Diffusion and surface reaction in porous cubical catalyst: A mathematical approach

Background: Catalysts are the most vital part of any chemical industry. Catalyst is a substance that affects the rate of reaction, but the catalyst itself does not take part in the reaction. Catalysts offer different pathways of reaction by diffusing the reactant inside it to provide a large surface area within a small volume, thus, lowering the activation energy of molecules for reaction. Most of the catalytic reactions take place in liquid-solid or gas-solid interface where catalysts are mostly porous in nature. Spherical and cubic-shaped catalyst particles are commonly used in different industries. Methods: In the first phase of the present study, the physics behind the diffusion inside the catalyst pellet has been discussed. In the second part, governing differential equations have been established at a steady-state condition. For solving the differential equation, the equation is made dimensionless. Physical boundary conditions were used to solve the diffusion equation. The assumption of writing the differential equation of the reaction is elementary. Then the Thiele modulus is derived in terms of the reaction and geometrical parameter (Length) Results and Conclusion: In the third part, the differential equation is solved for first-order reaction with some constant values of the Thiele modulus and three-dimensional plots are obtained using numerical analysis. After that, the obtained Thiele modulus and effectiveness factor plot are compared to draw the conclusion of reaction rate limited and internal diffusion limited.

The Emperor's New Markov Blankets

The free energy principle, an influential framework in computational neuroscience and theoretical neurobiology, starts from the assumption that living systems ensure adaptive exchanges with their environment by minimizing the objective function of variational free energy. Following this premise, it claims to deliver a promising integration of the life sciences. In recent work, Markov Blankets, one of the central constructs of the free energy principle, have been applied to resolve debates central to philosophy (such as demarcating the boundaries of the mind). The aim of this paper is twofold. First, we trace the development of Markov blankets starting from their standard application in Bayesian networks, via variational inference, to their use in the literature on active inference. We then identify a persistent confusion in the literature between the formal use of Markov blankets as an epistemic tool for Bayesian inference, and their novel metaphysical use in the free energy framework to demarcate the physical boundary between an agent and its environment. Consequently, we propose to distinguish between ‘Pearl blankets’ to refer to the original epistemic use of Markov blankets and ‘Friston blankets’ to refer to the new metaphysical construct. Second, we use this distinction to critically assess claims resting on the application of Markov blankets to philosophical problems. We suggest that this literature would do well in differentiating between two different research programs: ‘inference with a model’ and ‘inference within a model’. Only the latter is capable of doing metaphysical work with Markov blankets, but requires additional philosophical premises and cannot be justified by an appeal to the success of the mathematical framework alone.

The Importance of Mimicking Dermal-Epidermal Junction for Skin Tissue Engineering: A Review

There is a distinct boundary between the dermis and epidermis in the human skin called the basement membrane, a dense collagen network that creates undulations of the dermal–epidermal junction (DEJ). The DEJ plays multiple roles in skin homeostasis and function, namely, enhancing the adhesion and physical interlock of the layers, creating niches for epidermal stem cells, regulating the cellular microenvironment, and providing a physical boundary layer between fibroblasts and keratinocytes. However, the primary role of the DEJ has been determined as skin integrity; there are still aspects of it that are poorly investigated. Tissue engineering (TE) has evolved promising skin regeneration strategies and already developed TE scaffolds for clinical use. However, the currently available skin TE equivalents neglect to replicate the DEJ anatomical structures. The emergent ability to produce increasingly complex scaffolds for skin TE will enable the development of closer physical and physiological mimics to natural skin; it also allows researchers to study the DEJ effect on cell function. Few studies have created patterned substrates that could mimic the human DEJ to explore their significance. Here, we first review the DEJ roles and then critically discuss the TE strategies to create the DEJ undulating structure and their effects. New approaches in this field could be instrumental for improving bioengineered skin substitutes, creating 3D engineered skin, identifying pathological mechanisms, and producing and screening drugs.

Hyperpolarization and the physical boundary of Liouville space

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I=1/2, I=1, I=3/2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

Persistent Ventricle Partitioning in the Adult Zebrafish Heart

The vertebrate heart integrates cells from the early-differentiating first heart field (FHF) and the later-differentiating second heart field (SHF), both emerging from the lateral plate mesoderm. In mammals, this process forms the basis for the development of the left and right ventricle chambers and subsequent chamber septation. The single ventricle-forming zebrafish heart also integrates FHF and SHF lineages during embryogenesis, yet the contributions of these two myocardial lineages to the adult zebrafish heart remain incompletely understood. Here, we characterize the myocardial labeling of FHF descendants in both the developing and adult zebrafish ventricle. Expanding previous findings, late gastrulation-stage labeling using drl-driven CreERT2 recombinase with a myocardium-specific, myl7-controlled, loxP reporter results in the predominant labeling of FHF-derived outer curvature and the right side of the embryonic ventricle. Raised to adulthood, such lineage-labeled hearts retain broad areas of FHF cardiomyocytes in a region of the ventricle that is positioned at the opposite side to the atrium and encompasses the apex. Our data add to the increasing evidence for a persisting cell-based compartmentalization of the adult zebrafish ventricle even in the absence of any physical boundary.

Persistent ventricle partitioning in the adult zebrafish heart

The vertebrate heart integrates cells from the early-differentiating first heart field (FHF) and the later-differentiating second heart field (SHF) emerging from the lateral plate mesoderm. In mammals, this process forms the basis for the development of the left and right ventricle chambers and subsequent chamber septation. The single ventricle-forming zebrafish heart also integrates FHF and SHF lineages during embryogenesis, yet the contributions of these two myocardial lineages to the adult zebrafish heart remain incompletely understood. Here, we characterize the myocardial labeling of FHF descendants in both the developing and adult zebrafish ventricle. Expanding previous findings, late gastrulation-stage labeling using drl-driven CreERT2 recombinase with a myocardium-specific, myl7-controlled loxP reporter results in predominant labeling of FHF-derived outer curvature and the right side of the embryonic ventricle. Raised to adulthood, such lineage-labeled hearts retain broad areas of FHF cardiomyocytes in a region of the ventricle that is positioned at the opposite side to the atrium and encompasses the apex. Our data add to the increasing evidence for a persisting cell-based compartmentalization of the adult zebrafish ventricle even in the absence of any physical boundary.

Hyperpolarization and the Physical Boundary of Liouville Space

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region, and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I = 1 / 2, I = 1, I = 3 / 2, and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

Capabilities of inverse scheme for acoustic source localization at low frequencies

We present the capabilities of a recently developed inverse scheme for source localization at low frequencies within an arbitrary acoustic environment. The inverse scheme is based on minimizing a Tikhonov functional matching measured microphone signals with simulated ones. We discuss the sensitivity of all involved parameters, the precision of geometry and physical boundary modeling for the numerical simulation using the finite element (FE) method, and the automatic determination of the positions of the recording microphones being distributed around the object of investigation. Finally, we apply the inverse scheme to a real-world scenario and compare the obtained results to state-of-the-art signal processing approaches, e.g. Clean-SC.