Search Results (140)

The article presents a mathematical description of the thermal phenomena occurring both inside and on the surfaces of a homogeneous plate subjected to an external heat flux on one side. Analytical formulae for thermal excitation, with a given duration and constant power, are derived, enabling the determination of temperature increases on both the heated and unheated surfaces of the plate under specific heat transfer conditions to the surroundings. Convective heat transfer, with individual heat transfer coefficients on both sides of the slab, is considered; however, radiative heat loss can also be included. The solution of the problem obtained using two methods is presented: the method of separation of variables (MSV) and the Laplace transform (LT). The advantages and disadvantages of both analytical formulae, as well as the impact of various factors on the accuracy of the solution, are discussed. Among others, the MSV solution works well for a sufficiently long time, whereas the LT solution is better for a sufficiently short time. The theoretical considerations are illustrated with diagrams for several configurations, each representing various heat transfer conditions on both sides of the plate. The presented solution can serve as a starting point for further analysis of more complex geometries or multilayered structures, e.g., in non-destructive testing using active thermography. The developed theoretical model is verified for a determination of the thermal diffusivity of a reference material. The model can be useful for analyzing the method’s sensitivity to various factors occurring during the measurement process, or the method can be adapted to a pulse of known duration and constant power, which is much easier to implement technically than a very short impulse (Dirac) with high energy. Full article

Ru₃Sn₇ crystallizes in the cubic Ir₃Ge₇-type structure (space group Im3m), a class of intermetallic compounds. Previous studies focused primarily on its crystal structure, band calculations, and basic transport properties. Here, we report a systematic investigation of high-quality single crystals via electrical resistivity, Hall effect, specific heat, and thermal transport measurements. The T₃X₇ intermetallic family—with its diverse electronic ground states—provides an ideal platform for exploring such topology–property relationships. Ru₃Sn₇ exhibits metallic behavior, with consistent Hall effect and Seebeck coefficient data indicating a compensated electron-hole two-band system. Temperature-dependent modulation of electronic states near the Fermi surface alters charge carrier transport, which may imply the presence of a Lifshitz transition in Ru₃Sn₇. More importantly, magnetic quantum oscillations are observed for the first time, confirming the presence of two Dirac points in its band structure. 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

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

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

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

In this paper, we propose a recurrent neural network numerical method with the finite element method for partial differential equations to study the band gap structure and Dirac points in two-dimensional photonic crystals. Electromagnetic wave propagation is governed by Maxwell’s equations. We transform the partial differential equations into large-scale generalized eigenvalue problems by spatially discretising them using the finite element method. Compared with traditional numerical computation methods, neural networks can perform high-speed parallel computation. Existing neural network-based eigenvalue solvers are typically restricted to computing extremal eigenvalues of real symmetric matrix pairs. To overcome this limitation, we develop a novel RNN-based numerical scheme tailored for solving the band structure problem in photonic crystals. We validate our method by computing the dispersion relations of photonic crystals with periodic dielectric columns, achieving excellent agreement with the plane-wave expansion method. In addition, we calculate the Dirac points at the center of the Brillouin zone, which is crucial for understanding the unique optical properties of photonic crystals. We determine the precise filling ratios at which these Dirac points appear, thus providing insight into the relationship between geometrical and material parameters and the appearance of Dirac points. Full article

