This paper presents a mathematical and computational framework for a coupled fractional dual-phase-lag (FDPL) bioheat model describing nanoparticle-enhanced photothermal processes with thermally activated drug transport. The governing system consists of nonlinear fractional partial differential equations incorporating Caputo time derivatives to capture thermal memory effects and finite-speed heat propagation. The model integrates optical absorption, nanoparticle transport, temperature-dependent drug release, and Arrhenius-type thermal damage within a unified formulation. To efficiently solve the resulting system, a dual reciprocity boundary element method (DRBEM) is developed, transforming the governing equations into a sequence of boundary-only integral problems. Fractional temporal terms are discretized using the L1 scheme, while nonlinear coupling is treated via an iterative procedure. The proposed method significantly reduces computational complexity by avoiding volumetric discretization while preserving accuracy. The numerical scheme is validated against analytical fractional benchmarks and systematic convergence studies, demonstrating first-order temporal and second-order spatial accuracy. Additional simulations illustrate the influence of fractional order, nanoparticle concentration, and perfusion on temperature evolution and damage formation. The results confirm that the proposed framework provides an accurate and efficient approach for solving nonlinear fractional PDE systems arising in coupled heat transfer and transport phenomena.

In this work, we investigate essential definitions, defining G as a simple graph with vertices in Zn and subgraphs Γu and Γq as unit residue and quadratic residue graphs modulo n, respectively. The investigation extends to the degree of G, Γu, and Γq, illuminating the properties of these subgraphs in the context of quadratic congruences.

In this study, we investigate the impact of the XYZ-DM-Heisenberg model on quantum resources, including local quantum Fisher information, concurrence, and Jensen-Shannon coherence, in the presence of intrinsic decoherence. By exploring various spin-exchange interactions, with a focus on the role of the y-DM interaction, we reveal how these interactions affect quantum correlations and coherence dynamics. We find that the system transitions from separability to the generation of quantum properties when spin interactions are introduced. The specific parameter choices significantly influence the dynamic map of quantum functions. Notably, strong y-DM interaction, in combination with equal spin interaction, leads to pronounced fluctuations, while weak DM interaction results in sudden death and rebirth in the x direction. Additionally, ferro- and anti-ferromagnetic regimes impact the quantum functions differently. In the presence of intrinsic decoherence, fluctuations decrease, and coherence remains robust compared to the local quantum Fisher information and entanglement, reducing loss.

Studying the ability of atom-photon interactions, especially in two two-level atomic systems, to generate quantum information resources has recently become an important research topic in quantum information science. Therefore, this paper explores the ability of two moving atoms coupling with a coherent field through a two-photon transition to generate atomic quantum correlations by using local quantum uncertainty (LQU), local quantum Fisher information (LQFI) as well as logarithmic negativity (LN). Schrödinger equation is used to obtain the time evolution of the atom-cavity-atom interactions with an initial coherent cavity state and an initial atomic uncorrelated pure state. The generation of atomic LQU, LQFI, and LN correlations are exactly examined under the unitary interaction parameter effects, including the atom-cavity coupling strengths, the cavity field half-wave number, and the initial coherent state intensity. The atom-cavity-atom interaction parameters lead to notable changes in the amplitudes, speed, and regularity of the LQU, LQFI, and LN dynamics, which can be enhanced by increasing the initial coherent intensity. The cavity field half-wave number leads to generating atomic quantum correlations with regular oscillatory behavior. The sudden death-birth phenomenon of the logarithmic negativity depends on the atom-cavity-atom interaction and the atomic location parameter.

The q-rung orthopair fuzzy atmosphere is an innovative approach for handling unclear circumstances in a range of decision making problems. As compare to intuitionistic fuzzy sets, this one is more appropriate and adaptable because it evaluates the significance of ring theory while retaining the features of q-rung orthopair fuzzy sets. In this study, we characterize $ q $-rung orthopair fuzzy subring as a modification of the pythagorean fuzzy subring. We introduce the novel idea of $ q $-rung orthopair fuzzy subring and investigate the algebraic characteristics for the $ q $-rung orthopair fuzzy subrings. Furthermore, we establish the concept of $ q $-rung orthopair fuzzy quotient ring and $ q $-rung orthopair fuzzy left and right ideals. Also, we describe the $ q $-rung orthopair fuzzy level subring and associate axioms. Finally, we investigate how ring homomorphism influences the q-rung orthopair fuzzy subring and investigate there pre-images homomorphism on $ q $-ROFSR and different aspects of images.

