Many fundamental physical problems are modeled using differential equations, describing time- and space-dependent variables from conservation laws. Practical problems, such as surface morphology, ...particle interactions, and memory effects, reveal the limitations of traditional tools. Fractional calculus is a valuable tool for these issues, with applications ranging from membrane diffusion to electrical response of complex fluids, particularly electrolytic cells like liquid crystal cells. This paper presents the main fractional tools to formulate a diffusive model regarding time-fractional derivatives and modify the continuity equations stating the conservation laws. We explore two possible ways to introduce time-fractional derivatives to extend the continuity equations to the field of arbitrary-order derivatives. This investigation is essential, because while the mathematical description of neutral particle diffusion has been extensively covered by various authors, a comprehensive treatment of the problem for electrically charged particles remains in its early stages. For this reason, after presenting the appropriate mathematical tools based on fractional calculus, we demonstrate that generalizing the diffusion equation leads to a generalized definition of the displacement current. This modification has strong implications in defining the electrical impedance of electrolytic cells but, more importantly, in the formulation of the Maxwell equations in material systems.
We investigate how the changes on the electrode surface may influence the behavior of the constant–phase elements (CPE) and, consequently, electrical response of an electrolytic cell. This analysis ...is performed by using an experiment with Milli-Q water and stainless steel electrodes with three different types of polishment: smooth, fine sandpaper, and rough sandpaper. The experimental data is obtained from an Electrical Impedance Spectroscopy (EIS) measure and analyzed by means of an equivalent circuit with CPE elements.
Machine learning methods are becoming increasingly important for the development of materials science. In spite of this, the use of image analysis in the development of these systems is still recent ...and underexplored, especially in materials often studied via optical imaging techniques such as liquid crystals. Here we apply the recently proposed method of ordinal networks to map optical textures obtained from experimental samples of liquid crystals into complex networks and use this representation jointly with a simple statistical learning algorithm to investigate different physical properties of these materials. Our research demonstrates that ordinal networks formed by only 24 nodes encode crucial information about liquid crystal properties, thus allowing us to train simple machine learning models capable of identifying and classifying mesophase transitions, distinguishing among different doping concentrations used to induce chiral mesophases, and predicting sample temperatures with outstanding accuracy. The precision and scalability of our approach indicate it can be used to probe properties of different materials in situations involving large-scale datasets or real-time monitoring systems.
Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing ...and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality. Our approach builds upon nearest neighbor graphs to establish neighborhood relations and uses random walks to extract ordinal patterns and their distribution, thereby defining the k-nearest neighbor permutation entropy. This tool not only adeptly identifies variations in patterns of unstructured data, but also does so with a precision that significantly surpasses conventional measures such as spatial autocorrelation. Additionally, it provides a natural approach for incorporating amplitude information and time gaps when analyzing time series or images, thus significantly enhancing its noise resilience and predictive capabilities compared to the usual permutation entropy. Our research substantially expands the applicability of ordinal methods to more general data types, opening promising research avenues for extending the permutation entropy toolkit for unstructured data.
Machine learning algorithms have been available since the 1990s, but it is much more recently that they have come into use also in the physical sciences. While these algorithms have already proven to ...be useful in uncovering new properties of materials and in simplifying experimental protocols, their usage in liquid crystals research is still limited. This is surprising because optical imaging techniques are often applied in this line of research, and it is precisely with images that machine learning algorithms have achieved major breakthroughs in recent years. Here we use convolutional neural networks to probe several properties of liquid crystals directly from their optical images and without using manual feature engineering. By optimizing simple architectures, we find that convolutional neural networks can predict physical properties of liquid crystals with exceptional accuracy. We show that these deep neural networks identify liquid crystal phases and predict the order parameter of simulated nematic liquid crystals almost perfectly. We also show that convolutional neural networks identify the pitch length of simulated samples of cholesteric liquid crystals and the sample temperature of an experimental liquid crystal with very high precision.
Civil construction has grown inadvertently in Brazil, and, consequently, its demands for raw material. The production of such materials, as to any industrial process, yields wastewater effluents and ...has as destination, in general, water resources such as rivers and lakes. Nonetheless, government inspection cannot keep up with the number of starting companies, resulting in impunity due to lack of inspection. In the present work, the first of the kind, some chemical-physics aspects of wastewater effluents samples generated from grout industries were analyzed. The study shows that the pH of these samples lie outside the established limit by the national laws. The extremely alkaline pH and high conductivity of these effluents may cause severe damage to the aquatic environment in which they are disposed.
The Poisson-Nernst-Planck (PNP) diffusional model for the immittance or impedance spectroscopy response of an electrolytic cell in a finite-length situation is extended to a general framework. In ...this new formalism, the bulk behavior of the mobile charges is governed by a fractional diffusion equation in the presence of a reaction term. The solutions have to satisfy a general boundary condition embodying, in a single expression, most of the surface effects commonly encountered in experimental situations. Among these effects, we specifically consider the charge transfer process from an electrolytic cell to the external circuit and the adsorption-desorption phenomenon at the interfaces. The equations are exactly solved in the small AC signal approximation and are used to obtain an exact expression for the electrical impedance as a funcion of the frequency. The predictions of the model are compared to and found to be in good agreement with the experimental data obtained for an electrolytic solution of CdCl2H20.
Cytomegalovirus (CMV) infection is common among patients with human immunodeficiency virus (HIV) infection. Gastrointestinal (GI) involvement with tumor like lesion is a rare presentation. Our ...patient presented with rectal pain and findings concerning for malignancy. Subsequently our patient was diagnosed with acquired immunodeficiency syndrome (AIDS), CMV viremia and CMV proctitis.
A 37-year-old man who reported having sex with men presented with severe proctalgia and hematochezia. Imaging showed irregular rectal wall thickening concerning for malignancy. Sigmoidoscopy revealed a circumferential necrotic lesion suspicious for malignancy. Surprisingly, biopsy showed a cytopathic effect compatible with CMV infection. In addition to testing positive for CMV, patient was newly diagnosed with HIV/AIDS, hepatitis C, syphilis, and gonorrhea. CMV infection was treated with ganciclovir, which resulted in a significant response. Ganciclovir was later replaced with valganciclovir. Valganciclovir was continued and antiretroviral therapy (ART) was started as an outpatient and with resolution of symptoms.
CMV infection is one of the most common opportunistic infections among patients with HIV infection. Several cases of CMV colitis were reported among immunocompromised patients. Our patient’s presenting symptoms and direct visualization of rectal lesion were not only deceptive but also unique. As what looked like a rectal malignancy was later diagnosed as tissue invasive CMV by biopsy. Invasive CMV infection should be managed with ganciclovir.
GI CMV as the initial presentation of HIV is rare. Moreover, CMV proctitis can masquerade as a rectal cancer and clinicians should be aware of this rare presentation of CMV.
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