Path integral Monte Carlo approach to the structural properties and collective excitations of liquid $$^3{\text {He}}$$ without fixed nodes

Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic $$^4{\text {He}}$$ 4 He exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic $$^3{\text {He}}$$ 3 He is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid $$^3{\text {He}}$$ 3 He without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor $$S({\mathbf {q}})$$ S ( q ) , the momentum distribution $$n({\mathbf {q}})$$ n ( q ) , and the static density response function $$\chi ({\mathbf {q}})$$ χ ( q ) . In addition, the dynamic structure factor $$S({\mathbf {q}},\omega )$$ S ( q , ω ) is rigorously reconstructed from imaginary-time PIMC data. From simulations of $$^3{\text {He}}$$ 3 He , we derived the familiar phonon–maxon–roton dispersion function that is well-known for $$^4{\text {He}}$$ 4 He and has been reported previously for two-dimensional $$^3{\text {He}}$$ 3 He films (Nature 483:576–579 (2012)). The comparison of our new results for both $$S({\mathbf {q}})$$ S ( q ) and $$S({\mathbf {q}},\omega )$$ S ( q , ω ) with neutron scattering measurements reveals an excellent agreement between theory and experiment.

Magnetic Fields in Massive Star-forming Regions (MagMaR). II. Tomography through Dust and Molecular Line Polarization in NGC 6334I(N)

Here, we report ALMA detections of polarized emission from dust, CS(J = 5 → 4), and C33S(J = 5 → 4) toward the high-mass star-forming region NGC 6334I(N). A clear “hourglass” magnetic field morphology was inferred from the polarized dust emission, which is also directly seen from the polarized CS emission across velocity, where the polarization appears to be parallel to the field. By considering previous findings, the field retains a pinched shape that can be traced to clump length scales from the envelope scales traced by ALMA, suggesting that the field is dynamically important across multiple length scales in this region. The CS total intensity emission is found to be optically thick (τ CS = 32 ± 12) while the C33S emission appears to be optically thin ( τ C 33 S = 0.1 ± 0.01 ). This suggests that sources of anisotropy other than large velocity gradients, i.e., anisotropies in the radiation field, are required to explain the polarized emission from CS seen by ALMA. By using four variants of the Davis–Chandrasekhar–Fermi technique and the angle dispersion function methods (ADF), we obtain an average of the estimates for the magnetic field strength on the plane of the sky of B pos = 16 mG from the dust and B pos ∼ 2 mG from the CS emission, where each emission traces different molecular hydrogen number densities. This effectively enables a tomographic view of the magnetic field within a single ALMA observation.

Mathematical Modeling of Unsteady Solute Dispersion in Bingham Fluid Model of Blood Flow Through an Overlapping Stenosed Artery

An artery narrowing referred to as atherosclerosis or stenosis causes a reduction in the diameter of the artery. When blood flow through an artery consists of stenosis, the issue of solute dispersion is more challenging to solve. A mathematical model is developed to examine the unsteady solute dispersion in an overlapping stenosed artery portraying blood as Bingham fluid model. The governing of the momentum equation and the constitutive equation is solved analytically. The generalized dispersion model is imposed to solve the convective-diffusion equation and to describe the entire dispersion process. The dispersion function at steady-state decreases at the center of an artery as the stenosis height increase. A reverse behavior is shown at an unsteady-state. As the plug core radius, time and stenosis height increase, the dispersion function decreases at the center of an artery. There is a high amount of red blood cells at the center of the artery but no influences near the wall. Hence, this model is useful in transporting the drug or nutrients to the targeted stenosed region in the treatment of diseases and in understanding many physiological processes.

