Theoretical Physics Research Articles

The Interplay of Fantasy and Physics in King’s The Dark Tower: The Gunslinger: A Physicist’s Perspective

The paper aims to explore the existence of many worlds and their interconnections in Stephen King’s The Dark Tower: The Gunslinger. It draws on theoretical physicist Brian Greene’s concept of parallel universes. It also draws on the theoretical concept of Albert Einstein and Nathan Rosen as they have discussed in ‘Einstein-Rosen Bridge Theory’. This theory is commonly known as wormholes that connect different regions of space-time, enabling the journey from one world to another and back. Greene's theoretical underpinnings, proposing a vast ensemble of universes with distinct properties, find expressions in the narrative. King's narrative, exemplified by, among others, Jake's revival in Mid-World after a presumed death in a New York car accident, explicitly embraces the idea of parallel universes, each with unique physical laws that influence the concepts such as life and death. The narrative unfolds across disparate worlds, echoing Greene’s theoretical mapping of parallel universes, each governed by its unique set of physical laws and realities. In the narrative, the exploration of multiverse concepts employs fiction's imaginative license to investigate interconnected universes and the potential for transcendent journeys through the cosmic fabric. The theoretical backdrop finds resonance in the novel where characters navigate within the four-dimensional continuum, mirroring the speculative nature of multiverse theories. By intertwining the world of fantasy with the hypotheses of physics, the paper discusses the connections between seemingly disparate realms. This perspective bridges literature and theoretical physics, offering a compelling exploration of the speculative landscapes of parallel universes.

Dynamical Black holes in the FLRW universe

Observations show that massive black holes, thought to be at the center of galaxies and galaxy clusters, are dynamical objects and interact with their environments. Black holes are characterized by their mass and angular momentum, and they are time-varying objects embedded in the cosmological Friedman-Lemaitre-Robertson-Walker (FLRW) universe. Finding analytical solutions for the dynamical black holes with all these properties is very important in theoretical physics. In the present work, we obtain Einstein’s field equations for our predicted dynamical black hole geometry and obtain analytical solutions using the energy-momentum tensor obeying imperfect fluid dynamics. Misner-Sharp-Hernandez mass, turnaround radius, and apparent horizon are analyzed and compared with the recent observations.

Pore pressure prediction based on rock physics theory and its application in seismic inversion

Formation overpressure seriously affects drilling and downhole operation. Accurate prediction on the formation pore pressure can not only reduce the probability of drilling accidents, but also quantitatively evaluate the original formation pressure of underground pore space, which provides an important reference for site selection of carbon sink projects using underground space resources such as CO2 geological storage. It is therefore necessary to set up a widely applicable method that is based on rock physics theory and conforms to the characteristics of rock mechanics and fluid mechanic. This method is suitable for both logging prediction and seismic inversion of pore pressure. The traditional method of predicting pore pressure based on P-wave velocity has multiple solutions, and the prediction based on S-wave velocity which is not sensitive to fluid has new significance. Based on the Hertz-Mindlin petrophysical model that considering pressure variation and the Gassmann fluid substitution equation that addresses the change in fluid saturation, this paper firstly derived rock physical formulas for predicting pore pressure in logging, and then derived the intrinsic power function relationship between the effective pressure (Pe) and S-wave velocity (Vs) as well as S-wave impedance (Is). Based on this, a set of geophysical methods integrating S-wave velocity prediction, pore pressure prediction in well and seismic inversion is finally established. The efficacy of this method has been well validated, with an average error of 2.35% in S-wave velocities prediction, 4.5% in single-well pore pressure prediction. The results of seismic inversion of pore pressure are consistent with the phenomenon of overpressure development in actual working area. This method can be further extended to other areas, providing invaluable reference for underground operation such as oil and gas exploration and CO2 geological storage.

