Hasil untuk "Civil law"

Yuan Xinjie, Khalid M. Mosalam

Fire safety is crucial for ensuring the stability of building structures, yet evaluating whether a structure meets fire safety requirement is challenging. Fires can originate at any point within a structure, and simulating every potential fire scenario is both expensive and time-consuming. To address this challenge, we propose the concept of the Most Fire-Sensitive Point (MFSP) and an efficient machine learning framework for its identification. The MFSP is defined as the location at which a fire, if initiated, would cause the most severe detrimental impact on the building's stability, effectively representing the worst-case fire scenario. In our framework, a Graph Neural Network (GNN) serves as an efficient and differentiable agent for conventional Finite Element Analysis (FEA) simulators by predicting the Maximum Interstory Drift Ratio (MIDR) under fire, which then guides the training and evaluation of the MFSP predictor. Additionally, we enhance our framework with a novel edge update mechanism and a transfer learning-based training scheme. Evaluations on a large-scale simulation dataset demonstrate the good performance of the proposed framework in identifying the MFSP, offering a transformative tool for optimizing fire safety assessments in structural design. All developed datasets and codes are open-sourced online.

Stefan Heinz

The discovery of the law of the wall, the log-law including the von Karman constant, is seen to be one of the biggest accomplishments of fluid mechanics. However, after more than ninety years there is still a controversial debate about the validity and universality of the law of the wall. Clarity about this question matters: in absence of alternatives, a reliable and universal theory involving the law of the wall is needed to provide essential guideline for the validation of theory, computational methods, and experimental studies of very high Reynolds number (Re) flows. The paper presents an analysis of concepts used to derive controversial conclusions. It is shown that nonuniversality is a consequence of simplified modeling concepts, which leads to unrealizable models. On the other hand, realizability implies universality: models in consistency with physical requirements do not need to be adjusted to different flows. There are essential advantages of a universal law of the wall: it enables the design of accurate turbulence models and it provides a bridge between finite Re observations and asymptotic structural theories of turbulence.

Chang-Yu Guo, Chang-Lin Xiang

In this short note, we provide a partial extension of Rivière's convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.

Hirofumi Niibo, Jun Ueki

Based on our homological idelic class field theory, we formulate an analogue of the Hilbert reciprocity law on a rational homology 3-sphere endowed with an infinite link, in the spirit of arithmetic topology; We regard the intersection form on the unitary normal bundle of each knot as an analogue of the Hilbert symbol at each prime ideal to formulate the Hilbert reciprocity law, ensuring that cyclic covers of links are analogues of Kummer extensions.

Alexander Maloney, Daniel A. Roberts, James Sully

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model -- a joint generative data model and random feature model -- that captures this neural scaling phenomenology. By solving this model in the dual limit of large training set size and large number of parameters, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws, (ii) the way nonlinear feature maps, such as those provided by neural networks, enable scaling laws when trained on these datasets, (iii) the optimality of the equiparameterization scaling of training sets and parameters, and (iv) whether such scaling laws can break down and how they behave when they do. Key findings are the manner in which the power laws that occur in the statistics of natural datasets are extended by nonlinear random feature maps and then translated into power-law scalings of the test loss and how the finite extent of the data's spectral power law causes the model's performance to plateau.

Timo Kerremans, Peter Samuelsson, Patrick P. Potts

Fluctuations of thermodynamic observables, such as heat and work, contain relevant information on the underlying physical process. These fluctuations are however not taken into account in the traditional laws of thermodynamics. While the second law is extended to fluctuating systems by the celebrated fluctuation theorems, the first law is generally believed to hold even in the presence of fluctuations. Here we show that in the presence of quantum fluctuations, also the first law of thermodynamics may break down. This happens because quantum mechanics imposes constraints on the knowledge of heat and work. To illustrate our results, we provide a detailed case-study of work and heat fluctuations in a quantum heat engine based on a circuit QED architecture. We find probabilistic violations of the first law and show that they are closely connected to quantum signatures related to negative quasi-probabilities. Our results imply that in the presence of quantum fluctuations, the first law of thermodynamics may not be applicable to individual experimental runs.