Mathematical Analysis of Unsteady Solute Dispersion with Chemical Reaction Through a Stenosed Artery

One major kind of arterial disease in blood flow that attracted many researchers is arterial stenosis. Arterial stenosis occurs when a lumen of artery is narrowed by the accumulation of fats, cholesterols and lipids plaques at the inner layer of the wall of an artery. To treat this arterial disease, the drug (solute) is injected into the blood vessels. Injection of the drug into the blood vessel cause the occurrence of chemical reaction between the drug and blood proteins and it affects the effectiveness of the solute transportation in blood flow. Hence, this study examines the unsteady dispersion of solute with the influence of chemical reaction and stenosis height through a very narrow artery with a cosine-curved stenosis. The blood is treating as Herschel-Bulkley (H-B) fluid. The momentum and constitutive equations are solved analytically to gain velocity of H-B blood flow. The convective-diffusion equation is solved by applying the generalized dispersion model to gain the dispersion function of solute. The influence of chemical reaction, power-law index, plug flow radius and stenosis height on the solute dispersion process is investigated. The results are validated with the previous solution without the effect of chemical reaction and stenosis. The results showed a good conformity between the two solutions. An increase in the chemical reaction coefficient, stenosis height, power-law index and plug flow radius reduces the dispersion function. It is observed that the solute dispersion in blood flow is affected by chemical reaction and stenosis height. H-B fluid is an appropriate fluid to investigate the blood velocity and transportation of the drug in blood flow to the targeted stenosed region through a very narrow artery for the treatment of arterial diseases. The results of the present study can potentially be used to predict the changes of blood flow behavior and dispersion process in blood flow.

Ultrasonic unilateral double-position excitation lamb wave defect detection and quantification method for ground electrode of transmission tower

The power transmission tower’s ground electrode defect will affect its normal current dispersion function and threaten the power system’s safe and stable operation and even personal safety. Aiming at the problem that the buried grounding grid is difficult to be detected, this paper proposes a method for identifying the ground electrode defects of transmission towers based on single-side multi-point excited ultrasonic guided waves. The geometric model, ultrasonic excitation model, and physical model are established, and the feasibility of ultrasonic guided wave detection is verified through the simulation and experiment. In actual inspection, it is equally important to determine the specific location of the defect. Therefore, a multi-point excitation method is proposed to determine the defect’s actual position by combining the ultrasonic guided wave signals at different excitation positions. Besides, the precise quantification of flat steel grounding electrode defects is achieved through the feature extraction-neural network method. Field test results show that, compared with the commercial double-sided excitation transducer, the single-sided excitation transducer proposed in this paper has a lower defect quantization error in defect quantification. The average quantization error is reduced by approximately 76%.

Determination of concentration-dependent dispersion of propane in vapor extraction of heavy oil

Vapex (vapor extraction) is a solvent-based non-thermal in-situ heavy oil recovery process. In Vapex process, a vaporized hydrocarbon solvent is injected into an upper horizontal well where the solvent mixes with the heavy oil and reduces its viscosity. The diluted oil drains under gravity to a bottom production well. Two mechanisms control the production rates of heavy oil in Vapex: mass transfer of solvent into heavy oil, and gravity drainage. Both are governed by dispersion, which is composed of molecular diffusion, convection, and other mechanisms that enhance mixing in porous medium. The accurate determination of solvent dispersion in Vapex is essential to predict effectively the amount and time scale of oil recovery as well to optimize the field operations. Motivated by limited dispersion data in the literature, a novel technique is developed to determine experimentally the concentration-dependent dispersion coefficient of propane in Vapex process, The technique employs live oil production rates obtained from Vapex experiments at 21ºC and 0.790 MPa. The salient feature of this technique is that it does not impose any functional form on dispersion as a function of concentration, but allows its natural and realistic determination. The technique could be applied to determine other solvents dispersion coefficient used in the in-situ recovery of heavy oil. Propane dispersion coefficient is determined by the minimization of the difference in experimental and calculated cumulative live oil produced. The necessary conditions for the minimum are fundamentally derived, utilizing the theory of optimal control. A computational algorithm is formulated to calculate the propane dispersion function simultaneously with propane-heavy oil interface mass fraction. Physical models of glass beads of different permeabilities (204-51 Darcy) and drainage heights (25-45 cm) were used to conduct the Vapex experiments. The results show that dispersion of propane is a unimodal function of its concentration in heavy oil, and lies in the range, 0.5x10⁻⁵- 7.933x10⁻⁵ m²/s. Convectional mixing is promoted by higher model drainage heights and lower permeability. Finally, propane dispersion is correlated as a function of propane mass fraction in heavy oil and the packed medium permeability, as well as the drainage height.

