Benford's distribution in extrasolar world: Do the exoplanets follow Benford's distribution?

In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature in accordance with a logarithmic distribution law, which is referred to as Benford's law. The existence and applicability of this empirical law have been extensively studied by physicists, accountants, computer scientists, mathematicians, statisticians, etc., and it has been observed that a large number of data-sets related to diverse problems follow this distribution. However, applicability of Benford's law has been hardly tested for extrasolar objects. Motivated by this fact, this paper investigates the existence of Benford's distribution in the extrasolar world using Kepler data for exoplanets. The investigation has revealed the presence of Benford's distribution in various physical properties of these exoplanets. Further, Benford goodness parameters are computed to provide a quantitative measure of coincidence of real data with the ideal values obtained from Benford's distribution. The quantitative analysis and the plots have revealed that several physical parameters associated with the exoplanets (e.g., mass, volume, density, orbital semi-major axis, orbital period, and radial velocity) nicely follow Benford's distribution, whereas some physical parameters (e.g., total proper motion, stellar age and stellar distance) moderately follow the distribution, and some others (e.g., longitude, radius, and effective temperature) do not follow Benford's distribution. Further, some specific comments have been made on the possible generalizations of the obtained result, its potential applications in analyzing data-set of candidate exoplanets, and how interested readers can perform similar investigations on other interesting data-sets.Comment: 7 pages, 3 figures and one potrai

Multi-objective optimization of an industrial styrene reactor using Harmony Search Algorithm

Multi-objective optimization of industrial styrene reactor is done using Harmony Search algorithm. Harmony search algorithm is a recently developed meta-heuristic algorithm which is inspired by musical improvisation process aimed towards obtaining the best harmony. Three objective functions – productivity, selectivity and yield are optimized to get best combination of decision variables for styrene reactor. All possible cases of single and multi-objective optimization have been considered. Pareto optimal sets are obtained as a result of the optimization study. Results reveal that optimized solution using harmony search algorithm gives better operating conditions than industrial practice

Understanding order dynamics in magnetic and ferroelectric materials and devices for next generation computing

The von Neumann computing architecture comprises three main components: memory, logic, and interconnect. Traditionally, improvements in logic and processor performance, namely increased speed, reduced power consumption, footprint and cost, accomplished by Moore's law---the continuous down scaling of physical dimensions of complementary metal oxide semiconductor (CMOS) transistors---have driven computing performance. On the other hand, recent advancements in silicon (Si)-based specialized hardware accelerators, such as graphics processor units (GPUs) and tensor processing units (TPUs), that can process information at a much faster rate than central processing units (CPUs), have helped revolutionize modern-day data-intensive applications like machine learning (ML), artificial intelligence (AI), big data, and the internet of things (IoTs). The next generation of computing, however, faces two main challenges. First, Moore's law is anticipated to slow down significantly by the end of this decade as Si reaches its fundamental limits, thereby limiting processor performance, including that of GPUs. Second, the `Memory wall', characterized by excessive time and power consumption in the transfer of large sets of data between memory and logic units, due to a performance gap between the processor and the main memory, poses a restriction on the overall performance of the system. Sustainable computing for the future requires investigating the physics of CMOS-compatible materials, followed by building novel devices, and architectures that co-locate memory and logic. These devices and architectures should be compact, fast, energy-efficient, and scalable with problem size. This work focuses on investigating the dynamics of emerging materials, including ferromagnets (FMs), antiferromagnets (AFMs), and doped hafnia-based ferroelectrics (FEs). Ferromagnetic materials are non-volatile, scalable down to nanometer (nm) size, and capable of exhibiting various dynamics in the megahertz (MHz) to gigahertz (GHz) range when driven by electric current. Nanoscale-sized magnetic tunnel junction (MTJ) devices, comprising two ferromagnetic layers sandwiching an insulator layer, are CMOS-compatible and can operate as a single-bit memory, source of random numbers, or signal generators. AFMs constitute another class of magnetically ordered materials with negligible net magnetization. When integrated into a tunnel junction device, they could potentially offer electric current-driven switching and oscillation dynamics in the terahertz (THz) regime. Hafnia-based FE materials form yet another category of CMOS-compatible materials that could exhibit switching dynamics in the hundreds of MHz frequency regime when driven by electric voltage. These materials can be utilized in ferroelectric tunnel junctions (FTJs) or in the gate stack of ferroelectric field-effect transistors (FEFETs), enabling the operation of multi-state tunable memory or sources of random numbers. The research presented encompasses three main themes: numerical modeling frameworks to investigate material dynamics, exploration of various dynamics and their dependence on material parameters and external stimuli, and leveraging these dynamics for developing CMOS-compatible and energy-efficient devices and circuits. In this context, FM and AFM dynamics are modeled using the Landau-Lifshitz Gilbert (LLG) equation to study current-driven switching and oscillation dynamics. Analytic models, in agreement with numerical results, are developed as a function of material parameters and external stimuli. On the device front, applications such as true random number generators and spiking neuron emulators are explored for FMs and AFMs, respectively. Additionally, the nucleation-limited switching (NLS) model is employed to investigate field-driven dynamics in FE materials and devices. Finally, a FE oscillator-based room temperature Ising machine circuit for solving combinatorial optimization problems is proposed.Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo termsThe student, Ankit Shukla, accepted the attached license on 2024-04-05 at 21:39.The student, Ankit Shukla, submitted this Dissertation for approval on 2024-04-05 at 21:54.This Dissertation was approved for publication on 2024-04-10 at 09:58.DSpace SAF Submission Ingestion Package generated from Vireo submission #20315 on 2024-09-16 at 00:33:4

TLM-an obstacle or an advantage?

n the educational fraternity, we commonly use some terms such as pedagogy, learning practices, etc. The thing which is to be discussed as of now is a special word known as Teaching learning Materials or commonly known as TLMs. What does the word TLM? What is its utility? If I go by the definition of TLM, it means any aid that assists in teaching and learning of students may be categorised under this definition

How long, how high, how wide

This article describes and reflects upon the classroom experience of helping a group of children understand the concept of length. The activities are inspired by the Measurement PullOut published with the July 2015 issue of At Right Angle

Learning constitutional values through activities

In a democracy, the most exacting and challenging job of a citizen is citizenship. This is so because a citizen is responsible for selecting the government and to use this right, the individual must be capable of decision-making. Education plays a pivotal role to develop this competence by helping us develop our ability to think clearly and grasp new ideas. An ideal and rational public discourse requires the interest of all citizens, the availability of relevant information to all and well-developed critical thinking abilities among them. Education aims at developing these critical thinking abilities in the citizens, where each citizen can make his or her own decisions rationally and can understand intellectual integrity and sift truth from falsehood, facts from propaganda; reject partiality and radicalism. An educated mind has a scientific temperament and faith in outcomes based on data. It has the ability to receive and perceive new ideas