Search Results (795)

The paper outlines the hybrid framework of spin hydrodynamics, combining classical kinetic theory with the Israel–Stewart method of introducing dissipation. The local equilibrium expressions for the baryon current, the energy–momentum tensor, and the spin tensor of particles with spin 1/2 following the Fermi–Dirac statistics are obtained and compared with the earlier derived versions where the Boltzmann approximation was used. The expressions in the two cases are found to have the same form, but the coefficients are shown to be governed by different functions. The relative differences between the tensor coefficients in the Fermi–Dirac and Boltzmann cases are found to grow exponentially with the baryon chemical potential. In the proposed formalism, nonequilibrium processes are studied including mathematically possible dissipative corrections. Standard conservation laws are applied, and the condition of positive entropy production is shown to allow for the transfer between the spin and orbital parts of angular momentum. Full article

The Pennes bioheat equation is the most widely used model for describing heat transfer in living tissue during thermal exposure. It is derived from the classical Fourier law of heat conduction and assumes energy exchange between blood vessels and surrounding tissues. The literature presents various numerical methods for solving the bioheat equation, with exact solutions developed for different boundary conditions and geometries. However, analytical models based on this framework are rarely reported. This study aims to develop an analytical three-dimensional model using MATHEMATICA software, with subsequent mathematical validation performed through COMSOL simulations, to characterize heat transfer in biological tissues induced by laser irradiation under various therapeutic conditions. The objective is to refine the conventional bioheat equation by introducing three key improvements: (a) incorporating a non-Fourier framework for the Pennes equation, thereby accounting for the relaxation time in thermal response; (b) integrating Dirac functions and the telegraph equation into the bioheat model to simulate localized point heating of diseased tissue; and (c) deriving a closed-form analytical solution for the Pennes equation in both its classical (Fourier-based) and improved (non-Fourier-based) formulations. This paper investigates the nuanced relationship between the relaxation time parameter in the telegraph equation and the thermal relaxation time employed in the bioheat transfer equation. Considering all these aspects, the optimal thermal relaxation time determined for these simulations was 1.16 s, while the investigated thermal exposure time ranged from 0.01 s to 120 s. This study introduces a generalized version of the model, providing a more realistic representation of heat exchange between biological tissue and blood flow by accounting for non-uniform temperature distribution. It is important to note that a reasonable agreement was observed between the two modeling approaches: analytical (MATHEMATICA) and numerical (COMSOL) simulations. As a result, this research paves the way for advancements in laser-based medical treatments and thermal therapies, ultimately contributing to more optimized therapeutic outcomes. Full article

We introduce a modern methodology for constructing global analytical approximations of special functions over their entire domains. By integrating the traditional method of matching asymptotic expansions—enhanced with Padé approximants—with differential evolution optimization, a modern machine learning technique, we achieve high-accuracy approximations using elegantly simple expressions. This method transforms non-elementary functions, which lack closed-form expressions and are often defined by integrals or infinite series, into simple analytical forms. This transformation enables deeper qualitative analysis and offers an efficient alternative to existing computational techniques. We demonstrate the effectiveness of our method by deriving an analytical expression for the Fermi gas pressure that has not been previously reported. Additionally, we apply our approach to the one-loop correction in thermal field theory, the synchrotron functions, common Fermi–Dirac integrals, and the error function, showcasing superior range and accuracy over prior studies. Full article

The misfolding and aggregation of proteins into amyloidogenic assemblies are key features of several metabolic and neurodegenerative diseases. Human insulin has long been known to form amyloid fibrils under various conditions, which affects its bioavailability and function. Clinically, insulin aggregation at recurrent injection sites poses a challenge for diabetic patients who rely on insulin therapy. Furthermore, decreased responsiveness to insulin in type 2 diabetic (T2D) patients may lead to its overproduction and accumulation as aggregates. Earlier reports have reported that various factors such as pH, temperature, agitation, and the presence of lipids or other proteins influence insulin aggregation. Our present study aims to elucidate the effects of non–micellar anionic DMPG (1,2–dimyristoyl–sn–glycero–3–phosphoglycerol) lipids on insulin aggregation. Distinct pathways of insulin aggregation and intermediate formation were observed in the presence of DMPG using a ThT fluorescence assay. The formation of soluble intermediates alongside large insulin fibrils was observed in insulin incubated with DMPG via TEM, DLS, and NMR as opposed to insulin aggregates generated without lipids. ¹³C magic angle spinning solid–state NMR and FTIR experiments indicated that lipids do not alter the conformation of insulin fibrils but do alter the time scale of motion of aromatic and aliphatic side chains. Furthermore, the soluble intermediates were found to be more cytotoxic than fibrils generated with or without lipids. Overall, our study elucidates the importance of anionic lipids in dictating the pathways and intermediates associated with insulin aggregation. These findings could be useful in determining various approaches to avoid toxicity and enhance the effectiveness of insulin in therapeutic applications. Full article

