Full Numerical Solution Research Articles

Effectively flat potential in the Friedberg–Lee–Sirlin model

The Friedberg–Lee–Sirlin (FLS) model is a well-known renormalizable theory of scalar fields that provides for the existence of non-topological solitons. Since this model was proposed, numerous works have been dedicated to studying its classical configurations and its general suitability for various physical problems in cosmology, quantum chromodynamics, etc. In this paper, we study how Q-balls in effective field theory (EFT) reproduce non-topological solitons in the full FLS theory. We obtain an analytical description of the simplified model and compare the results with numerical calculations and perturbation theory. We also study the condensation of charged bosons on the domain wall. A full numerical solution allows us to check the EFT methods for this problem. The latter analysis is based on the application of EFT methods to significantly inhomogeneous configurations. We give an interpretation of the results in terms of the shifted boson mass and the vacuum rearrangement.

Solvation Forces Near Hydrophobic Surfaces: A Classical Density Functional Theory Study.

We use classical density functional theory (DFT) to model solvation interactions between hydrophobic surfaces, which we show to be characterized by depletion attraction at small surface to surface separations and a slowly decaying bipower law interaction at large separations. The solvation interaction originates from van der Waals (vdW) and Coulombic interactions between molecules in the polar solvent, e.g., water, and from the molecules thermal motion and finite volume. We investigate model hydrophobic surfaces represented by bubbles and nonpolar solids, e.g., aliphatic particles, and calculate in a DFT fashion the distribution of molecules in the interlaying solvent between two such surfaces and the hydrophobic excess force resulting from it. The interactions are largely attractive, which is well-known in measurement, albeit vdW attraction between molecules in solids and in the solvent may cause repulsion at certain interface to interface separations. We commence our analysis by suggesting an asymptotic analytical bipower law expression for the solvation interaction at large separations. Thereafter we present a full numerical solution, which is in good agreement with the analytical prediction and further explores the interaction at small surface to surface separations. Our theoretical results yield adhesion energies which agree with previous experiments.

A novel approach to model nance drying considering its shrinkage

Air drying is a viable preservation method to boost the accessibility of nance, a seasonal drupe with very short shelf life; however, information about nance drying is scarce, especially from a mass transfer (MT) standpoint. Besides, the lack of simple models considering the stone fraction (radius of inner stone/radius of nance) and the mesocarp shrinkage in drupes has caused most investigations rely on sphere and cube geometries, contributing to the unreliable estimation of MT properties. This study developed a discrete state-space (SS) formulation with analytical solution to describe nance drying which, unlike a variable separation (VS) solution, can consider a variable stone fraction, caused by outer boundary moving while flesh-pit interface remains still. Nance fruits were air dried (60, 70 and 80 °C) to obtain their moisture kinetics and shrinking behavior. Drying data were used to estimate water diffusivity (D) under rigid (VS and SS solutions) and shrinkable (SS and numerical solution) mesocarp assumptions. Nances lost about 60% of their initial volume at the end of drying, while stone fraction increased from 0.44 to 0.62. D values ranged from 5.3 to 6.7 (×10–10) m2/s with SS approach and variable stone fraction. The major source of error in D was not the formulation (SS or VS) when a rigid mesocarp was considered, but the values assigned to the nance radius (length for diffusion) and stone fraction, an initial or average value along process. SS diffusivities did not differ to those estimated with the full numerical solution under variable stone fraction (p>0.05), while VS parameters were overestimated by 44–46 % as a minimum. SS formulation can be applied to hollow cylinders and other geometries with 2D or 3D MT, while able to include non-isotropic shrinkage and evolving external conditions, a problem normally reserved to pure numerical implementations, offering substantial advantages over VS equations.

Mass transport in Couette flow

In this study we examine the large Péclet number, Pe, limit of a concentration boundary layer in Couette flow. The boundary layer has a thickness of order Pe−1/2. The asymptotic concentration is asymptotically obtained as an integral solution up to order Pe−1/2 using the Fourier sine transform. The asymptotic solution is found to be in good agreement with the full numerical solution for large Péclet numbers. Further, the effective diffusivity obtained from the asymptotic solution is found to be in good agreement with the effective diffusivity obtained from the full numerical solution for large Péclet numbers.

Nonlinear charge and energy transport in anharmonic quasi-two-dimensional systems.

We study the localized states of an extra electron in an anisotropic quasi-two-dimensional system in which the electron-lattice interaction and the anharmonicity of the lattice vibrations are dominant in one direction. This model describes layers of polydiacetylene or other polymer chains, beta sheets of polypeptides, multilevel microstructures of conjugated polymers, and other low-dimensional systems. It is shown that for appropriate parameter values of the system an extra electron can excite a soliton-like mobile wave of the lattice deformation, within which it can get self-trapped. Such a bound state of an electron and the lattice deformation form a nonlinear two-component polaron-like entity, which can propagate with minimum of the energy dissipation. Our findings are based on the variational approach and the full numerical solution of the coupled system of nonlinear equations. These results suggest that the experimentally measured charge and energy transport over macroscopic distances in the above-mentioned systems can be provided by the soliton mechanism and thus have a potential impact on the theoretical background of the numerous applications of low-dimensional materials in nanoelectronics.