Determination of concentration-dependent dispersion of propane in vapor extraction of heavy oil

Vapex (vapor extraction) is a solvent-based non-thermal in-situ heavy oil recovery process. In Vapex process, a vaporized hydrocarbon solvent is injected into an upper horizontal well where the solvent mixes with the heavy oil and reduces its viscosity. The diluted oil drains under gravity to a bottom production well. Two mechanisms control the production rates of heavy oil in Vapex: mass transfer of solvent into heavy oil, and gravity drainage. Both are governed by dispersion, which is composed of molecular diffusion, convection, and other mechanisms that enhance mixing in porous medium. The accurate determination of solvent dispersion in Vapex is essential to predict effectively the amount and time scale of oil recovery as well to optimize the field operations. Motivated by limited dispersion data in the literature, a novel technique is developed to determine experimentally the concentration-dependent dispersion coefficient of propane in Vapex process, The technique employs live oil production rates obtained from Vapex experiments at 21ºC and 0.790 MPa. The salient feature of this technique is that it does not impose any functional form on dispersion as a function of concentration, but allows its natural and realistic determination. The technique could be applied to determine other solvents dispersion coefficient used in the in-situ recovery of heavy oil. Propane dispersion coefficient is determined by the minimization of the difference in experimental and calculated cumulative live oil produced. The necessary conditions for the minimum are fundamentally derived, utilizing the theory of optimal control. A computational algorithm is formulated to calculate the propane dispersion function simultaneously with propane-heavy oil interface mass fraction. Physical models of glass beads of different permeabilities (204-51 Darcy) and drainage heights (25-45 cm) were used to conduct the Vapex experiments. The results show that dispersion of propane is a unimodal function of its concentration in heavy oil, and lies in the range, 0.5x10⁻⁵- 7.933x10⁻⁵ m²/s. Convectional mixing is promoted by higher model drainage heights and lower permeability. Finally, propane dispersion is correlated as a function of propane mass fraction in heavy oil and the packed medium permeability, as well as the drainage height.

A Wronskian method for elastic waves propagating along a tube

A technique involving the higher Wronskians of a differential equation is presented for analysing the dispersion relation in a class of wave propagation problems. The technique shows that the complicated transcendental-function expressions which occur in series expansions of the dispersion function can, remarkably, be simplified to low-order polynomials exactly, with explicit coefficients which we determine. Hence simple but high-order expansions exist which apply beyond the frequency and wavenumber range of widely used approximations based on kinematic hypotheses. The new expansions are hypothesis-free, in that they are derived rigorously from the governing equations, without approximation. Full details are presented for axisymmetric elastic waves propagating along a tube, for which stretching and bending waves are coupled. New approximate dispersion relations are obtained, and their high accuracy confirmed by comparison with the results of numerical computations. The weak coupling limit is given particular attention, and shown to have a wide range of validity, extending well into the range of strong coupling.

The velocity dispersion function of early-type galaxies and its redshift evolution: the newest results from lens redshift test

The redshift distribution of galactic-scale lensing systems provides a laboratory to probe the velocity dispersion function (VDF) of early-type galaxies (ETGs) and measure the evolution of early-type galaxies at redshift z ∼ 1. Through the statistical analysis of the currently largest sample of early-type galaxy gravitational lenses, we conclude that the VDF inferred solely from strong lensing systems is well consistent with the measurements of SDSS DR5 data in the local universe. In particular, our results strongly indicate a decline in the number density of lenses by a factor of two and a 20% increase in the characteristic velocity dispersion for the early-type galaxy population at z ∼ 1. Such VDF evolution is in perfect agreement with the ΛCDM paradigm (i.e., the hierarchical build-up of mass structures over cosmic time) and different from ”stellar mass-downsizing” evolutions obtained by many galaxy surveys. Meanwhile, we also quantitatively discuss the evolution of the VDF shape in a more complex evolution model, which reveals its strong correlation with that of the number density and velocity dispersion of early-type galaxies. Finally, we evaluate if future missions such as LSST can be sensitive enough to place the most stringent constraints on the redshift evolution of early-type galaxies, based on the redshift distribution of available gravitational lenses.