Real-time, high-resolution monitoring of chemically diverse water pollutants remains a critical challenge for smart water management. Here, we report a fully integrated, multi-modal nano-sensor array, combining graphene field-effect transistors, Ag/Au-nanostar surface-enhanced Raman spectroscopy substrates, and CdSe/ZnS quantum dot fluorescence, coupled to an edge-deployable CNN-LSTM architecture that fuses raw electrochemical, vibrational, and photoluminescent signals without manual feature engineering. The 45 mm × 20 mm microfluidic manifold enables continuous flow-through sampling, while 8-bit-quantised inference executes in 31 ms at <12 W. Laboratory calibration over 28,000 samples achieved limits of detection of 12 ppt (Pb²⁺), 17 pM (atrazine) and 87 ng L⁻¹ (nanoplastics), with R² ≥ 0.93 and a mean absolute percentage error <6%. A 24 h deployment in the Cherwell River reproduced natural concentration fluctuations with field R² ≥ 0.92. SHAP and Grad-CAM analyses reveal that the network bases its predictions on Dirac-point shifts, characteristic Raman bands, and early-time fluorescence-quenching kinetics, providing mechanistic interpretability. The platform therefore offers a scalable route to smart water grids, point-of-use drinking water sentinels, and rapid environmental incident response. Future work will address sensor drift through antifouling coatings, enhance cross-site generalisation via federated learning, and create physics-informed digital twins for self-calibrating global monitoring networks. Full article

The study of neuronal electrical activity and spatial organization is essential for uncovering the mechanisms that regulate neuronal electrophysiology and function. Mathematical models have been utilized to analyze the structural properties of neuronal networks, predict connectivity patterns, and examine how morphological changes impact neural network function. In this study, we aimed to explore the role of the actin cytoskeleton in neuronal signaling via primary cilia and to elucidate the role of the actin network in conjunction with neuronal electrical activity in shaping spatial neuronal formation and organization, as demonstrated by relevant mathematical models. Our proposed model is based on the polygamma function, a mathematical application of ramification, and a geometrical definition of the actin cytoskeleton via complex numbers, ring polynomials, homogeneous polynomials, characteristic polynomials, gradients, the Dirac delta function, the vector Laplacian, the Goldman equation, and the Lie bracket of vector fields. We were able to reflect the effects of neuronal electrical activity, as modeled by the Van der Pol equation in combination with the actin cytoskeleton, on neuronal morphology in a 2D model. In the next step, we converted the 2D model into a 3D model of neuronal electrical activity, known as a core-shell model, in which our generated membrane potential is compatible with the neuronal membrane potential (in millivolts, mV). The generated neurons can grow and develop like an organoid brain based on the developed mathematical equations. Furthermore, we mathematically introduced the signal transduction of primary cilia in neurons. Additionally, we proposed a geometrical model of the neuronal branching pattern, which we described as ramification, that could serve as an alternative mathematical explanation for the branching pattern emanating from the neuronal soma. In conclusion, we highlighted the relationship between the actin cytoskeleton and the signaling processes of primary cilia. We also developed a 3D model that integrates the geometric organization unique to neurons, which contains soma and branches, such that the mathematical model represents the interaction between the actin cytoskeleton and neuronal electrical activity in generating action potentials. Next, we could generalize the model into a cluster of neurons, similar to an organoid brain model. This mathematical framework offers promising applications in artificial intelligence and advancements in neural networks. Full article

