When two different groups of cells are placed next to each other, they compete with each other to get enough space to increase volume, and nutrients according to the kind and growth conditions. In order to further discuss the competition of normal and cancer cells in the human body, a modified Lotka-Volterra competition model is introduced to develop a symbiosis analysis model of cell groups. Lotka-Volterra equation is one of the mathematical models that is used to study the competition of these cell groups and has been applied to determine the dominant and recessive cell groups. In this work, we have modified this equation to obtain better results of cancer cells competition. Our obtained results show that by using the modified equation, the number of destroyed cells during the competition is also considered.

In the present work, we have investigated the interstitial fluid pressure within a spherical solid tumor under a tilted external magnetic field. A proper form of the fluid flow equations, mass, and momentum conservation laws has been used in addition to the sufficient boundary conditions. The interstitial fluid pressure is analytically calculated and the effect of various parameters on the behavior of the tumor is studied. The obtained results have been compared with the experimental data. Our calculations show that in a homogeneous tumor with no necrotic core, drug particles are distributed non-uniformly. This behavior occurred due to the interstitial pressure distribution. Also, we considered the critical tumor radius and critical necrotic radius and analyzed the pressure distribution for various parameters of necrotic radii. We showed that tumor radius has a critical size, and the drug particles transport to the tumors with a radius smaller than this critical size. Also, the magnetic field has a significant effect on this drug delivery. Thus, there is a critical necrotic radius in drug delivery, and therapeutic influences have occurred. We have studied the effect of the external magnetic field on the values of the critical necrotic radius. Our results are applicable to injecting anticancer drug agents into the human body.

In the research, the effects of the Rashba spin–orbit interaction (SOI) and magnetic field have been studied on the electronic and optical properties of a Frost–Musulin (FM) quantum dot. For this goal, the Schrödinger equation has been analytically solved by the Nikiforov–Uvarov (NU) procedure, and the energy states and the wave functions have been analytically derived. Using the analytical relations for optical properties, the total refractive index change (RIC) and absorption coefficient (AC) are calculated under a magnetic field with the Rashba SOI. The findings show that both the Rashba SOI and the magnetic field have a strong effect on the energy levels, RIC, and AC. The Rashba SOI causes the energy states to split into two branches, up and down. The peak locations of the RIC and AC move to higher energies when the magnetic field and Rashba coupling are increased.

In the research, a quantum dot (QD) under an external magnetic field is theoretically investigated. The confining potential applied to the charge carriers is chosen as the Frost-Musulin (FM) potential model. First, the energy eigenvalues and eigenstates have been analytically obtained by Nikiforov-Uvarov (NU) procedure. Then, an electric field is imposed on the system. The Stark shift effect (SSE) has been calculated and an analytical relation has been obtained in terms of the Jacobi polynomials. The findings show that the shift of electron energy states at large, and small electric fields are different. The shift is small at weak electric fields. The electron energy states decrease with the increment of the electric field. The electron states are increased by enhancing the system size. In summary, the SSE can be tuned by setting the electric field, the potential height, and the size of QD.

In this paper, a quantum heat engine (QHE) and a quantum refrigerator (QR) are theoretically studied using a quantum Stirling cycle (SC). The machine works with a working substance consisting of a two-qubit Heisenberg XYZ model under both homogeneous and inhomogeneous magnetic fields, and the Dzyaloshinskii-Moriya interaction (DMI). The influences of both magnetic fields are studied on the absorbed, and released heat, work done, efficiency, and performance coefficient (PC) of the Stirling engine and refrigerator. The findings show that the SC can operate as a QHE or QR. It depends on the proper selection of the system parameters. We can obtain a QHE or a QR with acceptable efficiency or performance coefficient. To this end, we increase both magnetic fields and choose suitable values for other system parameters thereby obtaining higher values for the PC. Also, we reduce both magnetic fields and obtain higher values for the efficiency of QHE. Considering homogeneous and inhomogeneous magnetic fields have different effects on machine efficiency, and refrigerator performance.