Gabriele Lobbia

We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category $\mathcal{K}$. In order to do that, we introduce the 2-category of relative monads in a 2-category $\mathcal{K}$ with relative monad morphisms and relative monad transformations as 1- and 2-cells, respectively. We relate our definition to the 2-category of monads in $\mathcal{K}$ defined by Street. Thanks to this view we prove two Beck-type theorems regarding relative distributive laws. We also describe what does it mean to have Eilenberg-Moore and Kleisli objects in this context and give examples in the 2-category of locally small categories.

Abhishek Dhar, Herbert Spohn

While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines the solution of Newton's equations of motion can be obtained with high precision and for a reasonably large number of particles. For simplified model systems one thereby arrives at a deeper understanding of the microscopic basis for Fourier's law. We report on recent, and not so recent, advances.

Nobuyoshi Komatsu

A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the $α$-th power of the Hubble parameter, where $α$ is a dimensionless constant for the power-law correction) in the acceleration equation, which can be derived from the holographic equipartition law. Interestingly, the value of the extra driving term in the present model is constrained by the second law of thermodynamics. From the thermodynamic constraint, the order of the driving term is found to be consistent with the order of the cosmological constant measured by observations. In addition, the driving term tends to be constant-like when $α$ is small, i.e., when the deviation from the Bekenstein-Hawking entropy is small.

Tariq Ahmad Mir

The occurrence of first significant digits of numbers in large data is often governed by a logarithmically decreasing distribution called Benford's law (BL), reported first by S. Newcomb (SN) and many decades later independently by F. Benford (FB). Due to its counter-intuitiveness the law was ignored for decades as a mere curious observation. However, an indication of its remarkable resurgence is the huge swell in the number of citations received by the papers of SN/FB. The law has come a long way, from obscurity to now being a regular subject of books, peer reviewed papers, patents, blogs and news. Here, we use Google Scholar (GS) to collect the data on the number of citations received by the articles citing the original paper of SN/FB and then investigate whether the leading digits of this citations data are distributed according to the law they discovered. We find that the citations data of literature on BL is in remarkable agreement with the predictions of the law.

C. M. Herdman, P. -N. Roy, R. G. Melko et al.

Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified theories. Using new exact microscopic numerical simulations of superfluid $^4$He, we demonstrate for the first time an area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principles underlying its physical origin, and present an "entanglement equation of state" showing how it depends on the density of the superfluid.

Peter K. G. Williams, Geoffrey C. Bower, Steve Croft et al.

Searches for slow radio transients and variables have generally focused on extragalactic populations, and the basic parameters of Galactic populations remain poorly characterized. We present a large 3 GHz survey performed with the Allen Telescope Array (ATA) that aims to improve this situation: ASGARD, the ATA Survey of Galactic Radio Dynamism. ASGARD observations spanned 2 years with weekly visits to 23 deg^2 in two fields in the Galactic Plane, totaling 900 hr of integration time on science fields and making it significantly larger than previous efforts. The typical blind unresolved source detection limit was 10 mJy. We describe the observations and data analysis techniques in detail, demonstrating our ability to create accurate wide-field images while effectively modeling and subtracting large-scale radio emission, allowing standard transient-and-variability analysis techniques to be used. We present early results from the analysis of two pointings: one centered on the microquasar Cygnus X-3 and one overlapping the Kepler field of view (l = 76°, b = +13.5°). Our results include images, catalog statistics, completeness functions, variability measurements, and a transient search. Out of 134 sources detected in these pointings, the only compellingly variable one is Cygnus X-3, and no transients are detected. We estimate number counts for potential Galactic radio transients and compare our current limits to previous work and our projection for the fully-analyzed ASGARD dataset.

Sergio del Campo, Ramon Herrera, Diego Pavon

This paper studies whether the generalized second law of thermodynamics is fulfilled in the transition from a generic initial Einstein static phase to the inflationary phase, with constant Hubble rate, and from the end of the latter to the conventional era of thermal radiation dominated expansion. As it turns out, the said law is satisfied provided the radiation component does not largely contribute to the total energy of the static phase.

