We introduce coefficient systems of pro-étale motives and pro-étale motivic spectra with coefficients in any condensed ring spectrum and show that they afford the six operations. Over locally étale bounded schemes, étale motivic spectra embed into pro-étale motivic spectra. We then use the framework of condensed category theory to define a solidification process for any $\widehat{\mathbb{Z}}$-linear condensed category. Pro-étale motives naturally enhance to a condensed category and we show that their solidification is very close to the category of solid sheaves defined by Fargues-Scholze, suitably modified to work on schemes: this is a rigidity result. As a consequence, we obtain that in contrast with the rigid-analytic setting, solid sheaves on schemes afford the six operations, and we obtain a solid realization functor of motives, extending the $\ell$-adic realization functor. The solid realization functor is compatible with change of coefficients, which allows one to recover the $\mathbb{Q}_\ell$-adic realization functor while remaining in a setting of presentable categories.
The dynamics of weighted translation operators on Lebesgue spaces, Orlicz spaces, and in general on solid Banach function spaces have been studied in numerous papers. Recently, the dynamics of weighted translations on weighted Orlicz spaces have also been studied by Chen and others. The main idea of this paper is to obtain a generalization of these results to the case of general weighted solid Banach function spaces. More precisely, in this paper, we characterize disjoint topologically transitive and disjoint supercyclic weighted composition operators on weighted solid Banach function spaces. This approach has applications in the dynamics of weighted translations on weighted Morrey spaces.
We consider the problem of packing a large square with nonoverlapping unit squares. Let $W(x)$ be the minimum wasted area when a large square of side length $x$ is packed with unit squares. In Roth and Vaughan's paper that proves the lower bound $W(x) \notin o(x^{1/2})$, a good square is defined to be a square with inclination at most $10^{-10}$ with respect to the large square. In this article, we prove that in calculating the asymptotic growth of the wasted space, it suffices to only consider packings with only good squares. This allows the lower bound proof in Roth and Vaughan's paper to be simplified by not having to handle bad squares.
Nonpolar atoms or molecules with low particle mass and weak inter-particle interactions can form quantum liquids and solids (QLS) at low temperatures. Excess electrons naturally bind to the surfaces of QLS in a vacuum, exhibiting unique quantum electronic behaviors in two and lower dimensions. This article reviews the historical development and recent progress in this field. Key topics include collective and individual electron transport on liquid helium, solid neon, and solid hydrogen; theoretical proposals and experimental efforts toward single-electron qubits on superfluid helium; the recent experimental realization of single-electron charge qubits on solid neon; and related theoretical calculations. Finally, we discuss and envision future exploration of quantum electronics in heterogeneous QLS systems.
Addressing the issue of submerged underwater trash is crucial for safeguarding aquatic ecosystems and preserving marine life. While identifying debris present on the surface of water bodies is straightforward, assessing the underwater submerged waste is a challenge due to the image distortions caused by factors such as light refraction, absorption, suspended particles, color shifts, and occlusion. This paper conducts a comprehensive review of state-of-the-art architectures and on the existing datasets to establish a baseline for submerged waste and trash detection. The primary goal remains to establish the benchmark of the object localization techniques to be leveraged by advanced underwater sensors and autonomous underwater vehicles. The ultimate objective is to explore the underwater environment, to identify, and remove underwater debris. The absence of benchmarks (dataset or algorithm) in many researches emphasizes the need for a more robust algorithmic solution. Through this research, we aim to give performance comparative analysis of various underwater trash detection algorithms.
Kiattisak Rattanadilok Na Phuket, Tussanee Srimachai, Chaiyoot Meengam
et al.
The development of RDF-5 fuel from community waste using natural rubber as a binder was investigated. The results showed that the calorific and heat values were increased proportionately to the amount of rubber added. The ratio with the highest calorific value was 50:50, followed by 75:25, 90:10, and 95:5. The calorific value was 40.67 MJ/kg (9720 kcal/kg), 40.24 MJ/kg (9,617 kcal/kg), 39.28 (9,389 kcal/kg) and 39.18 MJ/kg (9,365 kcal/kg), respectively. Compared with 100:0, have a calorific value of 38.84 MJ/kg (9,284 kcal/kg). The experimental addition of natural rubber as a binder makes the combustion process more complete, resulting in faster fuel ignition time or easier igniting, less ash content, and being environmentally friendly. The research team chose to develop the ratio of 95:5 because the economic analysis showed a fast payback period of only 5.72 years. So, the ratio of 95:5 is the optimal condition that can scale up to the industrial level. The production cost of RDF-5 is 1,935 baht/ton for 50 baht/kg of natural rubber. The amount of emission caused by the combustion process of RDF-5 (95:5) passed the standard. Therefore, the evaluation of this research found that RDF-5 fuels from community waste using natural rubber as a binder. It is one of the attractive alternatives to renewable fuel generation and solid waste management solutions and helps improve the environmental quality of communities.
We address the fundamental difference between solid-solid and liquid-liquid phase transitions within the Ericksen's nonlinear elasticity paradigm. To highlight ideas, we consider the simplest nontrivial 2D problem and work with a prototypical two-phase Hadamard material which allows one to weaken the rigidity and explore the nature of solid-solid phase transitions in a ``near-liquid'' limit. In the language of calculus of variations we probe limits of quasiconvexity in an ``almost liquid'' solid by comparing the thresholds for cooperative (laminate based) and non-cooperative (inclusion based) nucleation. Using these two types of nucleation tests we obtain for our model material surprisingly tight two-sided bounds on the elastic binodal without directly computing the quasiconvex envelope.