In the paper, the electronic properties of a quantum dot (QD) using the Frost–Musulin potential model are investigated taking into account both an external magnetic field and electron–electron interaction. For this purpose, the Schrödinger equation (SE) is analytically solved without considering electron–electron interaction by employing the Nikiforov–Uvarov (NU) procedure, and the energy levels and wave functions are determined. Then, the singlet–triplet (ST) transition is studied for different values of magnetic fields. According to our results, Both the dot size and magnetic field have key roles in the ground state transition. The ST transition of the ground state moves to lower magnetic fields as the QD size is increased. However the transition occurs at higher magnetic fields when the potential depth is increased. The transition for small QD size occurs only from 1S to 3P. But by increasing the QD size, another transition is also observed from 1D to 3F. These transitions occur at smaller magnetic fields when the QD size is increased.

In the paper, the thermodynamic properties (TPs) of lithium hydride (LiH) have been investigated using Manning-Rosen plus Hellmann potential within the statistical mechanics’ background. To this end, the Schrödinger equation (SE) has been analytically solved using the Nikiforov-Uvarov (NU) procedure, and the energy levels have been determined. Then, the partition function of the system and its thermodynamic properties such as the Gibbs free energy, enthalpy, and specific heat at constant pressure have been analytically determined by the Poisson summation formula. The average absolute deviations of the results from the empirical data are 1.981%, 1.623%, and 1.725% for specific heat, Gibbs free energy, and enthalpy, respectively. It is found that the potential model can be used to predict the TPs of the LiH molecule.

A plasmonic nanosensor is proposed and investigated its sensitivity using the optical properties of plasmonic nanoparticles. To this end, we first consider the nanosensor consisting of bowtie nanoparticles. Then, the nanosensor performance is examined under different factors such as the refractive index of the background environment, the height, and length of the nanoparticles. The proposed bowtie nanoparticles, in this work, are made of gold. The boundary element method is used to simulate the nanosensor. The extinction cross-section is computed in terms of wavelength and the effect of various factors on the resonance wavelength of localized surface plasmon is investigated. It is shown that the nanosensor investigated in this research has a high sensitivity to the changes in the refractive index of the studied sample. The sensitivity of the nanosensor is obtained as 650[Formula: see text]nm/RIIU. In addition, the required spectral range can be arbitrarily adjusted by the type of nanoparticles.

The magnetic properties of monolayers of hexagonal and tetragonal CrP have been studied using density functional calculations. Cohesive energy, phonon spectra, and Crystal Orbital Hamilton Population analysis were performed on both the magnetic and non-magnetic phases of h-CrP and t-CrP to determine the more stable phases. The results indicate that the ferromagnetic phase is unstable in h-CrP, but stable in t-CrP. The impact of strain on the electronic structure and magnetic properties of t-CrP was also studied. The findings suggest that this single-layer compound is a semi-metal with an indirect energy gap in the spin-down channel. Tensile strain slightly enhances the magnetic moment of the Cr atoms, while compressive strain reduces it. The compounds exhibit a consistent behavior with a total magnetic moment of μ _tot=6μ _B/cell across the range of applied strain.

It is well known that the lithium diatomic molecule has important potential application in engineering, and industry. For this purpose, in this research, the thermal properties of the lithium diatomic molecule are theoretically calculated taking into account both an external magnetic field and Aharonov-Bohm (AB) flux. To this end, the interaction in the diatomic molecule is proposed as an improved Scarf ΙΙ potential model (ISPM). The Schrödinger equation is solved using an appropriate Pekeris-like approximation form for the centrifugal barrier and the energy spectrum and wave functions are obtained. Then, the partition function is obtained to study the thermal properties of the lithium dimer. The calculated thermal properties of 7Li2 (2 3Πg) in this work are mean energy, entropy, specific heat, enthalpy, and Gibbs free energy. Our theoretical results are also compared with the experimental data. The findings show that the obtained results are in good agreement with experimental data. Without considering the magnetic field and AB flux, the deviation of specific heat, Gibbs free energy, and enthalpy are 3.73%, 4.96%, and 5.31%, respectively. By considering the magnetic field and AB flux, we find that the deviation of the aforementioned properties are 1.91%, 2.04%, and 2.32%, respectively. Therefore, it is found that the external magnetic field and AB flux have great influences on the thermal properties of lithium.

