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This study investigates the phenomenon of abnormally large amplitude intermittent spikes in a memristive Hindmarsh–Rose (MHR) neuron model. The analysis focusses on the effects of coupling strength variations between mutually coupled FitzHugh–Nagumo (FHN) and MHR neuron models. Both neuron models exhibit similar transitions at a critical coupling strength, the FHN neuron displays intermittent oscillations, whereas the MHR neuron occasionally generates intermittent spikes of significantly larger amplitude. The occurrence of extreme events within these spikes was validated using the probability distribution function (PDF). Furthermore, the two-parameter phase diagrams of the membrane input currents and coupling strength enabled the identification of extreme event (EE) and non-extreme event (NEE) regions in the MHR neuron model. The study also explores the underlying mechanisms responsible for the extreme amplitude of spikes observed in the MHR neuron.

This article investigates a (2 + 1)-dimensional nonlinear Broer–Kaup–Kupershmidt (BKK) equation and proposes an improved F-expansion method for obtaining analytical soliton solutions. We introduce the F-expansion technique, which involves a Riccati equation and hyperbolic functions. Using this approach, various solutions are obtained and some structures are constructed and classified into three categories: dromion solutions, local excitations and self-similar fractal structures. These solutions contribute to understanding the (2 + 1)-dimensional BKK and give vital insights into wave distributions. To obtain the dynamics of the solutions, some results are discussed and some local excitations and self-similar fractal structures (FSs) are presented. For the trial functions are emerged into the dromion solutions, the fractal structures which are self-similar are observed. The physical insight and the dynamics of the dromion solutions describing the wave propagation transmission in optical physics are discussed for different selections of rational polynomial trial functions in the solutions. The significance of this work lies in the successful application of the proposed method to achieve soliton solutions of (2 + 1)-dimensional BKK. Through symbolic calculation, the analytic soliton solutions are extracted, which is beyond the efforts of the previous literature. This method provides a new perspective for studying the BKK equation and its solutions. The results obtained enhance our understanding of the BKK behaviour and pave the way for the next work in this area.

We studied the late-time acceleration scenarios using a quintessence field initially trapped in a metastable false vacuum state. The false vacuum has non-zero vacuum energy and can drive exponential expansion if not coupled with gravity. Upon decay of the false vacuum, the quintessence field is released and begins to evolve. We assumed conditions where the effective scalar potential gradient must satisfy (nabla V_{text {eff}} > A), characterised by a pressure term approximately (Delta p / p > mathcal {O} (hbar )) invoking the string swampland criteria. We then derived the effective potential of the scalar with an upper bound on the coupling constant (lambda < 0.6). Further analysis revealed that (V_{text {eff}}) shows a slow-roll behaviour for (0.1> lambda > -0.04) in the effective dark energy equation of state (EoS) (-0.8< w_0 < -0.4), stabilising at points between (1< A < 2.718). Our results suggest a stable scalar decoupled from its initial metastable state can indeed lead to a more stable Universe at later times. However, slight deviations in parameter orders can potentially violate the swampland criteria if (V_{text {eff}}) grows too rapidly. Since this is not something we expect, it opens up the possibility that the current dark energy configuration might be a result of a slowly varying scalar potential rather than being arbitrary.

A generalised relativistic transformation for thermodynamic variables is derived in this study using the basic energy–momentum relationship of special relativity. We posit that momentum undergoes changes akin to a time coordinate and treat it as a thermodynamic potential analogous to energy potential. Additionally, we presume that momentum transforms similarly to a time coordinate. We analyse two mutually exclusive conditions to simplify generalised transformations. In one condition, the transformations are as follows: volume ( V = gamma V' ), internal energy ( U = gamma U' ), temperature ( T = gamma T' ) and pressure ( P = P' ), where ( gamma ) represents the Lorentz factor. The primed variables correspond to the moving frame, while the unprimed variables correspond to the stationary frame. The other condition yields ( V = V'/gamma ), ( U = U'/gamma ), ( T = T'/gamma ), ( P = P' ). Since the first law of thermodynamics is an energy conservation statement and Maxwell and other thermodynamic relationships are mathematical constructs based on the first law, it is expected that such relationships should remain invariant in all frames for relativistic thermodynamic transformations. We demonstrate that the ideal gas equation, Maxwell relationships and other thermodynamic relationships (for example, ( (partial U/partial V)_T = -P + T(partial P/partial T)_V )) remain invariant under these two sets of transformations. Furthermore, we show that, although the ideal gas equation and Maxwell relationships remain invariant for many transformations reported earlier, ( (partial U/partial V)_T = -P + T(partial P/partial T)_V ) remains invariant only for the Sutcliffe transformation (( V = V'/gamma ), ( U = gamma U' ), ( T = gamma T' ), ( P = gamma ^2 P' )). We establish that when ( U ), heat ( Q ) and work ( W ) transform similarly, all thermodynamic relationships remain invariant, and such a formalism is mathematically consistent.

