Given a classical gas described by the truncated correlation functions of all orders, we prove convergence of an expansion of the pair interaction part of the (unknown) potential in terms of the truncated correlation functions of all orders, at infinite volume.
We report an experimental study of the magnetic-field dependence of the optically pumped valley polarization in an epitaxial tungsten diselenide (WSe$_2$) monolayer grown by molecular-beam epitaxy (MBE) on a hexagonal boron nitride (hBN) substrate. Circularly polarized photoluminescence (PL) measurements reveal that applying a weak out-of-plane magnetic field, on the order of 0.1 T, dramatically increases the effectiveness of the optical orientation of the emission associated with defect-bound localized excitons. We compare the obtained results with the earlier studies on the reference exfoliated monolayers, discussing both qualitative similarity as well as quantitative differences. Our observations are further supplemented by the results of time-resolved PL measurements, which confirm the pseudospin relaxation time of approximately 25 ps, a value significantly shorter than the $\approx$100 ps previously reported for mechanically exfoliated samples.
We investigate a coupled atmosphere-ocean model including the mechanical and thermodynamical interaction between the two fluids for the mid-latitudes. The formulation combines a multilayer quasi-geostrophic dynamical framework with temperature equations incorporating long- and short-wave radiative forcing, as in energy balance models. Within a suitable functional framework, we establish the existence and uniqueness of solutions, and their continuous dependence on the radiation parameters. We also prove that the long-time dynamics are described by a finite-dimensional global attractor and, moreover, that the system possesses a finite set of determining modes that governs its asymptotic behaviour. In particular, we show that the long-term evolution of the ocean's temperature can be reconstructed solely from observations of the velocity fields across the model's layers.
This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinear setting that is paradigmatic in geophysical fluid dynamics and various applications. Two algorithms are proposed to address this problem: one that iteratively reconstructs forcing and another that provides a continuous-time reconstruction. Convergence is shown to be guaranteed provided that observational resolution is sufficiently high and algorithmic parameters are properly tuned according to the prior information; these conditions are quantified precisely. The class of reconstructable forces identified here include those which are time-dependent and potentially inject energy at all length scales. This significantly expands upon the class of forces in previous studies, which could only accommodate those with band-limited spectra. The second algorithm moreover provides a conceptually streamlined approach that allows for a more straightforward analysis and simplified practical implementation.
Upcoming deep optical surveys, such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), will scan the sky to unprecedented depths, detecting billions of galaxies. However, this amount of detections will lead to the apparent superposition of galaxies in the images, a phenomenon known as blending, that can affect the accurate measurement of individual galaxy properties. In particular, galaxy shapes play a crucial role in estimating the masses of large-scale structures, such as galaxy clusters, through weak gravitational lensing. This proceeding introduces a new catalog matching algorithm, friendly, designed for detecting and characterizing blends in simulated LSST data for the Dark Energy Science Collaboration (DESC) Data Challenge 2. The aim of this algorithm is to combine several matching procedures, as well as a probabilistic method to quantify blended systems. By removing the resulted 27% of galaxies affected by blending from the dataset, we demonstrate that the amplitude of the excess surface mass density weak lensing profile - potentially biased low due to blending - may be partially corrected.
We establish a criterion for the existence of a representing Radon measure for linear functionals defined on a unital commutative real algebra $A$, which we assume to be generated by a vector space $V$ endowed with a Hilbertian seminorm $q$. Such a general criterion provides representing measures with support contained in the space of characters of $A$ whose restrictions to $V$ are $q-$continuous. This allows us in turn to prove existence results for the case when $V$ is endowed with a nuclear topology. In particular, we apply our findings to the symmetric tensor algebra of a nuclear space.
Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analysed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis however meets with the challenge that in the model under study, the noise configuration is spatially degenerate as the stochastic forcing acts only on the top layer. Exponential convergence of solutions laws to the invariant measure is established, implying a spectral gap of the associated Markov semigroup on a space of Hölder continuous functions. The approach provides a general framework for generalised coupling techniques suitable for applications to dissipative SPDEs. In case of the two-layer quasi-geostrophic model, the results require the second layer to obey a certain passivity condition.
We consider the class of all linear functionals $L$ on a unital commutative real algebra $A$ that can be represented as an integral w.r.t. to a Radon measure with compact support in the character space of $A$. Exploiting a recent generalization of the classical Nussbaum theorem, we establish a new characterization of this class of moment functionals solely in terms of a growth condition intrinsic to the given linear functional. To the best of our knowledge, our result is the first to exactly identify the compact support of the representing Radon measure. We also describe the compact support in terms of the largest Archimedean quadratic module on which $L$ is non-negative and in terms of the smallest submultiplicative seminorm w.r.t. which $L$ is continuous. Moreover, we derive a formula for computing the measure of each singleton in the compact support, which in turn gives a necessary and sufficient condition for the support to be a finite set. Finally, some aspects related to our growth condition for topological algebras are also investigated.
Upcoming deep optical surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time will scan the sky to unprecedented depths and detect billions of galaxies. This amount of detections will however cause the apparent superposition of galaxies on the images, called blending, and generate a new systematic error due to the confusion of sources. As consequences, the measurements of individual galaxies properties such as their redshifts or shapes will be impacted, and some galaxies will not be detected. However, galaxy shapes are key quantities, used to estimate masses of large scale structures, such as galaxy clusters, through weak gravitational lensing. This work presents a new catalog matching algorithm, called friendly, for the detection and characterization of blends in simulated LSST data for the DESC Data Challenge 2. By identifying a specific type of blends, we show that removing them from the data may partially correct the amplitude of the $ΔΣ$ weak lensing profile that could be biased low by around 20% due to blending. This would result in impacting clusters weak lensing mass estimate and cosmology.
Researchers are applying evolutionary theory to cancer by changing treatments before tumors have time to develop resistance。 Mathematical models suggest that rapid, carefully timed switches between multiple therapies could improve cure rates
Cosmic expansion allows distant galaxies to move away faster than light, while still letting us see ancient light they emitted when they were much closer。 Eventually, accelerating expansion will push nearly every galaxy beyond our Local Group out of sight, making the Universe appear almost empty
Scientists have created an “electron lighthouse” that uses laser light to launch and steer electrons through a semiconductor without an applied electrical field。 The quantum effect could eventually improve optical sensors, communications, imaging, and information storage
A new theoretical study offers a possible explanation for how the Universe can grow more complex without violating the second law of thermodynamics。 Using a quantum gravity framework called Gravity from Entropy, mathematician Ginestra Bianconi found that the Universe’s total entropy may rise as space expands, even while entropy within each unit of
A new analysis suggests the Sun holds far more silver than earlier estimates indicated。 More advanced models of the solar atmosphere raised the calculated amount by 55 percent, bringing it into much closer agreement with ancient meteorites。 The technique may also help scientists track the cosmic origins of silver and other heavy elements
Researchers have created self-destructing living plastic that uses engineered bacteria to completely break itself down when activated。 The material degrades in just six days without creating microplastics, offering a potential new solution for single-use plastic waste