In this work, the phase transition from normal to superconductivity state of two metal clusters, vanadium and aluminum particles, are theoretically studied by changing size and resistance parameter. We obtained the heat capacity integral of Grossman's theory considering that the first zero of the partition functions is located in the complex temperature plane. Then, we used the experimental data of the heat capacity of aluminum metal clusters and vanadium particles to determine the unknown integral coefficients of the heat capacity of Grossman's theory. Based on the obtained coefficients, we discussed the classification of the phase transition of the aforementioned metal clusters. Also, the obtained coefficients have been used to plot the heat capacity of aluminum metal clusters and vanadium particles. Finally, we compared the obtained heat capacity with the experimental results. A good agreement between our results and the experimental data has been obtained.

Experimentally and numerically, measurements have been presented for new type of magnetic field sensor based on combining multimode optical fiber and magnetic ferrofluid. The ferrofluid was filled in a capillary tube around a 15 mm uncladded region of optical fiber. Three uncladded geometries cylindrical, D-shaped and 2D-shaped, have been investigated to study the effect of geometry on sensing performance. Results illustrate that the geometry of the optical fiber has a significant impact on the evanescent waves which propagate from the sensing region into the ferrofluid tube. The obtained results expressed that among all studied cases, the D-shaped configuration has the best performance designing an optical fiber-based magnetic field sensor, since the best measured sensor features such as linearity, sensitivity, response time and recovery time for this case are R2 = 0.9865, 0.01795 μW/mT, 3.15 s and 0.26 s, respectively.

The current study looks at how the Kratzer confinement potential affects the linear, third-order nonlinear, and total optical absorption coefficients (ACs) of a single electron in a multilayered spherical quantum dot (MSQD) by using the finite element method within the effective mass approximation. The variation of the transition energy has been investigated for two allowed transitions, 1p-2s and 2s-2p. Furthermore, we investigated the variation of the linear, third-order nonlinear, and total optical absorption coefficients as a function of the incident photon energy for several transitions while accounting for the effect of the Kratzer confinement potential. The findings show that the optical ACs and transition energy are strongly influenced by the Kratzer confinement potential.

Due to the increasing importance of nanosensors in the early diagnosis of diseases, the need for high-performance nanosensors is one of the goals of researchers. In this paper, a structure consisting of plasmonic nanoshells with spherical and ellipsoidal geometry has been proposed to calculate the refractive index (RI) changes in the range of 1–3. The sensitivity of the proposed nanosensor has been computed, and the effective factors on the performance of the nanosensor, including geometry, material, core dimensions, shell thickness, and RI of the surrounding environment are studied. To this end, various nanostructures have been modeled using the boundary element method. It has been shown that ellipsoidal nanoshells are more sensitive to RI changes than spherical nanoshells. Also, the results show that nanoshells with a core and shell made of plasmonic metals (bimetallic nanoshell) can exponentially increase the sensitivity of the nanosensor.

To design nanosensors based on localised surface plasmon (LSP), a structure is considered consisting of metal nanoparticles and study the influence of nanoparticles size, material, geometry, and background refractive index (RI) on its performance. We propose a nanosensor based on nanoplasmonic and investigate its sensitivity. The boundary element method is employed to calculate the extinction cross-section and sensitivity of the proposed sensor. We study the effect of various parameters on LSP resonance. Our calculations about extinction, scattering, and absorption spectra have been compared with experimental data. According to the comparison, it is deduced the boundary element method provides acceptable results. It is shown that the proposed nanosensor is very sensitive to the variation of sample RI. Moreover, it is possible to adjust the required spectral range by changing the geometry and material of nanoparticles. Here, the highest sensitivity is obtained for cubic nanoparticles made of silver.