Non-chiral vertex operator algebra associated to Lorentzian lattices and Narain CFTs

Frenkel, Lepowsky, and Meurman constructed a vertex operator algebra (VOA) associated to any even, integral, Euclidean lattice. In the language of physics, these are examples of chiral conformal field theories (CFT). In this paper, we define non-chiral vertex operator algebra and some associated notions. We then give a construction of a non-chiral VOA associated to an even, integral, Lorentzian lattice and construct their irreducible modules. We obtain the moduli space of such modular invariant non-chiral CFTs based on even, self-dual Lorentzian lattices of signature (m,n)(m,n) assuming the validity of a technical result about automorphisms of the lattice. We finally show that Narain conformal field theories in physics are examples of non-chiral VOA. Our formalism helps us to identify the chiral algebra of Narain CFTs in terms of a particular sublattice and give us the decomposition of its partition function into sum of characters.

Exploring the truth and beauty of theory landscapes with machine learning

Theoretical physicists describe nature by i) building a theory model and ii) determining the model parameters. The latter step involves the dual aspect of both fitting to the existing experimental data and satisfying abstract criteria like beauty, naturalness, etc. We use the Yukawa quark sector as a toy example to demonstrate how both of those tasks can be accomplished with machine learning techniques. We propose loss functions whose minimization results in true models that are also beautiful as measured by three different criteria — uniformity, sparsity, or symmetry.

Empowering vocational students: Exploring mobile learning for sustainable high-level cognition in authentic contexts

Early studies show that learning with mobile devices, also known as mobile learning, improves students’ learning in authentic contextual learning–i.e., learning connected to the real world. However, no empirical evidence has yet to firmly prove the effects of mobile technology on specific student skillsets such as learning scalability which means learning can be applied in various scenarios and learning sustainability which means learning can be sustained in real-world environments. Therefore, this study aims to explore the effect of learning using a mobile app called mobile Smart-Physics on learning cognitive levels, learning scalability (e.g., number of learning locations and number of experimental data), and learning sustainability (e.g., number of completed assignments). Eleventh-grade vocational high school students volunteered for this quasi-experiment and were divided into an experimental group (EG), which used Smart-Physics, and a control group (CG), which used a mobile Ubiquitous-Physics (U-Physics) app. The findings show that the EG significantly outperformed the CG concerning learning cognitive levels, learning scalability and learning sustainability. Smart-Physics features enabled the students to tackle technical and pedagogical difficulties during physical investigations in real-world environments and, in some cases, improved their task accomplishment and sustained their motivation to learn. Location awareness promoted the students’ authentic experiential learning, which sharpened their ability to apply learning in real-world environments and upload more experimental data. Feedback helped the students consolidate their physics theories and practical experiences, thereby generating more learning records with meaningful multimedia content like experimental graphs, tables, and notes in various learning locations. Therefore, we encourage practitioners to use smart learning environment features in their learning tools and activity designs.

AI-driven research in pure mathematics and theoretical physics

AI-driven research in pure mathematics and theoretical physics

Laplacian renormalization group: an introduction to heterogeneous coarse-graining

The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification into a relatively small set of universality classes. The RG is the most powerful tool for investigating organizational scales within dynamic systems. However, the application of RG techniques to complex networks has presented significant challenges, primarily due to the intricate interplay of correlations on multiple scales. Existing approaches have relied on hypotheses involving hidden geometries and based on embedding complex networks into hidden metric spaces. Here, we present a practical overview of the recently introduced Laplacian RG (LRG) for heterogeneous networks. First, we present a brief overview that justifies the use of the Laplacian as a natural extension of well-known field theories to analyze spatial disorder. We then draw an analogy to traditional real-space RG procedures, explaining how the LRG generalizes the concept of ‘Kadanoff supernodes’ as block nodes that span multiple scales. These supernodes help mitigate the effects of cross-scale correlations due to small-world properties. Additionally, we rigorously define the LRG procedure in momentum space in the spirit of the Wilson RG. Finally, we show different analyses for the evolution of network properties along the LRG flow following structural changes when the network is properly reduced.

Group theory in physics: an introduction with mathematica

Group theory in physics: an introduction with mathematica

Max Delbruck: Founder of Molecular Genetics.

Max Delbrück (1906-1981) attended the University of Gottingen, where he studied astrophysics initially, switching later to theoretical physics. He earned his PhD in physics from Gottingen in 1930. Delbruck then moved to England and Denmark. It was during this time that he met Niels Bohr and his argument that quantum mechanics might have a wider application to biology-inspired Delbruck to pursue biology.