Stability of coherent-solitonic states for Gross-Pitaevskii equation with parabolic potential

We investigate analytically and numerically the linear stability of coherent-solitonic states of the Gross-Pitaevskii equation with parabolic potential. The two lowest-order states are linearly stable. For small enough nonlinearity, either positive or negative, higher states with low intensity develop a limited number of unstable perturbation modes. When the state intensity is raised above a threshold, its stabilization occurs. The full numerical solution of the Gross-Pitaevskii equation confirms that the linear analysis gives an adequate description of solution stability properties for low-order states and moderate propagation lengths.

Flow and deformation due to periodic loading in a soft porous material

Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically investigated. Here, we fill this gap by identifying and exploring the complete parameter space associated with periodic deformations in the context of a one-dimensional model problem. We use large-deformation poroelasticity to consider a wide range of loading periods and amplitudes. We identify two distinct mechanical regimes, distinguished by whether the loading period is slow or fast relative to the characteristic poroelastic timescale. We develop analytical solutions for slow loading at any amplitude and for infinitesimal amplitude at any period. We use these analytical solutions and a full numerical solution to explore the localisation of the deformation near the permeable boundary as the period decreases and the emergence of nonlinear effects as the amplitude increases. We show that large deformations lead to asymmetry between the loading and unloading phases of each cycle in terms of the distributions of porosity and fluid flux.

Hydraulic head change predictions in groundwater models using a probabilistic neural network

Groundwater resource management is an increasingly complicated task that is expected to only get harder and more important with future climate change and increasing water demands resulting in an increasing need for fast and accurate decision support systems. Numerical flow simulations are accurate but slow, while response matrix methods are fast but only accurate in near-linear problems. This paper presents a method based on a probabilistic neural network that predicts hydraulic head changes from groundwater abstraction with uncertainty estimates, that is both fast and useful for non-linear problems. A generalized method of constructing and training such a network is demonstrated and applied to a groundwater model case of the San Pedro River Basin. The accuracy and speed of the neural network are compared to results using MODFLOW and a constructed response matrix of the model. The network has fast predictions with results similar to the full numerical solution. The network can adapt to non-linearities in the numerical model that the response matrix method fails at resolving. We discuss the application of the neural network in a decision support framework and describe how the uncertainty estimate accurately describes the uncertainty related to the construction of the training data set.

Defining relative humidity in terms of water activity: III. Relations to dew-point and frost-point temperatures

Relative humidity (RH) is a fundamental quantity used in many fields of engineering and science, and in particular in meteorology and climate research. Relative fugacity (RF) and, equivalently, relative activity of water vapour in humid air have recently been proposed as a physically well-founded, unambiguous common metrological reference quantity for several conventional but mutually inconsistent definitions of RH. The RF definition is valid is valid under real-gas conditions and above boiling and sublimation temperatures. While differences between RH and RF mostly remain within uncertainties of typical present-day RH measurements, such systematic discrepancies are expected to be of substantial climatological relevance. Consequently, interdisciplinary harmonisation of RH definitions is overdue within the SI framework. Dew-point and frost-point temperatures are preferred measurands in humidity metrology using, for example, chilled-mirror hygrometers. Here, relations are presented for estimating RF from those temperatures, based on equations of state of the 2011 IUGG 5IUGG: International Union of Geodesy and Geophysics, https://iugg.org/. standard TEOS-10, the ‘international thermodynamic equation of seawater—2010’. Recommendations are given for numerically computing RF using the open-source TEOS-10 SIA library 6 6SIA Library: Sea-Ice-Air Library of TEOS-10, http://teos-10.org.. The asymptotic limiting laws of RF for nearly saturated humid air exhibit the familiar form of Clausius–Clapeyron-like equations, despite departing from ideal-gas assumptions. Under various practical conditions, these simple equations may cover the full humidity range with only minor residuals compared to the full numerical TEOS-10 solution for RF.