The aim of this work is to present an original, relatively simple, and elegant approach to the analysis of long rectangular plates subjected to uniformly distributed vertical loads acting on various surfaces. Plate analysis is important in many fields, especially where components are either rectangular plates or can be approximated as such. The Transfer Matrix Method is increasingly used in research, as evidenced by the references cited. The advantages of this method lie in the simplicity of its algorithm, the ease of implementation in programming, and its straightforward integration into optimization software. The approach consists of discretizing the rectangular plate by sectioning it with planes parallel to the short sides—i.e., perpendicular to the two long edges. This results in a set of beams, each with a length equal to the width of the plate, a height equal to the plate’s thickness, and a unit width. Each unit beam has support at its ends that replicate the edge conditions of the plate along its long sides. In the study presented, the rectangular plate is embedded along its two long edges, meaning the unit beam is considered embedded at both ends. The Transfer Matrix Method is particularly valuable because it lends itself well to iterative calculations, making it easy to develop software capable of analyzing long rectangular plates quickly. This makes it especially useful for shape optimization applications, which we intend and hope to pursue in future studies. Full article

We consider the macroscopic motion of the normal component of superfluid ³He-A in global thermodynamic equilibrium within the context of the Zubarev statistical operator method. We formulate the corresponding effective theory in the language of the functional integral. The effective Lagrangian comprising macroscopic motion of fermionic excitations is calculated explicitly for the emergent relativistic fermions of the superfluid ³He-A phase immersed in a non-trivial bosonic background due to a space- and time-dependent matrix-valued vierbein featuring nonzero torsion as well as the Nieh–Yan anomaly. We do not consider the dynamics of the superfluid component itself and thereby its backreaction effects due to normal component macroscopic flow. It is treated as an external background within which the emergent relativistic fermions of the normal component move. The matrix-valued vierbein formulation comprises an additional two-dimensional internal spin space for the two axially charged Weyl fermions living at the Fermi points, which may be replaced by one featuring a Dirac fermion doublet with a real-valued vierbein, an axial Abelian gauge field, and a spin connection gauge field mixing the Dirac and internal spin spaces. We carry out this change of description in detail and determine the constraints on the superfluid background as well as the the normal component motion as determined from the Zubarev statistical operator formalism in global thermodynamic equilibrium. As an application of the developed theory, we consider macroscopic rotation around the axis of pure integer mass vortices. The corresponding thermodynamic quantities of the normal component are analyzed. Our formulation incorporates both superfluid background flow and macroscopic motion flow of the normal component and thereby enables an analysis of their interrelation. Full article

Topological insulators (TIs) can be widely applied in the fields of ultrafast optical and spintronic devices owing to the existence of topologically protected gapless Dirac surface states. However, the study of ultrafast dynamics of carriers in TIs remains elusive. In this work, the carrier dynamics of Li-doped Bi_2−xSe₃ single crystals were investigated by femtosecond (fs) transient optical spectroscopy (ΔR/R(t) signals). The temperature dependence for the relaxation rates of the electron–electron interaction and electron–phonon coupling is consistent with the results of electrical transport, which indicates the carrier dynamics of TI is highly related with carrier concentrations. We find that the carrier type and concentration of Bi₂Se₃ can be tuned by Li doping, leading to a metal-insulation transition at low temperatures (T ≤ 55 K), indicating that electron–electron interactions are dominant at low temperature. For T > 55 K, electron–phonon coupling in the bulk carriers becomes the main electric transport mechanism. Full article

We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the set of all stable perturbations of the system, known as the ‘versal unfolding’. This construction yields a comprehensive classification of qualitatively distinct solutions and their metamorphoses into new topological forms, parametrized by the codimension of the bifurcation in each case. We illustrate these ideas through bifurcations in the simplest Friedmann models, the Oppenheimer-Snyder black hole, the evolution of causal geodesic congruences in cosmology and black hole spacetimes, crease flow on event horizons, and the Friedmann–Lemaître equations. Finally, we list open problems and briefly discuss emerging aspects such as partial differential equation stability of versal families, the general relativity landscape, and potential connections between gravitational versal unfoldings and those of the Maxwell, Dirac, and Schrödinger equations. Full article

