Two-Point Oscillation for a Class of Second-Order Damped Linear Differential Equations

Using the comparison theorem, the two-point oscillation for linear differential equation with damping term is considered, where . Results are obtained that or imply the two-point oscillation of the equation

Physics-Informed Convolutional Decoder (PICD): A novel approach for direct inversion of heterogeneous subsurface flow

In this study, we present the development and application of the physics-informed convolutional decoder (PICD) framework for inverse modeling of heterogenous groundwater flow. PICD stands out as a direct inversion method, eliminating the need for repeated forward model simulations. The framework leverages both data-driven and physics-driven approaches by integrating monitoring data and domain knowledge (governing equation, boundary conditions, and initial conditions) into the inversion process. PICD utilizes a convolutional decoder to effectively approximate the spatial distribution of hydraulic heads, while Karhunen Loeve expansion (KLE) is employed to parameterize hydraulic conductivities. During the training process, the stochastic vector in KLE and the parameters of the convolutional decoder are adjusted simultaneously, ensuring that the predictions align with available measurements and adhere to domain-specific knowledge. The final optimized stochastic vectors correspond to the estimation of hydraulic conductivities, and the trained convolutional decoder demonstrates the ability to predict the evolution and distribution of hydraulic heads in heterogeneous fields. To validate the effectiveness of the proposed PICD framework, various scenarios of groundwater flow are examined. Results demonstrate the framework's capability to accurately estimate heterogeneous hydraulic conductivities and to deliver satisfactory predictions of hydraulic heads, even with sparse measurements. The proposed PICD framework emerges as a promising tool for efficient and informed groundwater flow inverse modeling.Comment: 29 pages, 7 figure

Time-resolved 3D visualization of air injection in a liquid-saturated refractive-index-matched porous medium

The main goal of this work is to implement and validate a visualization method with a given temporal/spatial resolution to obtain the dynamic three-dimensional (3D) structure of an air plume injected into a deformable liquid-saturated porous medium. The air plume develops via continuous air injection through an orifice at the bottom of a loose packing of crushed silica grains. The packing is saturated by a glycerin-water solution having the same refractive index and placed in a rectangular glass container. By using high-speed image acquisition through laser scanning, the dynamic air plume is recorded by sequential tomographic imaging. Due to the overlap between adjacent laser sheets and the light reflection, air bubbles are multiply exposed in the imaging along the scanning direction. Four image processing methods are presented for the removal of these redundant pixels arising from multiple exposure. The respective results are discussed by comparing the reconstructed air plume volume with the injected one and by evaluating the morphological consistency of the obtained air plume. After processing, a 3D dynamic air flow pattern can be obtained, allowing a quantitative analysis of the air flow dynamics on pore-scale. In the present experimental configuration, the temporal resolution is 0.1s and the spatial resolution is 0.17mm in plane and about 1mm out of plane of the laser shee

Entropy and Its Quantum Thermodynamical Implication for Anomalous Spectral Systems

The state function entropy and its quantum thermodynamical implication for two typical dissipative systems with anomalous spectral densities are studied by investigating on their low-temperature quantum behavior. In all cases it is found that the entropy decays quickly and vanishes as the temperature approaches zero. This reveals a good conformity with the third law of thermodynamics and provides another evidence for the validity of fundamental thermodynamical laws in the quantum dissipative region.Comment: 10 pages, 3 figure

Nanoscale Nitrogen Doping in Silicon by Self-Assembled Monolayers

International audienceThis Report presents a nitrogen-doping method by chemically forming self-assembled monolayers on silicon. Van der Pauw technique, secondary-ion mass spectroscopy and low temperature Hall effect measurements are employed to characterize the nitrogen dopants. The experimental data show that the diffusion coefficient of nitrogen dopants is 3.66 × 10−15 cm2 s−1, 2 orders magnitude lower than that of phosphorus dopants in silicon. It is found that less than 1% of nitrogen dopants exhibit electrical activity. The analysis of Hall effect data at low temperatures indicates that the donor energy level for nitrogen dopants is located at 189 meV below the conduction band, consistent with the literature valu