Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.Comment: 32 page

The GL 569 Multiple System

We report the results of high spectral and angular resolution infrared observations of the multiple system GL 569 A and B that were intended to measure the dynamical masses of the brown dwarf binary believed to comprise GL 569 B. Our analysis did not yield this result but, instead, revealed two surprises. First, at age ~100 Myr, the system is younger than had been reported earlier. Second, our spectroscopic and photometric results provide support for earlier indications that GL 569 B is actually a hierarchical brown dwarf triple rather than a binary. Our results suggest that the three components of GL 569 B have roughly equal mass, ~0.04 Msun.Comment: 29 pages, 10 figures, accepted for publication in the Astrophysical Journal; minor corrections to Section 5.1; changed typo in 6.

Use of Perylene Diimides in Synthetic Photochemistry

Perylene diimides (PDIs) are valuable organic chromophores that stand out for their outstanding optical and redox properties. Owing to these features, PDIs have emerged as prominent dyes capable of acting as photocatalysts for numerous relevant organic transformations. This Minireview highlights the recent advances in the application of PDIs in organic photocatalysis. The various mechanistic pathways of the photo-reduction reaction of aryl halides, recently proposed in independent studies, are discussed with an eye to unsolved challenges and forward-looking opportunities regarding the use of PDIs within this field

Denoising Diffusion Models on Model-Based Latent Space

With the recent advancements in the field of diffusion generative models, it has been shown that defining the generative process in the latent space of a powerful pretrained autoencoder can offer substantial advantages. This approach, by abstracting away imperceptible image details and introducing substantial spatial compression, renders the learning of the generative process more manageable while significantly reducing computational and memory demands. In this work, we propose to replace autoencoder coding with a model-based coding scheme based on traditional lossy image compression techniques; this choice not only further diminishes computational expenses but also allows us to probe the boundaries of latent-space image generation. Our objectives culminate in the proposal of a valuable approximation for training continuous diffusion models within a discrete space, accompanied by enhancements to the generative model for categorical values. Beyond the good results obtained for the problem at hand, we believe that the proposed work holds promise for enhancing the adaptability of generative diffusion models across diverse data types beyond the realm of imagery

Breakdown rates and macroinvertebrate colonisation of alder (Alnus glutinosa) leaves in an acid lake (Lake Orta, N Italy), before, during and after a liming intervention

To test the effectiveness of the liming intervention on Lake Orta, the speed of leaves decay and of colonisation processes by macrobenthonic fauna were studied on alder leaves (Alnus glutinosa) placed on the bottom of the lake and recovered after appropriate time intervals. Experiments were performed at two sites (North and South) and two depths (-3 and –18 m), during three successive winters: 1988-1989 (pre-liming), 1989-1990 (liming), 1990-1991 (post-liming). Two main results emerged: 1) alder leaves, which are known to have a medium to high decaying speed in a number of aquatic environments, behave in Lake Orta as a low speed species. Decaying processes in the three years are significantly different only in station N3, where the mean breakdown rate in 1988- 1989 is more than twice that measured in the two subsequent winters. 2) The species richness of colonising benthic fauna is low: the community is made up almost exclusively of Chironomidae, which form 70 to 100% of the whole population; among them, the genus Phenopsectra is always present, while Tanytarsus was collected only during the first year and in the less deep sampling sites. The mean population abundances were higher before liming

Tailoring the Chemical Structure of Nitrogen-Doped Carbon Dots for Nano-Aminocatalysis in Aqueous Media

Amine-rich carbon dots (NCDs) have become promising nano-aminocatalytic platforms in organic synthesis. These nanomaterials can be effectively produced through straightforward bottom-up approaches using inexpensive nitrogen-containing molecular precursors as a starting material. However, to date, there is still a limited understanding of how the molecular features of these precursors affect the catalytic activity of the resulting nanoparticles. This study concerns the production of a new family of NCDs, which use l-arginine and different alkyl diamines as starting materials. The surface amines of all these NCDs were comprehensively characterized, thus allowing us to provide a correlation between the structural features of the nanoparticles and their catalytic performance with a selected amino-catalyzed organic transformation. Importantly, the most active nano-aminocatalysts, namely, NCDs-3, were then used as a basis for the formation of a wide variety of functionalized organic compounds in water under mild reaction conditions

Indentation modulus, indentation work and creep of metals and alloys at the macro-scale level: Experimental insights into the use of a primary Vickers hardness standard machine

In this work, the experimental method and the calculation model for the determination of indentation moduli, indentation work, and indentation creep of metallic materials, by means of macroscale-level forces provided by a primary hardness standard machine at the National Institute of Metrological Research (INRIM) at the at room temperature were described. Indentation moduli were accurately determined from measurements of indentation load, displacement, contact stiffness and hardness indentation imaging and from the slope of the indentation unloading curve by applying the Doerner-Nix linear model; indentation work, representing the mechanical work spent during the force application of the indentation procedure, was determined by calculating the areas under the loading–unloading indentation curve, through fitting experimental data with a polynomial law. Measurements were performed with a pyramidal indenter (Vickers test). The applied force was provided by a deadweight machine, and the related displacement was measured by a laser interferometric system. Applied forces and the occurring indentation depths were simultaneously measured: The resulting loading–unloading indentation curve was achieved. Illustrative tests were performed on metals and alloy samples. Discussion and comments on the suitability of the proposed method and analysis were reported

Electron-Electron Bremsstrahlung Emission and the Inference of Electron Flux Spectra in Solar Flares

Although both electron-ion and electron-electron bremsstrahlung contribute to the hard X-ray emission from solar flares, the latter is normally ignored. Such an omission is not justified at electron (and photon) energies above $\sim 300$ keV, and inclusion of the additional electron-electron bremsstrahlung in general makes the electron spectrum required to produce a given hard X-ray spectrum steeper at high energies. Unlike electron-ion bremsstrahlung, electron-electron bremsstrahlung cannot produce photons of all energies up to the maximum electron energy involved. The maximum possible photon energy depends on the angle between the direction of the emitting electron and the emitted photon, and this suggests a diagnostic for an upper cutoff energy and/or for the degree of beaming of the accelerated electrons. We analyze the large event of January 17, 2005 observed by RHESSI and show that the upward break around 400 keV in the observed hard X-ray spectrum is naturally accounted for by the inclusion of electron-electron bremsstrahlung. Indeed, the mean source electron spectrum recovered through a regularized inversion of the hard X-ray spectrum, using a cross-section that includes both electron-ion and electron-electron terms, has a relatively constant spectral index $\delta$ over the range from electron kinetic energy $E = 200$ keV to $E = 1$ MeV. However, the level of detail discernible in the recovered electron spectrum is not sufficient to determine whether or not any upper cutoff energy exists.Comment: 7 pages, 5 figures, submitted to Astrophysical Journa

Smooth stable and unstable manifolds for stochastic partial differential equations

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's method. Then, we prove the smoothness of these invariant manifolds

Approximating the coefficients in semilinear stochastic partial differential equations

We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical Brownian motion on a Hilbert space H. We prove continuous dependence of the compensated solutions X(t)-e^{tA}X_0 in the norms L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n are uniformly sectorial and converge to A in the strong resolvent sense, and that the approximating nonlinearities F_n and G_n are uniformly Lipschitz continuous in suitable norms and converge to F and G pointwise. Our results are applied to a class of semilinear parabolic SPDEs with finite-dimensional multiplicative noise.Comment: Referee's comments have been incorporate