A Numerical Method for Investigating Fractionali Volterra-Fredholm Integro-Differential Model

In this article, we investigate the fractional Volterra-Fredholm integro-differential equations. These equations appear in several applications such as control theory, biology, and particle dynamics in physics. We derive a numerical method based on the operational matrix method to solve this class of integro-differential equations. We prove the existence and uniqueness of the ex-act solution. Additionally, we demonstrate the uniform convergence of the numerical solutions to the exact solution. We present several numerical examples to show the numerical efficiency of the proposed method. In the first example, we choose a linear problem and find that the approximate solution converges to the exact solution when the number of block pulse functions is very large. In the next two examples, we consider the nonlinear case and compute the L2-local truncation error since exact solutions are not available. The error was of order 10−12. Furthermore, we sketch the graph of the approximate solutions for different values of the fractional derivative to observe the influence of the fractional derivative on the profile of the solutions. Theoretical and numerical results show that the proposed method is accurate and can be applied to other nonlinear problems in science.

From quantum field theory to the quantum method the inverse problem On the 90th anniversary of the birth of academician L.D. Faddeev

The article is dedicated to the life and work of a theoretical physicist and mathematician, a full member of the USSR Academy of Sciences and RAS L.D. Faddeev (1934−2017), the formation of his scientific school. Faddeev’s works on scattering theory, quantum field theory, classical and quantum theory of integrable systems were included in the golden fund of world science and largely determined the face of modern mathematical physics. The author of the article is an employee of the Laboratory of Mathematical Problems of Physics created by L.D. Faddeev at the St. Petersburg Department of the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences since its foundation.

Revealing the Essence of Differential and Integral Calculus based on Scientific Philosophy

As it is known in the way where the basic equations of mathematical analysis and mathematical physics were taken as a basis it was possible to come to the main results of the Cantor set theory. However, contradictions and paradoxes were inherent to the results obtained in this field. In the way where the basic equations of theoretical physics, as well as empirical and probabilistic physics were taken as a basis, it was possible to arrive at the basic results of quantum theory. The results obtained in this area proved to be very useful in describing the experimental data. This was a sign of their truth. Therefore, there is reason to come to the following conclusion. That taking as a basis the ideas and results obtained in the field of quantum theory, there is a possibility to come to the disclosure of the essence of differential and integral calculus. As well as the results obtained in the field of new set theory. The main purpose of this work is an attempt to solve this problem.

Analysis of Complex Entities in Algebra B

We present an exploration of algebra B, a recently published unital and non-associative algebra. Unique complex entities emerged from this algebra, distinct from both quaternion and complex number systems, which we termed treons. We defined the treonic number system and established an isomorphism between this system and the real vector space. Our findings revealed that the treonic representation maintained structural integrity under the defined operations. Based on this foundation, we proceed to determine Euler identity for algebra B within the treonic system. By presenting the fundamental definitions and properties of algebra B, we derived a generalized version of Euler identity applicable within this algebra. This formula revealed the emergence of hyperbolic trigonometric entities, extending the applicability of Euler identity beyond traditional complex numbers. Our results provide a theoretical foundation for a deeper understanding of the properties and behaviors of complex entities within this expanded algebraic framework, thus enabling new theoretical developments and practical applications in the realms of advanced mathematics and theoretical physics.

From the standard model to M-theory: The development of string theory

String theory is now the most competitive theory of quantum gravity, and it takes an important role in theoretical physics. In this article, we introduced why we need string theory and how string theory is formed. The importance of string theory is described through general relativity and the Standard Model of particle physics. String theory is originally discovered to describe strong interaction. While a better model for strong interaction was developed, string theory was found to be a candidate for a theory about quantum gravity. The first version of string theory is the bosonic string theory, which was constructed in 26-dimensional space and used to describe bosons. After supersymmetry was introduced, the dimensions were reduced to 10, and the theory is hence called the superstring theory. In the first superstring revolution, 5 different superstring theories were constructed and compactified on the 6-dimensional Calabi-Yau manifold. In the second superstring revolution, the idea of different dualities was introduced in string, as well as D-branes. Hence, it was found that the 5 different superstrings can be unified to get the 11-dimensional M-theory.