Accurately controlling the mechanical properties of silicon is essential for developing high-performance micro-devices and systems. In this study, we investigate the influence of phosphorus doping on the elastic constants of silicon across a wide temperature range using a combination of tight-binding simulations and deformation potential theory. The mechanical properties were derived using Keyes’s framework integrated with Fermi–Dirac statistics. The Goodwin–Skinner–Pettifor functional form was applied to estimate dopant-induced stress potentials and their effect on lattice stiffness. In particular, we investigated the change in elastic constants and their temperature dependence under ultra-high doping concentrations. The results show a monotonic decrease in c₁₁ and a non-monotonic increase in c₁₂ with both temperature and doping, while c₄₄ remains relatively unaffected, consistent with experimental and theoretical studies. These changes are attributed to anisotropic carrier redistribution among conduction band valleys and strain-modulated interactions between valleys. The novelty of this work lies in the explicit, atomistically informed calculation of deformation potential constants using tight-binding parameters specific to phosphorus doping in silicon, enabling the accurate prediction of temperature-dependent elastic constants and anisotropic mechanical behaviour in emerging microsystem applications. Full article

The almost complete eradication of fire from grasslands in North America has led to non-linear hysteretic transitions to shrub- and woodlands that the reintroduction of low-intensity fire is unable to reverse. We explore the ability of the extreme ends of variation in fire behavior to help overcome hysteretic threshold behaviors in huisache (Vachellia farnesiana) encroached grasslands. We contrasted experimental fire treatments with unburned control areas to assess the ability of extreme fires burned during drought to alter the density and structure of huisache. We found that extreme fires reduced the density of huisache by over 30% compared to control plots, both through driving huisache mortality and reducing the number of new recruits following treatments. For instance, extreme fire drove 48% huisache mortality compared to 4% in control treatments. For surviving plants, the number of stems increased but the crown area did not significantly change. Prescribed fire, conducted under the right conditions, can drive high mortality in one of the most notorious encroaching species in the southern U.S. Great Plains. With the fire conditions observed in this study likely to increase under future climate projections, utilizing extreme fire as a management tool for huisache will help scale up management to meet the growing extent of woody encroachment into grasslands. Full article

Recent measurements of the band properties of AlN and GaN by fluorescence yield absorption and soft X-ray emission spectroscopies revealed that their valence band (VB) is composed of two separate subbands. The upper VB subband of GaN is composed of gallium sp and nitrogen p orbitals; the lower subband consists of metal d and nitrogen s orbitals. These findings were confirmed by extensive ab initio simulations. These results are not consistent with the standard tetrahedrally coordinated semiconductors, which are bonded by sp³-hybridized orbitals of metal and nonmetal atoms. The new analysis techniques and ab initio simulations create a new picture, allowing the calculation of overlap integrals to determine the bond order in these crystals. According to these results, bonding occurs between resonant p-states of nitrogen and sp³-hybridized metal orbitals in tetrahedral nitrides, allowing tetrahedral symmetry to be maintained. A similar resonant bonding mechanism is observed in hexagonal BN, where the p orbitals of nitrogen create three resonant states necessary for maintaining the planar symmetry of the lattice. In addition, nonresonant $\pi$-type bonds in BN are created by the overlap of $p_z$ orbitals of boron and nitrogen. BN bonding differs from that in graphene, where carbon states are fully sp²-hybridized. Additionally, $\pi$-type bonds in graphene have no ionic contributions, which leads to the formation of Dirac states with linear dispersion close to the K point, closing the band gap. Full article

We present high-precision multi-configuration Dirac–Hartree–Fock (MCDHF) calculations for the metastable states of ${\mathrm{Pr}}^{9+}$ and ${\mathrm{Nd}}^{10+}$ ions, systematically investigating their energy levels, transition properties, Landé $g_J$ factors, and hyperfine interaction constants. Our results show excellent agreement with available experimental data and theoretical benchmarks, while resolving critical configuration assignment discrepancies through detailed angular momentum coupling analysis. The calculations highlight the significant role of Breit interaction and provide the first theoretical predictions of electric quadrupole hyperfine constants ($B_{\mathrm{hfs}}$). These findings deliver essential atomic data for the development of next-generation optical clocks and establish lanthanide highly charged ions as exceptional candidates for precision tests of fundamental physics. Full article