The solid torus core recognition problem is the problem that, given a knot in the solid tours, decides whether the knot is the core of the solid torus. That problem is in NP since the thickened torus recognition problem is in NP. We give an alternate proof of that fact and prove that the problem is in co-NP. It is also proved that the Hopf link recognition problem is in NP and co-NP as a corollary of this result.
This paper addresses the computation of normalized solid angle measure of polyhedral cones. This is well understood in dimensions two and three. For higher dimensions, assuming that a positive-definite criterion is met, the measure can be computed via a multivariable hypergeometric series. We present two decompositions of full-dimensional simplicial cones into finite families of cones satisfying the positive-definite criterion, enabling the use of the hypergeometric series to compute the solid angle measure of any polyhedral cone. Additionally, our second decomposition method yields cones with a special tridiagonal structure, reducing the number of required coordinates for the hypergeometric series formula. Furthermore, we investigate the convergence of the hypergeometric series for this case. Our findings provide a powerful tool for computing solid angle measures in high-dimensional spaces.
Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected solid angle from arbitrarily shaped polygons are derived using the Gauss-Bonnet theorem. This is accomplished by transforming the projected solid angle integral to an integral over a spherical patch, which is then reduced by Gauss-Bonnet to a simple summation over its edges, allowing the projected solid angle to be computed exactly. Application of the formulae allows exact calculation of projected solid angle over discrete intervals which may be used for computing radiative flux to surfaces or view factors to free space.
Christian Esposito, Olaf Hartig, Ross Horne
et al.
The Solid specification aims to empower data subjects by giving them direct access control over their data across multiple applications. As governments are manifesting their interest in this framework for citizen empowerment and e-government services, security and privacy represent pivotal issues to be addressed. By analyzing the relevant legislation, notably GDPR, and international standards, namely ISO/IEC 27001:2011 and 15408, we formulate the primary security and privacy requirements for such a framework. Furthermore, we survey the current Solid protocol specifications regarding how they cover the highlighted requirements, and draw attention to potential gaps between the specifications and requirements. We also point out the contribution of recent academic work presenting novel approaches to increase the security and privacy degree provided by the Solid project. This paper has a twofold contribution to improve user awareness of how Solid can help protect their data and to present possible future research lines on Solid security and privacy enhancements.
The interplay of strong Coulomb interactions and of topology is currently under intense scrutiny in various condensed matter and atomic systems. One example of this interplay is the phase competition of fractional quantum Hall states and the Wigner solid in the two-dimensional electron gas. Here we report a Wigner solid at $ν=1.79$ and its melting due to fractional correlations occurring at $ν=9/5$. This Wigner solid, that we call the reentrant integer quantum Hall Wigner solid, develops in a range of Landau level filling factors that is related by particle-hole symmetry to the so called reentrant Wigner solid. We thus find that the Wigner solid in the GaAs/AlGaAs system straddles the partial filling factor $1/5$ not only at the lowest filling factors, but also near $ν=9/5$. Our results highlight the particle-hole symmetry as a fundamental symmetry of the extended family of Wigner solids and paint a complex picture of the competition of the Wigner solid with fractional quantum Hall states.
Yu. A. Freiman, V. V. Vengerovsky, Alexander F. Goncharov
The thermal expansion at constant pressure of solid CD$_4$ III is calculated for the low temperature region where only the rotational tunneling modes are essential and the effect of phonons and librons can be neglected. It is found that in mK region there is a giant peak of the negative thermal expansion. The height of this peak is comparable or even exceeds the thermal expansion of solid N$_2$, CO, O$_2$ or CH$_4$ in their triple points. It is shown that like in the case of light methane, the effect of pressure is quite unusual: as evidenced from the pressure dependence of the thermodynamic Grüneisen parameter (which is negative and large in the absolute value), solid CD$_4$ becomes increasingly quantum with rising pressure.
Alexander J. Pearse, Thomas E. Schmitt, Elliot J. Fuller
et al.
Several active areas of research in novel energy storage technologies, including three-dimensional solid state batteries and passivation coatings for reactive battery electrode components, require conformal solid state electrolytes. We describe an atomic layer deposition (ALD) process for a member of the lithium phosphorus oxynitride (LiPON) family, which is employed as a thin film lithium-conducting solid electrolyte. The reaction between lithium tert-butoxide (LiO$^t$Bu) and diethyl phosphoramidate (DEPA) produces conformal, ionically conductive thin films with a stoichiometry close to Li$_2$PO$_2$N between 250 and 300$^\circ$C. The P/N ratio of the films is always 1, indicative of a particular polymorph of LiPON which closely resembles a polyphosphazene. Films grown at 300$^\circ$C have an ionic conductivity of $6.51\:(\pm0.36)\times10^{-7}$ S/cm at 35$^\circ$C, and are functionally electrochemically stable in the window from 0 to 5.3V vs. Li/Li$^+$. We demonstrate the viability of the ALD-grown electrolyte by integrating it into full solid state batteries, including thin film devices using LiCoO$_2$ as the cathode and Si as the anode operating at up to 1 mA/cm$^2$. The high quality of the ALD growth process allows pinhole-free deposition even on rough crystalline surfaces, and we demonstrate the fabrication and operation of thin film batteries with the thinnest (<100nm) solid state electrolytes yet reported. Finally, we show an additional application of the moderate-temperature ALD process by demonstrating a flexible solid state battery fabricated on a polymer substrate.