Max Tegmark

I use cosmology examples to illustrate that the second law of thermodynamics is not old and tired, but alive and kicking, continuing to stimulate interesting research on really big puzzles. The question "Why is the entropy so low?" (despite the second law) suggests that our observable universe is merely a small and rather uniform patch in a vastly larger space stretched out by cosmological inflation. The question "Why is the entropy so high" (compared to the complexity required to describe many candidate "theories of everything") independently suggests that physical reality is much larger than the part we can observe.

Alejandra Kandus, Christos G. Tsagas

We generalise the relativistic expression of Ohm's law by studying a multi-fluid system of charged species using the 1+3 covariant formulation of general relativistic electrodynamics. This is done by providing a fully relativistic, fully nonlinear propagation equation for the spatial component of the electric 4-current. Our analysis proceeds along the lines of the non-relativistic studies and extends previous relativistic work on cold plasmas. Exploiting the compactness and transparency of the covariant formalism, we provide a direct comparison with the standard Newtonian versions of Ohm's law and identify the relativistic corrections in an unambiguous way. The generalised expression of Ohm's law is initially given relative to an arbitrary observer and for a multi-component relativistic charged medium. Then, the law is written with respect to the Eckart frame and for a hot two-fluid plasma with zero total charge. Finally, we apply our analysis to a cold proton-electron plasma and recover the well known magnetohydrodynamic expressions. In every step, we discuss the approximations made and identify familiar effects, like the Biermann-battery and the Hall effect.

A. Riera, J. I. Latorre

We review a number of ideas related to area law scaling of the geometric entropy from the point of view of condensed matter, quantum field theory and quantum information. An explicit computation in arbitrary dimensions of the geometric entropy of the ground state of a discretized scalar free field theory shows the expected area law result. In this case, area law scaling is a manifestation of a deeper reordering of the vacuum produced by majorization relations. Furthermore, the explicit control on all the eigenvalues of the reduced density matrix allows for a verification of entropy loss along the renormalization group trajectory driven by the mass term. A further result of our computation shows that single-copy entanglement also obeys area law scaling, majorization relations and decreases along renormalization group flows.

Qiuping A. Wang

We show that the zeroth law of thermodynamics holds within an alternative version of nonextensive statistical mechanics based on {\it incomplete probability distribution}. The generalized zeroth law leads to a generalized definition of thermodynamic functions which are possible to be used for systems with important nonextensivity (nonadditivity) in energy, volume or other external variables.

Shinji Mukohyama

The generalized second law of black hole thermodynamics was proved by Frolov and Page for a quasi-stationary eternal black hole. However, realistic black holes arise from a gravitational collapse, and in this case their proof does not hold. In this paper we prove the generalized second law for a quasi-stationary black hole which arises from a gravitational collapse.

P. Castorina, T. S. Deisboeck, P. Gabriele et al.

Comparing both, the more conventional Gompertz tumor growth law (GL) and the ``Universal'' law (UL), recently proposed and applied to cancer,we have investigated the growth law's implications on various radiotherapy regimen. According to GL, the surviving tumor cell fraction could be reduced 'ad libidum', independently of the initial tumor mass,simply by increasing the number of treatments. On the contrary, if tumor growth dynamics would indeed follow the Universal scaling law, there is a lower limit of the survival fraction that cannot be reduced any further regardless of the total number of treatments. This finding can explain the so called ``tumor size effect'' and re-emphasizes the importance of early diagnosis as it implies that radiotherapy may be successful provided the tumor mass at treatment onset is rather small. Taken together with our previous works, implications of these findings include revisiting standard radiotherapy regimen and overall treatment protocols.

Zhipeng Li, Lin Cong, Huajia Wang

The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law ${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over d}}), d = 1, 2 >..., 9$. Illustrations of Benford's Law from both theoretical and real-life sources on both science and social science areas are shown in detail with some novel ideas and generalizations developed solely by the authors of this paper. Three tests, Chi-Square test, total variation distance, and maximum deviations are adopted to examine the fitness of the datasets to Benford's distribution. Finally, applications of Benford's Law are summarized and explored to reveal the power of this mathematical principle.