An experimental and numerical case study of thermal and mechanical consequences induced by laser welding process

In this study, an experimental benchmark with different welding conditions is developed. In-situ diagnostics tools (high-speed camera, thermocouple) and ex-situ diagnostics devices (high-resolution digital microscope, measuring arm, X-Ray diffraction device) are exploited to measure various physical quantities. These measurements set up a complete database of laser welding benchmarks, which can establish a relationship between welding parameters and thermo-mechanical consequences. Meanwhile, the finite element method is used to investigate such a process and understand the multi-physics coupling problems behind the process. Numerical and experimental comparisons are performed in two steps. Firstly, the molten pool morphology and temperature evolution are employed to calibrate the 3D volumetric heat source. Secondly, a thermo-mechanical coupling is carried out by imposing the thermal strain calculated from the calibrated thermal model. Thermo-elastoplastic models with isotropic and kinematic hardening are used to compute the distortion and residual stresses. Mechanical results (distortions and residual stresses) of numerical models are compared with those of the benchmark. Overall, a good correlation is found. Thus, this paper provides a full experimental case study and numerical solution for laser welding process, which allows researchers to validate their numerical models and also gives some insights for modeling welding processes.

Theoretical framework to predict the acoustophoresis of axisymmetric irregular objects above an ultrasound transducer array.

Acoustic radiation force and torque arising from wave scattering are able to translate and rotate matter without contact. However, the existing research mainly focused on manipulating simple symmetrical geometries, neglecting the significance of geometric features. For the nonspherical geometries, the shape of the object strongly affects its scattering properties, and thus the radiation force and torque as well as the acoustophoretic process. Here, we develop an analytical framework to calculate the radiation force and torque exerted on the sound-hard or the sound-soft, axisymmetric particles excited by a user-customized transducer array based on a conformal transformation approach, capturing the significance of the geometric features. The derivation framework is established under the computation coordinate system (CCS), whereas the particle is assumed to be static. For the dynamic processes, the rotation of particle is converted as the opposite rotation of transducer array, achieved by employing a rotation transformation to tune the incident driving field in the CCS. Later, the obtained radiation force and torque in the CCS should be transformed back to the observation coordinate system for force and torque analysis. The radiation force and torque exerted on particles with different orientations are validated by comparing the full three-dimensional numerical solution in different phase distributions. It is found that the proposed method presents superior computational accuracy, high geometric adaptivity, and good robustness to various geometric features, while the computational efficiency is more than 100 times higher than that of the full numerical method. Furthermore, it is found that the dynamic trajectories of particles with different geometric features are completely different, indicating that the geometric features can be a potential degree of freedom to tune acoustophoretic process. The ability to predict the acoustophoretic process of nonspherical particles above a user-customized transducer array has improved our understanding of the effect of shape asymmetry, which can also be used to verify the effectiveness of acoustic tweezers in manipulating nonspherical objects.

Nonlinear Seepage Mathematical Model of Fractured Tight Stress Sensitive Reservoir and Its Application

A tight reservoir can only have industrial production value after fracturing. After volume fracturing, there are artificial fracturing zones and fracturing unmodified zones composed of a matrix, microfractures, and main fractures. There are also pressure-sensitive effects and nonlinear seepage in the matrix. There is an unsteady channeling flow between the matrix and microfractures and main fractures and a threshold pressure gradient in the matrix. The fluid flow between the three media and the transfer flow between the media are very complex. Aiming at the problem of poor simulation accuracy because the above characteristics of tight reservoir fracturing development are not considered in the current commercial numerical simulation software Eclipse, CMG, and VIP, the triple medium coupling nonlinear mathematical model of tight reservoir fracturing development matrix/microfractures/main fractures was established in this study, and the discrete mathematical model was constructed using the full implicit numerical solution method. The model considered the effects of threshold fracturing gradient and nonlinear seepage on the reverse side of seepage. In terms of pressure-sensitive effect, the latest generalized pressure-sensitive effect calculation model, considering rock physical parameters established by authors, was adopted. In terms of matrix/fracture transfer flow, the nonlinear matrix/fracture transfer flow model considering threshold pressure gradient and pressure-sensitive effect established by authors was adopted. Finally, a tight reservoir numerical simulation software was developed based on a triple medium coupling nonlinear model. The software was used to simulate the development effect of turbidite tight reservoir in Wang 587 Block of Jiyang depression, Shengli Oilfield. The results showed that the fitting accuracy of the new model was 13.3% higher than that of Eclipse, and the calculation results were more in line with the production practice of tight reservoirs. The new model established an important theoretical basis for scientifically and effectively guiding the development of tight reservoirs.

Non-isothermal effects in the slippage condition and absolute viscosity for an electroosmotic flow

In this work, we have developed a novel asymptotic analysis using perturbation techniques for an electroosmotic flow in a rectangular microchannel, considering that the absolute viscosity η is a function of temperature; a situation that affects also the slip condition at the walls of the microchannel, u=−sη∂u∂n. The physical importance of this temperature dependence is based on the presence of the applied external electric field on the electrolyte solution, which originates the Joule heating effect that disturbances the isothermal hydrodynamic behavior. The above leads to a significant increase of the volumetric flow rate for this non-isothermal condition in comparison to the purely isothermal electroosmotic flow. This result is simultaneously controlled by the heat losses to the ambient and the slip effect: the lower the presence of the heat dissipation mechanism on the outer walls of the microchannel and the higher the sliding condition, the higher the values of the volumetric flow rate. The above trend differs substantially from the isothermal case and finds its justification in the recognition of the presence of the Joule heating effect that induces significant longitudinal and transverse temperature gradients along the microchannel. Considering the proper limitations of the asymptotic analysis, we compare the present asymptotic results with a full numerical solution of the governing equations, which are composed of the continuity, momentum, and energy equations for the electrolyte flow, together with the Poisson–Boltzmann.

