Schmidt Values Research Articles

An inclined magnetic field and slip effect on heat and mass transfer analysis in the peristaltic flow of immiscible fluid through an asymmetric porous channel

In this work, authors have studied peristaltic flow of immiscible type of couple stress and Newtonian fluid via an asymmetric horizontal channel filled with porous material by taking slippage into account at the channel wall which was ignored in previous published literature under the influence of thermal radiation and magnetic field. The study of peristaltic flow of considered immiscible fluids will play an important role in maximizing system efficiency, reducing energy losses, and improving performance of various fluid transport. In the present problem, the linearized form of governing equations has been solved by direct method with the use of Mathematica 14 software to obtained the closed form solutions of various flow variables. In this work, the impacts of various influencing factors on the model's flow, thermal, and concentration properties have been analyzed graphically. The work presented here leads to the significant result that large Schmidt number values in a porous filled duct reduces the mass diffusivity. Another key finding of this work is that the formation of entropy is reduced when low permeability porous material is used. Our research concludes that entropy creation in the asymmetric porous channel is decreased when the slip length increases on the channel's static borders.

Resistance of some outdoor pavements to destructive combined effects in cold regions

ABSTRACT This study aims to investigate some physical and mechanical properties and resistance to triple-combined effect (abrasion, freeze-thaw and de-icing salt) of Interlocking concrete block pavement (ICBP), concrete cube pavement (CCP), concrete kerb (CK) and natural basalt stone pavement (BSP) products. The pavement products were supplied in different types/varieties from manufacturers in Erzurum-Turkey. The Bohme abrasion test was performed at the end of every 5 cycles with NaCl solution freeze-thaw cycles in addition to the physical and mechanical tests, which are important in applications. As a result, while the BSP and CK concrete pavements completed a total of 60 cycles without disintegrating with the least mass loss against the triple-combined effect, the concrete cube pavement-colourless (CCP-C) product disintegrated in the shortest time. It was determined that there can be significant differences in the mechanical and durability properties of the same type of ICBP products from different manufacturers. It was seen that the use of iron oxide-based pigments and colour type positively affect the mechanical and durability properties of Dry-cast Concrete (DCC) pavements. Additionally, it was determined that there are strong positive relationships between the durability performance of pavements and their compressive strength and Schmidt values, and negative relationships with their porosity.

Schmidt number's impact during the growth of mc-silicon ingot through directional solidification furnace for photovoltaic applications: A computational investigation

The use of multi-crystalline silicon for photovoltaic solar cell applications is highly advantageous due to its low manufacturing costs. In this study, numerical simulations were conducted to investigate mass transport phenomena during the directional solidification of molten silicon for different Schmidt values at the critical Prandtl number of 0.01. The simulations were performed using the diffusion model and convection-conduction equations as the framework for the incompressible Navier-Stokes equation. The finite-volume method was used to carry out computations in a two-dimensional (2D) axisymmetric model. The diffusion flux of impurities (oxygen, carbon, and nitrogen) and dopants (phosphorus and boron) during the mc-silicon growth process was examined for Schmidt numbers Sc=0.5, Sc=5, and Sc=10. It was found that the Schmidt number Sc=0.5 is suitable for producing higher-grade mc-silicon ingots by regulating the production of impurities and dopants. The simulation results obtained in this study may provide a better understanding of the mc-silicon growth process and can be used to improve the production of high-quality mc-silicon ingots for photovoltaic applications.

Nuclear magnetic moment of the neutron-rich nucleus O21

The ground-state magnetic dipole moment of the neutron-rich $^{21}\mathrm{O}$ isotope has been measured via $\ensuremath{\beta}$-ray-detected nuclear magnetic resonance ($\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{NMR}$) spectroscopy by using a spin-polarized secondary beam of $^{21}\mathrm{O}$ produced from the $^{22}\mathrm{Ne}$ primary beam. From the present measurement, the $g$ factor $|{g}_{\mathrm{exp}}(^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.})|=0.6036(14)$ has been determined. Based on the comparison of this value with Schmidt values, we unambiguously confirm the $\ensuremath{\nu}{d}_{5/2}$ configuration with spin and parity assignments ${I}^{\ensuremath{\pi}}=5/{2}^{+}$ for the $^{21}\mathrm{O}$ ground state, suggested by previously reported studies. Consequently, the magnetic moment has been determined as ${\ensuremath{\mu}}_{\mathrm{exp}}(^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.})=(\ensuremath{-})1.5090(35){\ensuremath{\mu}}_{N}$. The obtained experimental magnetic moment is in good agreement with the predictions of the shell-model calculations using the USD, YSOX, and SDPF-M interactions as well as random phase approximation (RPA) calculations. This observation indicates that the $^{21}\mathrm{O}$ nucleus in its ground state does not manifest any anomalous structure and is not influenced by the proximity of the drip line.