Steric and energetic investigations of adsorption isotherms of methylene blue on new polymeric multi-layered material-based k-carrageenan and alginate

In this research study, we examined the adsorption behavior of methylene blue (MB) on a novel biosorbent made of polyelectrolyte multilayers (PEM) biopolymeric material at three different temperatures. Various models derived from statistical physics formalism were employed to analyze the adsorption isotherms. An alternative approach based on the application of multilayer models from statistical physics theory was used to better investigate the adsorption mechanisms of MB on the PEM grafting material. We adjusted various parameters within this model across temperatures of 295K, 313 K, and333K, and these parameters played a crucial role in comprehending the adsorption mechanism. In addition, this approach revealed that the MB dye is linked through a multilayer process on the PEM grafting material with ‘non-parallel’ configurations and multimolecular process. The PEM grafting material showed maximum adsorption capacities ranging from 632.23 mg⁄g to 463.76 mg⁄g for the removal of MB over a pH of 6. The calculated adsorption energies ranged from 11.6 to 18.65kJ/mol, indicating that the MB adsorption process was primarily of a physisorption nature influenced by both hydrogen bonding and van der Waals interactions. Thus, the theoretical analysis indicated that this low-cost adsorbent material (PEM grafting) is a promising material for the removal of MB dye from the solution. Additionally, we examined the adsorption behavior by calculating the entropy, the free energy and the internal energy which govern the adsorption process of MB onto the PEM grafting material.

Triple Symmetric Sums of Circular Binomial Products

By employing the generating function approach, 16 triple sums for circular binomial products of binomial coefficients are examined. Recurrence relations and generating functions are explicitly determined. These symmetric sums may find potential applications in the analysis of algorithms, symbolic calculus, and computations in theoretical physics.

Physical theory of two-stage thermalization

Physical theory of two-stage thermalization

On the Continuity Equation in Space–Time Algebra: Multivector Waves, Energy–Momentum Vectors, Diffusion, and a Derivation of Maxwell Equations

Historically and to date, the continuity equation (C.E.) has served as a consistency criterion for the development of physical theories. In this paper, we study the C.E. employing the mathematical framework of space–time algebra (STA), showing how common equations in mathematical physics can be identified and derived from the C.E.’s structure. We show that, in STA, the nabla equation given by the geometric product between the vector derivative operator and a generalized multivector can be identified as a system of scalar and vectorial C.E.—and, thus, another form of the C.E. itself. Associated with this continuity system, decoupling conditions are determined, and a system of wave equations and the generalized analogous quantities to the energy–momentum vectors and the Lorentz force density (and their corresponding C.E.) are constructed. From the symmetry transformations that make the C.E. system’s structure invariant, a system with the structure of Maxwell’s field equations is derived. This indicates that a Maxwellian system can be derived not only from the nabla equation and the generalized continuity system as special cases, but also from the symmetries of the C.E. structure. Upon reduction to well-known simpler quantities, the results found are consistent with the usual STA treatment of electrodynamics and hydrodynamics. The diffusion equation is explored from the continuity system, where it is found that, for decoupled systems with constant or explicitly dependent diffusion coefficients, the absence of external vector sources implies a loss in the diffusion equation structure, transforming it into Helmholtz-like and wave equations.

Design of a Facility for Simultaneous Irradiation with Two Ion Beams based on the HIPR Accelerator for Simulations Neutron Influence

Ion accelerator facility is a powerful tool to simulate neutron irradiation effects in reactor materials. Defects in the crystal lattice arise and the accumulation of transmutation products (helium and hydrogen) occurs in the structure of the material under the action of neutrons in the structural materials of nuclear installations. At Kurchatov Complex for Theoretical and Experimental Physics the heavy ion accelerator HIPr (heavy ion prototype) is used to simulate radiation damage in steels and alloys using a 5.6 MeV Fe2+ ion beam. The second beam line is designed at the HIPr facility to simultaneously implant helium (or hydrogen) into the region of defects. The second beam line provides a beam of helium ions with energy up to 300 keV. The report presents a description of second beam line design and a status of construction the second beam line.