This study explores the reconstruction method within the framework of (f(Q, {mathbb {T}})) gravity by utilising the new agegraphic dark energy (A(mathbb {DE)}) model, where Q represents non-metricity and ({mathbb {T}}) is the trace of the energy–momentum tensor. The (f(Q, {mathbb {T}})) new A({{mathbb {D}}}{{mathbb {E}}}) model is developed through a non-interacting correspondence approach. This theoretical model is then examined in the context of a flat Friedmann–Robertson–Walker (FRW) cosmological framework, which is defined by a power-law scale factor and a pressureless perfect fluid. This modified gravity framework effectively captures different stages of the evolution of the Universe. The reconstructed model is employed to calculate the equation of state parameter, phase planes and the squared speed of sound. The equation of state parameter indicates a quintessence phase, the (omega _{mathbb{D}mathbb{E}})–(omega '_{mathbb{D}mathbb{E}}) plane reveals the freezing region and the (textbf{r})–(textbf{s}) phase plane corresponds to the Chaplygin gas model. Additionally, the squared sound speed parameter suggests instability in the current cosmic evolution. Our study demonstrates that (f(Q, {mathbb {T}})) gravity provides an accurate and comprehensive framework for explaining cosmic expansion, effectively encompassing the dynamics across all stages of the Universe’s evolution.

This study employs a deep neural network (DNN) model to investigate nuclear level density (NLD) using experimental data obtained using the Oslo method. The work focusses on lanthanide nuclei and period-5 nuclei; the DNN model predictions are compared with experimental results. Also, we compare our results with the HFB(+)Cmb (Hartree–Fock–Bogoliubov plus combinatorial) model results retrieved from the RIPL3 data. The DNN model demonstrates higher performance, yielding root mean square (RMS) error values of 0.098 (textrm{MeV}^{-1}) for lanthanides and 0.101 (hbox {MeV}^{-1}) for period-5 nuclei across a comprehensive spectrum of excitation energies. The observed nuclear level densities at very low excitation energies display anomalous behaviour that may be attributed to the nuclear pairing and shell corrections. These phenomena become less pronounced at higher excitation energies, leading to a more uniform level density trend. Even–even nuclei experience significant effects from pairing at lower excitation energies, changing the level density pattern. The present study predicts NLD using the DNN model for selected isotopes where experimental data are unavailable.

The Ramsey theory-based approach to the phase transitions of the second order is suggested. The phase transitions of the second order are seen as the switching of physical interactions(/)chemical bonds between the entities forming the primitive cell of the material. Such a switching is typical for phase change materials. The phase transition of the second order takes place if the energy of the primitive cell is kept constant by changing the spatial order of the chemical bonds. The breaking of the initial symmetry of the cell accompanies the switching of interactions between the entities forming the primitive cell. The order parameter(/)the degree of ordering characterising the ordering within the primitive cell is re-defined. The introduced degree of ordering quantifies the ordering of links(/)interactions(/)chemical bonds between entities constituting the 2D lattice, whereas, the classical ‘Landau degree of order’ quantifies the symmetry breaking under variation in spatial locations of these entities. The suggested approach is generalised easily for 3D primitive cells. The thermal capacity of the non-symmetrical phase is larger than that of the symmetrical phase. For the primitive cells consisting of six interacting entities, the Ramsey theory predicts the inevitable appearance of unstable monochromatic triangles, when the links correspond to attraction or repulsion interactions. The situation becomes different for the primitive cells of five interacting entities.

The nonlinear unsteady flows restricted by moving surfaces have gained particular significance in numerous technological, engineering, industrial, mechanical and biological processes. The flow caused by oscillatory stretched surfaces has attracted particular attention due to its fascinating properties, such as in fluidic oscillators, oscillating jets, oscillation problems, etc. Nanofluids have recently gained much attention due to their potential in numerous applications across various industries. The primary use of the nanomaterials is to increase the effectiveness of heat transfer in various systems. Due to the importance of biomaterial’s in different industrial, technological and engineering systems, the process of bioconvection in nanomaterials has attained reputation in recent years. To lead this exploration, an unsteady bio-convective flow of Oldroyd-B nanomaterial across a bi-directional oscillatory stretched surface is investigated here. Heat generation and thermic radiation have been employed to inspect heat transfer attributes. Furthermore, the effects of magnetic force, chemical reaction and activation energy were employed for the whole analysis. Apposite makeovers were used to convert the deduced nonlinear system to non-dimensional expressions. To yield the series solution, an analytic procedure, namely the homotopy analysis technique (HAM) was adopted. Various graphs were plotted to deliberate the effects of the associated variables on concentration, micro-organism, velocities and temperature profiles. Numeric data were organised in different tables to discuss the importance of different variables on the motile density, local Nusselt and local Sherwood numbers. It has been observed that bidirectional velocities display opposite trends for relaxation and retardation variables. It has further been perceived that amplitudes of velocities periodically decelerate for increase in Hartman number. Greater estimations of heat generation, Brownian motion, thermophoresis and thermic radiation effectively improve the temperature within the nanofluid whereas it diminishes by varying the Prandtl number. Concentration profile declined with Schmidt number, reaction rate and temperature difference variables, while opposite scenario occurred for thermophoresis and activation energy parameters. Moreover, distribution of micro-organisms’ increases for Hartmann number but drops because of greater estimates of the micro-organisms concentration difference, bio-convective Peclet and Lewis numbers.

This article focusses on the ((3+1))-dimensional Yu–Toda–Sassa–Fukuyama (YTSF) model, which is a type of physical model with complex and nonlinear characteristics describing wave propagation in a medium. By using the technique of generalised exponential rational function (GERF), different types of analytical solutions are obtained successfully, including exponential rational solutions, hyperbolic solutions and trigonometric solutions. Subsequently, their dynamic behaviours and temporal-spatial evolutions are investigated through the visualisation of partial solutions. In addition, we discuss the significance of these findings to comprehend nonlinear wave phenomena and outline the future research directions.