Microstructure and mechanical properties of TC4/NiTi bionic gradient heterogeneous alloy prepared by multi-wire arc additive manufacturing

TC4/NiTi multi-materials structure components have been successfully fabricated via multi-wire arc additive manufacturing (MWAAM). Here we show the interface characteristics and mechanical properties of TC4/NiTi multi-materials structure component under bionic gradient interlayer build strategy. The results indicated that MWAAM TC4/NiTi gradient heterogeneous alloy with ultimate compression strength (1533.33 ± 26 MPa) was obtained. The excellent compression behaviour was mainly contributed to the excellent transition of gradient region indicated by EBSD analysis showing fine grain sizes and smaller difference Schmidt factor values. The phase composition from TC4 region to NiTi region had evolved with the increasing of NiTi content as follows: α-Ti + β-Ti → α-Ti + NiTi2 → NiTi2 → NiTi2 + NiTi → NiTi + Ni3Ti. The microhardness of the gradient heterogeneous alloy ranged from 310 ± 8 HV to 230 ± 11 HV, and the highest hardness value was 669.6 ± 12 HV in region B due to the precipitation of NiTi2 strengthening phase. The ultimate fracture stress and strain of sample were 1533.33 ± 26 MPa and 28.3 ± 6% respectively. The irrecoverable strain of MWAAM TC4/NiTi gradient heterogeneous alloy gradually approached 2.75% during 10 load/unload cycles of compression test.

Correction to: Estimating the brittleness values of carbonated rocks with Shore, Schmidt, and Leeb hardness values

Correction to: Estimating the brittleness values of carbonated rocks with Shore, Schmidt, and Leeb hardness values

Analytical investigation of magnetized 2D hybrid nanofluid (GO + ZnO + blood) flow through a perforated capillary

The hydrothermal features of unsteady, incompressible, and laminar hybrid nanofluid motion through a porous capillary are analytically studied in the magnetic field presence. The hybrid nanofluid (GO + ZnO + Blood) is synthesized by blending nanomaterials of graphene oxide and zinc oxide with blood acting as the host fluid. The mathematical model of the flow comprises of a coupled nonlinear set of partial differential equations (PDEs) satisfying appropriate boundary conditions. These equations are reduced to ordinary differential equations (ODEs) by using similarity transformations and then solved with homotopy analysis method (HAM). The impacts of various pertinent physical parameters over the hybrid nanofluid state functions are examined by displaying 2 D graphs. It has been observed that the fluid velocity mitigates with the varying strength of M, A 0, N 0, and N 1. The enhancing buoyancy parameter ϵ augments the fluid velocity. The increasing Prandtl number causes to reduce, while the enhancing A 0, B, and N 2 augment the hybrid nanofluid temperature. The fluid concentration mitigates with the higher Schmidt number values and A 0, and augments with the increasing Soret number strength. The augmenting magnetic field strength causes to enhance the fluid friction, whereas the convective heat transfer increases with the Prandtl number rising values. The rising Sherwood number drops the mass transfer rate of the fluid. The achieved results are validated due to the agreement with the published results. The results of this computation will find applications in biomedicine, nanotechnology, and fluid dynamics.

Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1)U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrixproductstate representation and the singlesite reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L=501L=501 while accounting for N_{\rm ph}=63 phonons per site with high precision in the CDW phase.

Numerical Investigation of Heat and Mass Transport in the Flow over a Magnetized Wedge by Incorporating the Effects of Cross-Diffusion Gradients: Applications in Multiple Engineering Systems

The flow over a wedge is significant and frequently occurs in civil engineering. It is significant to investigate the heat and mass transport characteristics in the wedge flow. Therefore, the analysis is presented to examine the effects of preeminent parameters by incorporating the cross-diffusion gradients in the energy and mass constitutive relations. From the analysis, it is perceived that the temperature drops against a higher Prandtl number. Due to concentration gradients in the energy equation, the temperature rises slowly. Moreover, it is examined that the mass transfer significantly reduces due to Schmidt effects and more mass transfer is pointed against the Soret number. The shear stresses increase due to stronger magnetic field effects. The local thermal performance of the fluid enhances against more dissipative fluid, and DuFour effects reduced it. Furthermore, the mass transport rate drops due to higher Soret effects and increases against multiple Schmidt number values.

