-up rate, concentration, weak limits and limiting profile decomposition of blow-up solutions with small super critical mass.

On the sharp interface limit of a phase field model for near spherical two phase biomembranes

We consider sharp interface asymptotics for a phase field model motivated by lipid raft formation on near spherical biomembranes involving a coupling between the local mean curvature and the local composition. A reduced diffuse interface energy depending only on the membrane composition is introduced and a \Gamma -limit is derived. It is shown that the Euler–Lagrange equations for the limiting functional and the sharp interface energy coincide. Finally, we consider a system of gradient flow equations with conserved Allen–Cahn dynamics for the phase field model. Performing a formal asymptotic analysis, we obtain a system of gradient flow equations for the sharp interface energy coupling geodesic curvature flow for the phase interface to a fourth order PDE free boundary problem for the surface deformation.

Sharp energy regularity and typicality results for Hölder solutions of incompressible Euler equations

This paper is devoted to show a couple of typicality results for weak solutions $v\in C^\theta$ of the Euler equations, in the case $\theta 0}W^{\frac{2\theta}{1-\theta} + \varepsilon,p}(I)$ for any open $I \subset [0,T]$, are a residual set in $X_\theta$. This, in particular, partially solves [9, Conjecture 1]. We also show that smooth solutions form a nowhere dense set in the space of all the $C^\theta$ weak solutions. The technique is the same and what really distinguishes the two cases is that in the latter there is no need to introduce a different complete metric space with respect to the natural one.