Physics

In this paper, we try to create an effective mathematical model for the well-known slayer exciter transformer circuit. We aim to analyze various aspects of the slayer-exciter circuit, by using physical and computational methods. We use a computer simulation for data collection of various parameters pertaining to the circuit. Using this data, we generate plots for various components and parameters. We also derive an approximate equation to maximize the secondary output voltage generated by the circuit. We also discuss a possible method to construct such a circuit using low-cost materials.

Since the evolution of digital computers, the storage of data has always been in terms of discrete bits that can store values of either 1 or 0. Hence, all computer programs (such as MATLAB), convert any input continuous signal into a discrete dataset. Applying this to oscillating signals, such as audio, opens a domain for processing as well as editing. The Fourier transform, which is an integral over infinite limits, for the use of signal processing is discrete. The essential feature of the Fourier transform is to decompose any signal into a combination of multiple sinusoidal waves that are easy to deal with. The discrete Fourier transform (DFT) can be represented as a matrix, with each data point acting as an orthogonal point, allowing one to perform complicated transformations on individual frequencies. Due to this formulation, all the concepts of linear algebra and linear transforms prove to be extremely useful here. In this paper, we first explain the theoretical basis of audio ...

This paper examines the incommensurability thesis-one of the most important and controversial ideas to emerge from the simultaneous work of Kuhn and Feyerabend. In the first half, I discuss three aspects of incommensurability-methodological incommensurability (the view that each paradigm supplies different standards of evaluation), observational incommensurability (the view that the theories we accept alter how we see the world), and finally, semantic incommensurability (which claims that as paradigms change, the very meanings of central theoretical terms also change). In the latter half, I tackle the general arguments of physicists against incommensurability by primarily considering the so called unifying cube of physics. I show that the cube of physics does not get rid of incommensurability, but rather favours it.

A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if at least one of these causal geodesics is past incomplete. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I matter fields in an arbitrarily finite number of dimensions. In the spirit of Joshi and Dwivedi (1993 Phys. Rev. D 47 5357), and Goswami and Joshi (2007 Phys. Rev. D 76 084026), beginning with regular initial data, we derive two distinct (but not mutually exclusive) conditions, which we call the positive root condition (PRC) and the simple positive root condition (SPRC), that serve as necessary and sufficient conditions, respectively, for the existence of naked singularities. In doing so, we generalize the results of both the aforementioned works. We further restrict the PRC and the SPRC by imposing the curvature growth condition (CGC) of Clarke and Krolak (1985 J. Geom. Phys. 2(2) 127) on all causal curves that satisfy the causal convergence condition. The CGC then gives a sufficient condition ensuring that the naked singularities implying the PRC and implied by the SPRC, are of strong curvature type and hence correspond to the inextendibility of the spacetime. Using the CGC, we extend the results of Mosani et. al. (2020 Phys. Rev. D 101 044052) (that hold for dimension N = 4) to the case N = 5, showing that strong curvature naked singularities can occur in this case. However, for the case N ≥ 6, we show that past-incomplete causal curves that identify naked singularities do not satisfy the CGC. These results shed light on the validity of the cosmic censorship conjectures in arbitrary dimensions.

Since the evolution of digital computers, the storage of data has always been in terms of discrete bits that can store values of either 1 or 0. Hence, all computer programs (such as MATLAB), convert any input continuous signal into a discrete dataset. Applying this to oscillating signals, such as audio, opens a domain for processing as well as editing. The Fourier transform, which is an integral over infinite limits, for the use of signal processing is discrete. The essential feature of the Fourier transform is to decompose any signal into a combination of multiple sinusoidal waves that are easy to deal with. The discrete Fourier transform (DFT) can be represented as a matrix, with each data point acting as an orthogonal point, allowing one to perform complicated transformations on individual frequencies. Due to this formulation, all the concepts of linear algebra and linear transforms prove to be extremely useful here. In this paper, we first explain the theoretical basis of audio processing using linear algebra, and then focus on a simulation coded in MATLAB, to process and edit various audio samples. The code is open ended and easily expandable by just defining newer matrices which can transform over the original audio signal. Finally, this paper attempts to highlight and briefly explain the results that emerge from the simulation. * More precisely, the usefulness of linear algebra for the same.