Local matrix product operators: Canonical form, compression, and control theory

We present a new method for compressing matrix product operators (MPOs) which represent sums of local terms, such as Hamiltonians. Just as with area law states, such local operators may be fully specified with a small amount of information per site. Standard matrix product state (MPS) tools are ill-suited to this case, due to extensive Schmidt values that coexist with intensive ones, and Jordan blocks in the transfer matrix. We ameliorate these issues by introducing an "almost Schmidt decomposition" that respects locality. Our method is "$\varepsilon$-close" to the accuracy of MPS-based methods for finite MPOs, and extends seamlessly to the thermodynamic limit, where MPS techniques are inapplicable. In the framework of control theory, our method generalizes Kung's algorithm for model order reduction. Several examples are provided, including an all-MPO version of the operator recursion method (Lanczos algorithm) directly in the thermodynamic limit. All results are accompanied by practical algorithms, well-suited for the large MPOs that arise in DMRG for long-range or quasi-2D models.

Renormalization group approach to symmetry protected topological phases

A defining feature of a symmetry protected topological phase (SPT) in one-dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Matrix product state renormalization

The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this compression as an application of Wilson's numerical renormalization group along the imaginary time direction appearing in the path integral representation of the state. The location of the physical index is considered as an impurity in the transfer matrix and static MPS correlation functions are reinterpreted as dynamical impurity correlations. Coarse-graining the transfer matrix is performed using a hybrid variational ansatz based on matrix product operators, combining ideas of MPS and the multi-scale entanglement renormalization ansatz. Through numerical comparison with conventional MPS algorithms, we explicitly verify the impurity interpretation of MPS compression, as put forward by [V. Zauner et al., New J. Phys. 17, 053002 (2015)] for the transverse-field Ising model. Additionally, we motivate the conceptual usefulness of endowing MPS with an internal layered structure by studying restricted variational subspaces to describe elementary excitations on top of the ground state, which serves to elucidate a transparent renormalization group structure ingrained in MPS descriptions of ground states.

Magnetic moments in odd-ACd isotopes and coupling of particles with zero-point vibrations

Background: The coupling of the last nucleon with configurations in the ground state of the even-even core is known to augment the single quasiparticle fragmentation pattern. In a recent experimental study by Yordanov \emph{et al.} the values of the magnetic dipole and electric quadrupole moments of the $11/2^-$ state in a long chain of Cd isotopes were found to follow a simple trend which we try to explain by means of incorporating long-range correlations in the ground state. Purpose: Our purpose is to study the influence of the ground-state correlations (GSC) on the magnetic moments and compare our results with the data for the odd-A Cd isotopes. Method: In order to evaluate if the additional correlations have bearing on the magnetic moments we employ an extension to the quasiparticle-phonon model (QPM) which takes into account quasiparticle$\otimes$phonon configurations in the ground state of the even-even core to the structure of the odd-A nucleus wave function. Results: It is shown that the values for the magnetic moments which the applied QPM extension yields deviate further from the Schmidt values. The latter is in agreement with the measured values for the Cd isotopes. Conclusions: The GSC exert significant influence on the magnetic dipole moments and reveal a potential for reproducing the experimental values for the studied cadmium isotopes.

Effect of core polarization on magnetic dipole moments in deformed odd-mass nuclei

Magnetic properties of deformed odd-mass nuclei are studied within a nonrelativistic mean-field-plus-pairing approach, namely the Skyrme-Hartree-Fock-BCS approach with self-consistent blocking. For an odd number of nucleons these approaches lead to the breaking of the time-reversal invariance. The deviation from the Schmidt values of the isoscalar magnetic dipole moment is known to result from a subtle balance between core-polarization effects and meson-exchange current effects. However, the former are usually calculated in the random phase approximation without time-reversal symmetry breaking at the mean-field level. In this work we show that if one takes into account this symmetry breaking already in the mean-field solution, the correction from core polarization yields a significant contribution to the empirical quenching of the spin gyromagnetic ratios as compared to the free values in deformed odd-mass nuclei. Moreover, we calculate magnetic dipole moments in the Bohr and Mottelson unified-model description with self-consistent blocked mean-field intrinsic states. The obtained results in the $A\ensuremath{\sim}100$ and $A\ensuremath{\sim}180$ mass regions as well as for three actinide nuclei compare favorably with experimental data.