The peculiar electronic properties of graphene, including the universal dc conductivity and the pseudodiffusive shot noise, are usually found in a small vicinity close to the charge neutrality point, away from which the electron’s effective mass raises, and nanostructures in graphene start to behave similarly to familiar Sharvin contacts in semiconducting heterostructures. Recently, it was pointed out that as long as abrupt potential steps separate the sample area from the leads, some graphene-specific features can be identified relatively far from the charge neutrality point. These features include greater conductance reduction and shot noise enhancement compared to the standard Sharvin values. The purpose of this paper is twofold: First, we extend the previous analysis based on the effective Dirac equation, and derive the formulas that allow the calculation of the arbitrary charge transfer cumulant for doped graphene. Second, the results of the analytic considerations are compared with numerical simulations of quantum transport on the honeycomb lattice for selected nanosystems for which considerations starting from the Dirac equation cannot be directly adapted. For a wedge-shaped constriction with zigzag edges, the transport characteristics can be tuned from graphene-specific (sub-Sharvin) values to standard Sharvin values by varying the electrostatic potential profile in the narrowest section. A similar scenario is followed by the half-Corbino disk. In contrast, a circular quantum dot with two narrow openings showing a mixed behavior appears: the conductance is close to the Sharvin value, while the Fano factor approaches the value characterizing the symmetric chaotic cavity. Carving a hole in the quantum dot to eliminate direct trajectories between the openings reduces the conductance to sub-Sharvin value, but the Fano factor is unaffected. Our results suggest that experimental attempts to verify the predictions for the sub-Sharvin transport regime should focus on systems with relatively wide openings, where the scattering at the sample edges is insignificant next to the scattering at the sample–lead interfaces. Full article

In recent years, field-effect transistors (FETs) based on graphene have attracted significant interest due to their unique electrical properties and their potential for biosensing and molecular detection applications. This study uses FETs with a nanocrystalline graphite (NCG) channel to detect DNA nucleobases. The exceptional electronic properties of NCG, and its high surface area, enable strong π–π stacking interactions with DNA nucleobases, promoting efficient adsorption and stabilization of the biomolecules. The direct attachment of nucleobases to the NCG channel leads to substantial changes in the device’s electrical characteristics, which can be measured in real time to assess DNA binding and sequence recognition. This method enables highly sensitive, label-free DNA detection, opening up new possibilities for rapid genetic analysis and diagnostics. Understanding the interactions between DNA nucleobases and graphene-based materials is crucial for advancing genetic research and biotechnology, paving the way for more accurate and efficient diagnostic tools. Full article

Colloidal quantum dots (QDs) and graphene hybrids have emerged as promising platforms for optoelectronic and biosensing applications due to their unique photophysical and electronic properties. This study investigates the fundamental mechanism underlying the photoluminescence (PL) quenching and recovery in graphene–QD hybrid systems using single-layer graphene field-effect transistors (SLG-FETs) and time-resolved photoluminescence (TRPL) spectroscopy. We demonstrate that PL quenching and its recovery are primarily driven by charge transfer, as evidenced by an unchanged fluorescence lifetime upon quenching. Density functional theory calculations reveal a significant charge redistribution at the graphene–QD interface, corroborating experimental observations. We also provide a simple analytical quantum mechanical model to differentiate charge transfer-induced PL quenching from resonance energy transfer. Furthermore, we leverage the charge transfer mechanism for ultrasensitive biosensing to detect biomarkers such as immunoglobulin G (IgG) at femtomolar concentrations. The sensor’s electrical response, characterized by systematic shifts in the Dirac point of SLG-FETs, confirms the role of analyte-induced charge modulation in PL recovery. Our findings provide a fundamental framework for designing next-generation graphene-based biosensors with exceptional sensitivity and specificity. Full article

Layered perovskites have been actively studied due to their outstanding electronic and optical properties as well as kinetic stability. Layered perovskites with hexagonal symmetry have special electronic properties, such as the Dirac cone in the band structure, similar to graphene. In the presented study, the heterostructure of single-layer all-inorganic lead-free hexagonal perovskite of the A₃B₂X₉ type (A = Cs, Rb, K; B = In, Sb; X = Cl, Br) and graphene (Gr) was studied. The structural and electronic characteristics of A₃B₂X₉ and the A₃B₂X₉/Gr composite were calculated using density functional theory. It was found that graphene is not deformed, while the main deformation is observed only in perovskite. B-X bonds have different sensitivities to stretching or compression. The Fermi level of the A₃In₂X₉/Gr composite can be shifted down from the Dirac point, which can be used to create optoelectronic devices or as spacer layers for graphene-based resonant tunneling nanostructures. Full article