A proposed nanosensor based on hybrid nanoshells consisting of a core of metal nanoparticles and a coating of molecules is simulated by plasmon-exciton coupling in semi classical approach. We study the interaction of electromagnetic radiation with multilevel atoms in a way that takes into account both the spatial and the temporal dependence of the local fields. Our approach has a wide range of applications, from the description of pulse propagation in two-level media to the elaborate simulation of optoelectronic devices, including sensors. We have numerically solved the corresponding system of coupled Maxwell-Liouville equations using finite difference time domain (FDTD) method for different geometries. Plasmon-exciton hybrid nanoshells with different geometries are designed and simulated, which shows more sensitive to environment refractive index (RI) than nanosensor based on localized surface plasmon. The effects of nanoshell geometries, sizes, and quantum emitter parameters on the sensitivity of nanosensors to changes in the RI of the environment were investigated. It was found that the cone-like nanoshell with a silver core and quantum emitter shell had the highest sensitivity. The tapered shape of the cone like nanoshell leads to a higher density of plasmonic excitations at the tapered end of the nanoshell. Under specific conditions, two sharp, deep LSPR peaks were evident in the scattering data. These distinguishing features are valuable as signatures in nanosensors requiring fast, noninvasive response.

The influence of attractive term of interaction potential on heat capacities (𝐶𝑝, 𝐶𝑣) and sound speed of real gases Ar, Kr and Xe is investigated. Two different potential models were introduced and the second virial coefficient of the potentials was analytically determined. The introduced potentials include different attractive terms. By using the two potential models, we have determined heat capacities at constant pressure and volume and speed of sound of aforementioned gases. Our obtained data have been compared with available results. The obtained data show that the potential attractive term has a key role in determining the thermodynamic functions of the gases. It is revealed that the obtained heat capacities by using both potentials are in good agreement with experimental data. But, the obtained results by potential model (1) have more agreements with experimental data. The speed of sound of Ar determined by model (1) at high pressure and temperatures are in good agreement with available data. The sound speed of Kr computed by the model (2) at high temperatures and low pressure has good agreement with experimental data. Finally, sound velocity of Xe determined by the model (2) at high temperatures and pressures gives more agreement in comparison with available data.

In this work, a quantum Stirling machine as a heat engine or a refrigerator is investigated. The working substance of the machine is considered a two-qubit Heisenberg XYZ model under a magnetic field and the Dzyaloshinskii–Moriya interaction (DMI). We investigate the effects of magnetic field and the temperature of hot and cold baths on the absorbed heat, released heat, work done, efficiency, and performance coefficient of the Stirling heat engine and the Stirling refrigerator. It is deduced that with proper selection of the system parameters, the Stirling cycle can be operated as a heat engine or refrigerator with sufficient efficiency and performance coefficient. With rising the temperature of the hot bath and choosing proper values for other system parameters, the performance coefficient reaches the Carnot refrigerator. The heat engine efficiency can be increased by reducing the magnetic field.

In the article, a quantum Stirling machine is proposed and its behavior as a quantum heat engine (QHE) or a refrigerator is investigated. The working substance of the machine is considered as a 2D and 3D spin chain model under a magnetic field and the Dzyaloshinskii-Moriya interaction (DMI). The effects of a magnetic field, the temperature of a cold bath, DMI, and the system dimension have been studied on the efficiency and performance coefficient of the Stirling heat engine and the Stirling refrigerator. It is deduced that with proper selection of the system parameters, and system dimension the Stirling cycle can be operated as a QHE or quantum refrigerator with sufficient efficiency, and performance coefficient. By decreasing the temperature of the cold bath and considering a 3D model without DMI, the system works as a QHE with a maximum efficiency of 33%. Also, by considering a 2D model with DMI and rising the magnetic field, the system works as a quantum refrigerator with a maximum performance coefficient approximately of 7.1. Therefore, we can say that the maximum efficiency or performance coefficient can be obtained by the appropriate selection of system parameters and dimensions.

To investigate nanosensors based on localized surface plasmon, a structure consisting of a conical nanoshell has been considered and the factors affecting its performance has been studied. The factors are the refractive index of the background environment, dimensions, and the nanoshell material. A nanosensor consisting of an Au@Cu 2− x S nanoshell with a Cu 2− x S semiconductor shell and a gold core has been proposed and its sensitivity has been investigated. The sensitivity of this Cu 2− x S nanoshell reaches 1505 nm/ RIU , which is more than bimetallic nanoshells. Using the boundary element method and calculating the extinction cross-section in terms of wavelength, the dependence of the resonance wavelength of the localized surface plasmon on different parameters has been investigated. It is shown that the nanosensor investigated in this research has a high sensitivity to the changes in the refractive index of the studied sample. In addition, the required spectral range can be arbitrarily adjusted by the type of nanoparticles.