The work considers a qubit interacting off-resonantly a nonlinear Kerr-like quantum-harmonic-oscillator cavity field through nonlinear intensity-dependent and one-photon interactions. The analytical solution for the master equation is obtained when the qubit starts with an excited pure state while the harmonic-oscillator field starts with a coherent state. The dynamics of the phase space Husimi-distribution and its Wehrl-Husimi entropy entanglement/mixedness is explored under the effects of the atom-field detuning, Kerr-like nonlinearity as well as atomic spontaneous-emission dissipation. For resonant case, the Wehrl-Husimi entropy qubit-oscillator entanglement and atomic mixedness are generated (due to the unitary nonlinear intensity-dependent evolution) with a regular oscillatory behavior. For off-resonant case, the quantum coherence is generated partially with a high-frequency irregular oscillatory behavior. The Kerr-like nonlinearity and the atomic spontaneous dissipation lead to enhancing the generated atomic mixedness Wehrl-Husimi entropy enhances and stabilizing the atomic state in a maximally mixed state. The phase space Husimi-distribution information dynamics of the corresponding the generated atomic mixed states confirms the vital link between the formed interference Husimi-distributions and the generated atomic Wehrl-Husimi entropy mixedness. It is found that the dynamics of the Husimi-distribution information and its Wehrl-Husimi entropy is highly sensitive to the qubit-cavity detuning, Kerr-like nonlinearity as well as the dissipation.

The thermoelectric properties of parallel arrays of organic molecules on a surface offer the potential for large-area, flexible, solution processed, energy harvesting thin-films, whose room-temperature transport properties are controlled by quantum interference (QI). Recently, it has been demonstrated that constructive QI (CQI) can be translated from single molecules to self-assembled monolayers (SAMs), boosting both electrical conductivities and Seebeck coefficients. However, these CQI-enhanced systems are limited by rigid coupling of the component molecules to metallic electrodes, preventing the introduction of additional layers which would be advantageous for their further development. These rigid couplings also limit our ability to suppress the transport of phonons through these systems, which could act to boost their thermoelectric output, without comprising on their impressive electronic features. Here, through a combined experimental and theoretical study, we show that cross-plane thermoelectricity in SAMs can be enhanced by incorporating extra molecular layers. We utilize a bottom-up approach to assemble multi-component thin-films that combine a rigid, highly conductive 'sticky'-linker, formed from alkynyl-functionalised anthracenes, and a 'slippery'-linker consisting of a functionalized metalloporphyrin. Starting from an anthracene-based SAM, we demonstrate that subsequent addition of either a porphyrin layer or a graphene layer increases the Seebeck coefficient, and addition of both porphyrin and graphene leads to a further boost in their Seebeck coefficients. This demonstration of Seebeck-enhanced multi-component SAMs is the first of its kind and presents a new strategy towards the design of thin-film thermoelectric materials.

Correction for ‘Molecular-scale thermoelectricity: as simple as ‘ABC’’ by Ali Ismael et al., Nanoscale Adv., 2020, 2, 5329–5334, DOI: 10.1039/D0NA00772B.

A major potential advantage of creating thermoelectric devices using self-assembled molecular layers is their mechanical flexibility. Previous reports have discussed the advantage of this flexibility from the perspective of facile skin attachment and the ability to avoid mechanical deformation. In this work, we demonstrate that the thermoelectric properties of such molecular devices can be controlled by taking advantage of their mechanical flexibility. The thermoelectric properties of self-assembled monolayers (SAMs) fabricated from thiol terminated molecules were measured with a modified AFM system, and the conformation of the SAMs was controlled by regulating the loading force between the organic thin film and the probe, which changes the tilt angle at the metal-molecule interface. We tracked the thermopower shift vs. the tilt angle of the SAM and showed that changes in both the electrical conductivity and Seebeck coefficient combine to optimize the power factor at a specific angle. This optimization of thermoelectric performance via applied pressure is confirmed through the use of theoretical calculations and is expected to be a general method for optimising the power factor of SAMs.

The authors regret that the name of one of the authors (Troy L. R. Bennett) was shown incorrectly in the original article. The corrected author list is as shown above. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

If the Seebeck coefficient of single molecules or self-assembled monolayers (SAMs) could be predicted from measurements of their conductance-voltage (G-V) characteristics alone, then the experimentally more difficult task of creating a set-up to measure their thermoelectric properties could be avoided. This article highlights a novel strategy for predicting an upper bound to the Seebeck coefficient of single molecules or SAMs, from measurements of their G-V characteristics. The theory begins by making a fit to measured G-V curves using three fitting parameters, denoted a, b, c. This 'ABC' theory then predicts a maximum value for the magnitude of the corresponding Seebeck coefficient. This is a useful material parameter, because if the predicted upper bound is large, then the material would warrant further investigation using a full Seebeck-measurement setup. On the other hand, if the upper bound is small, then the material would not be promising and this much more technically demanding set of measurements would be avoided. Histograms of predicted Seebeck coefficients are compared with histograms of measured Seebeck coefficients for six different SAMs, formed from anthracene-based molecules with different anchor groups and are shown to be in excellent agreement.