This paper studies the boundedness and convergence properties of the sequences generated by strict and weak contractions in metric spaces, as well as their fixed points, in the event that finite jumps can take place from the left to the right limits of the successive values of the generated sequences. An application is devoted to the stabilization and the asymptotic stabilization of impulsive linear time-varying dynamic systems of the n-th order. The impulses are formalized based on the theory of Dirac distributions. Several results are stated and proved, namely, (a) for the case when the time derivative of the differential system is impulsive at isolated time instants; (b) for the case when the matrix function of dynamics is almost everywhere differentiable with impulsive effects at isolated time instants; and (c) for the case of combinations of the two above effects, which can either jointly take place at the same time instants or at distinct time instants. In the first case, finite discontinuities of the first order in the solution are generated; that is, equivalently, finite jumps take place between the corresponding left and right limits of the solution at the impulsive time instants. The second case generates, equivalently, finite jumps in the first derivative of the solution with respect to time from their left to their right limits at the corresponding impulsive time instants. Finally, the third case exhibits both of the above effects in a combined way. Full article

An electric field applied to the Bernal-stacked bilayer graphene opens an energy gap; its reversal in some regions creates domain walls and leads to the appearance of one-dimensional chiral gapless states localized at the walls. Here, we investigate the energy structure of bilayer graphene with superlattice potential defined by an external electric field. The calculations are performed within an atomistic π-electron tight-binding approximation. We study one-dimensional and two-dimensional superlattices formed by arrays of electric-field walls in the zigzag and armchair directions and investigate different field polarizations. Chiral gapless states discretize due to the superlattice potential and transform into minibands in the energy gap. As the main result, we show that the minibands can cross at the Fermi level for some field polarizations. This leads to a new kind of two-dimensional gapless states of topological character that form Dirac-like cones at the crossing points. This also has application potential: changing the field polarization can close the energy gap and change the character of the superlattice from semiconducting to metallic. Full article

Polycyclic aromatic hydrocarbons (PAHs) are one of the most toxic environmental pollutants, which are very harmful to the human body. It is crucial to find convenient and effective detection methods of PAHs for preventing and controlling environmental pollution. Low-dimensional material-based field effect transistor (FET) sensors exhibit the advantages of a small size, simple structure, fast response, and high sensitivity. In this work, graphene (Gr) has been selected as the channel material for FET sensors for PAH detections. Through π-π electron stacking interactions, PAHs could be spontaneously adsorbed on the surface of the Gr and affect its electronic carrier transport behavior. Based on the relationship between the concentrations and the changes in the Dirac point of the Gr, the sensor achieved an effective response to PAHs in a broad range from 10⁻¹⁰ to 10⁻⁶ mol/L and a limit of detection of 10⁻¹⁰ mol/L was obtained, which was lower than that provided by the World Health Organization (3.46 × 10⁻⁹ mol/L), in drinking water. The results demonstrate a great application of the FET sensors in environmental analysis, and provide an important way for rapid and in situ monitoring of PAHs. Full article

Nitrogen-based fertilizers are crucial in agriculture for maintaining soil health and increasing crop yields. Soil microorganisms transform nitrogen from fertilizers into ${\mathrm{N}\mathrm{O}}_3^{-}$–N, which is absorbed by crops. However, some nitrogen is converted to nitrous oxide (N₂O), a greenhouse gas with a warming potential about 300-times greater than carbon dioxide (CO₂). Agricultural activities are the main source of N₂O emissions. Monitoring N₂O can enhance soil health and optimize nitrogen fertilizer use, thereby supporting precision agriculture. To achieve this, we developed ionic liquid-gated graphene field-effect transistor (FET) sensors to measure N₂O concentrations in agricultural soil. We first fabricated and tested the electrical characteristics of the sensors. Then, we analyzed their transfer characteristics in our developed N₂O evaluation system using different concentrations of N₂O and air. The sensors demonstrated a negative shift in transfer characteristic curves when exposed to N₂O, with a Dirac point voltage difference of 0.02 V between 1 and 10 ppm N₂O diluted with pure air. These results demonstrate that the ionic liquid-gated graphene FET sensor is a promising device for N₂O detection for agricultural soil applications. Full article