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New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits.

ABSTRACT: This study proposes an explanation for the physical power flow in planar circuits by analogy to theoretical two-dimensional circuits using a new mathematical model based on Geometric Algebra (GA) and 2D Maxwell's equations. In contrast with traditional 3D physics in the observable real world, the magnetic field can be defined as a bivector instead of an axial vector allowing to obtain the Poynting Vector directly in a 2D flat world, where physical variables of planar circuits can be obtained. This approach is presented here for the first time to the best of the author's knowledge. Previous investigations have focused on simplifications and symmetries of real 3D circuits studied mainly in the phasor and frequency domain. In this work, the electromagnetic power flow phenomenon is analyzed on a completely 2D time-domain basis and derived directly from the undisputed Maxwell equations, formulated in two dimensions. Several cases of special interest in AC multi-phase circuits are presented using the proposed technique, bringing a new simplified approach to the measurement of power flow exchange between the source and the load. It suggests a new way to understand energy propagation from a purely physical point of view.

SUBMITTER: Montoya FG

PROVIDER: S-EPMC9860059 | biostudies-literature | 2023 Jan

REPOSITORIES: biostudies-literature

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New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits.

Montoya Francisco G FG Prado Xabier X Arrabal-Campos Francisco M FM Alcayde Alfredo A Mira Jorge J

Scientific reports 20230120 1

This study proposes an explanation for the physical power flow in planar circuits by analogy to theoretical two-dimensional circuits using a new mathematical model based on Geometric Algebra (GA) and 2D Maxwell's equations. In contrast with traditional 3D physics in the observable real world, the magnetic field can be defined as a bivector instead of an axial vector allowing to obtain the Poynting Vector directly in a 2D flat world, where physical variables of planar circuits can be obtained. Th ...[more]

PMID: 36670146

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Project description:BackgroundRepeated expenditure of energy and its generation of damaging strain are required to injure the lung by ventilation (VILI). Mathematical modeling of passively inflated, single-compartment lungs with uniform parameters for resistance and compliance indicates that standard clinical modes (flow patterns) differ impressively with respect to the timing and intensity of energy delivery-the intracycle power (ICP) that determines parenchymal stress and strain. Although measures of elastic ICP may accurately characterize instantaneous rates of global energy delivery, how the ICP component delivered to a compartment affects the VILI-linked variable of strain is determined by compartmental mechanics, compartmental size and mode of gas delivery. We extended our one-compartment model of ICP to a multi-compartment setting that varied those characteristics.Main findingsThe primary findings of this model/simulation indicate that: (1) the strain and strain rate experienced within a modeled compartment are nonlinear functions of delivered energy and power, respectively; (2) for a given combination of flow profile and tidal volume, resting compartmental volumes influence their resulting maximal strains in response to breath delivery; (3) flow profile is a key determinant of the maximal strain as well as maximal strain rate experienced within a multi-compartment lung. By implication, different clinician-selected flow profiles not only influence the timing of power delivery, but also spatially distribute the attendant strains of expansion among compartments with diverse mechanical properties. Importantly, the contours and magnitudes of the compartmental ICP, strain, and strain rate curves are not congruent; strain and strain rate do not necessarily follow the compartmental ICP, and the hierarchy of amplitudes among compartments for these variables may not coincide.ConclusionsDifferent flow patterns impact how strain and strain rate develop as compartmental volume crests to its final value. Notably, as inflation proceeds, strain rate may rise or fall even as total strain, a monotonic function of volume, steadily (and predictably) rises. Which flow pattern serves best to minimize the maximal strain rate and VILI risk experienced within any sector, therefore, may strongly depend on the nature and heterogeneity of the mechanical properties of the injured lung.

Project description:Liposomal formulations for the treatment of cancer and other diseases are the most common form of nanotechnology enabled pharmaceuticals (NEPs) submitted for market approval and in clinical application today. The accurate characterization of their physical-chemical properties is a key requirement; in particular, size, size distribution, shape, and physical-chemical stability are key among properties that regulators identify as critical quality attributes. Here we develop and validate an optimized method, based on multi-detector asymmetrical-flow field flow fractionation (MD-AF4) to accurately and reproducibly separate liposomal drug formulations into their component populations and to characterize their associated size and size distribution, whether monomodal or polymodal in nature. In addition, the results show that the method is suitable to measure liposomes in the presence of serum proteins and can yield information on the shape and physical stability of the structures. The optimized MD-AF4 based method has been validated across different instrument platforms, three laboratories, and multiple drug formulations following a comprehensive analysis of factors that influence the fractionation process and subsequent physical characterization. Interlaboratory reproducibility and intra-laboratory precision were evaluated, identifying sources of bias and establishing criteria for the acceptance of results. This method meets a documented high priority need in regulatory science as applied to NEPs such as Doxil and can be adapted to the measurement of other NEP forms (such as lipid nanoparticle therapeutics) with some modifications. Overall, this method will help speed up development of NEPS, and facilitate their regulatory review, ultimately leading to faster translation of innovative concepts from the bench to the clinic. Additionally, the approach used in this work (based on international collaboration between leading non-regulatory institutions) can be replicated to address other identified gaps in the analytical characterization of various classes of NEPs. Finally, a plan exists to pursue more extended interlaboratory validation studies to advance this method to a consensus international standard.

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New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits.

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New mathematical model based on geometric algebra for physical power flow in theoretical two-dimensional multi-phase power circuits.

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