Nuclear ground-state spin and magnetic moment of 21Mg

We present the results of combined laser spectroscopy and nuclear magnetic resonance studies of 21Mg. The nuclear ground-state spin was measured to be I=5/2 with a magnetic moment of μ=−0.983(7)μN. The isoscalar magnetic moment of the mirror pair (F21,Mg21) is evaluated and compared to the extreme single-particle prediction and to nuclear shell-model calculations. We determine an isoscalar spin expectation value of 〈σ〉=1.15(2), which is significantly greater than the empirical limit of unity given by the Schmidt values of the magnetic moments. Shell-model calculations taking into account isospin non-conserving effects, are in agreement with our experimental results.

Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei

Effects of core polarization and tensor coupling on the magnetic moments in Λ13C, Λ17O, and Λ41Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of pΛ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for pΛ states from the Schmidt values are found to increase with nuclear mass number.

Time-odd triaxial relativistic mean field approach for nuclear magnetic moments

The time-odd triaxial relativistic mean field approach is developed and applied to the investigation of the ground-state properties of light odd-mass nuclei near the double-closed shells. The nuclear magnetic moments including the isoscalar and isovector ones are calculated and good agreement with Schmidt values is obtained. Taking $^{17}$F as an example, the splitting of the single particle levels (around $~0.7$ MeV near the Fermi level), the nuclear current, the core polarizations, and the nuclear magnetic potential, i.e., the spatial part of the vector potential, due to the violation of the time reversal invariance are investigated in detail.

Charge radii and nuclear moments aroundSn

Laser spectroscopy measurements have been carried out on the very neutron-rich tin isotopes with the COMPLIS experimental setup. Using the 5s 2 5p 2 3 P 0 → 5s 2 5p6s 3 P 1 optical transition, hyperfine spectra of 126–132 Sn and 125 m ,127 m ,129 m –131 m Sn where recorded for the first time. The variation of the mean square charge radius ( δ 〈 r 2 〉 ) between these nuclei and the nuclear moments of the isomers and the odd isotopes were thus measured. From the quadrupole moments values, all these nuclei appear to be spherical. The experimental magnetic moments are thus compared with the Schmidt values calculations. Moreover, the measured δ 〈 r 2 〉 are compared with several mean field calculations.

Charge radii and nuclear moments around 132Sn

Laser spectroscopy measurements have been carried out on the very neutron-rich tin isotopes with the COMPLIS experimental setup. Using the 5s 25p 2 3P 0 → 5s 25p6s 3P 1 optical transition, hyperfine spectra of 126–132Sn and 125 m,127 m,129 m–131 m Sn where recorded for the first time. The variation of the mean square charge radius ( δ 〈 r 2 〉 ) between these nuclei and the nuclear moments of the isomers and the odd isotopes were thus measured. From the quadrupole moments values, all these nuclei appear to be spherical. The experimental magnetic moments are thus compared with the Schmidt values calculations. Moreover, the measured δ 〈 r 2 〉 are compared with several mean field calculations.

Magnetic dipole moments of odd-oddN=Znuclei

The experimental data of the magnetic dipole moments of low-lying states in odd-odd $N=Z$ nuclei, which has increased recently by a factor of 2, are revisited within the simple shell model, taking the wave functions to be of the form ${\ensuremath{\Psi}}_{\mathrm{core}}(J=0,T=0){\ensuremath{\Psi}}_{\mathrm{np}}(J,T=0).$ Good agreement with the updated experimental data is obtained within the $\mathrm{jj}$-coupling scheme ${\ensuremath{\Psi}}_{\mathrm{np}}[{(\mathrm{nlj})}^{2}J,(T=0)],$ using the Schmidt values for the $g$ factor and also by using effective $g$ factor deduced from nearby odd-$A$ nuclei. We have also carried out a calculation of \ensuremath{\mu} within the $\mathrm{LS}$-coupling scheme ${\ensuremath{\Psi}}_{\mathrm{np}}[{(1/2)}^{2}{S(\mathrm{nl})}^{2}L,J,(T=0)]$ and also obtained good agreement with data. The success of these simple models in reproducing the experimental data is discussed.