Dynamics of bubble walls at the electroweak phase transition

First order phase transitions in the early universe naturally lead to the production of a stochastic background of gravitational waves and to the generation of a matter-antimatter asymmetry. The dynamics of the phase transition is affected by the density perturbations in the hot plasma. We address this topic by providing, for the first time, a full numerical solution to the linearized Boltzmann equation for the top quark species coupled to the Higgs field during a first order phase transition at the electroweak scale. Differently from the traditional approaches, our results do not depend on any ansatz and can fully describe the non-equilibrium distribution functions of the particle species in the plasma.

A radial hydraulic fracture driven by a Herschel–Bulkley fluid

We analyse the influence of fluid yield stress on the propagation of a radial (penny-shaped) hydraulic fracture in a permeable reservoir. In particular, the Herschel–Bulkley rheological model is adopted that includes yield stress and non-linearity of the shear stress. The rock is assumed to be linear elastic, and the fracture is driven by the point source fluid injection with a constant volumetric rate. The fracture propagation condition follows the theory of linear elastic fracture mechanics, and Carter’s leak-off law is selected to govern the fluid exchange process between the fracture and formation. The numerical solution of the problem is found using the algorithm based on Gauss–Chebyshev quadrature and Barycentric Lagrange interpolation techniques. We also construct an approximate solution with the help of the global fluid balance equation and the near-tip region asymptote. The latter approximation is computationally efficient, and we estimate its accuracy by comparing the primary crack characteristics such as opening, pressure, and radius with those provided by the full numerical solution. We present examples corresponding to typical field cases and demonstrate that the addition of yield stress can lead to a shorter radius and wider opening compared to the corresponding case with simpler power-law fluid rheology. Further, we quantify the limiting propagation regimes (or vertex solutions) characterised by the dominance of a particular physical phenomenon. Relative to the power-law results, there are two new vertices that are associated with the domination of yield stress: storage-yield-stress and leak-off-yield-stress. To understand the influence of various problem parameters, we utilise the constructed approximate solution to investigate the dimensionless parametric space of the problem, in which the applicability domains of the limiting solutions are quantified. This enables one to quickly determine whether yield stress provides a strong influence for given problem parameters. • Analysis of the impact of fluid yield stress on radial fracture propagation. • Comparison with the power-law rheological model. • Numerical and rapid semi-analytical approximate solutions for the problem. • Construction of the dimensionless parameter space for the problem. • Quantitative identification of parameters for which yield stress is important.

Structure of ultra-magnetised neutron stars

In this review we discuss self-consistent methods to calculate the global structure of strongly magnetised neutron stars within the general-relativistic framework. We outline why solutions in spherical symmetry cannot be applied to strongly magnetised compact stars, and elaborate on a consistent formalism to compute rotating magnetised neutron star models. We also discuss an application of the above full numerical solution for studying the influence of strong magnetic fields on the radius and crust thickness of magnetars. The above technique is also applied to construct a “universal” magnetic field profile inside the neutron star, that may be useful for studies in nuclear physics. The methodology developed here is particularly useful to interpret multi-messenger astrophysical data of strongly magnetised neutron stars.

Near-field target strength of finite cylindrical shell in water

In this study, near-field acoustic scattering from a finite elastic cylindrical shell is investigated based on a previous cylinder method. An analytic expression for scattered pressure is derived in the form of a Kirchhoff–Helmholtz integral with the assumption that the field induced on the cylinder surface is determined by the canonical solution of an infinite elastic cylindrical shell. A useful approximate solution of the integral is obtained in the near-field zone of the receiver and then applied to formulate the near-field target strength. The results of the approximate solution are compared with the full numerical solution and experimental data measured using a linear frequency-modulated continuous-wave pulse at a frequency range of 5 to 25 kHz in a water tank in a laboratory. The results indicate consistency, except for some discrepancies due to experimental restrictions. The approximate solution is validated via finite element modeling using COMSOL Multiphysics. Moreover, the range dependency of the near-field formula and the effect of the end-caps in the finite cylindrical shell are investigated through simulations.

Large- N theory of critical Fermi surfaces

We describe the large $N$ saddle point, and the structure of fluctuations about the saddle point, of a theory containing a sharp, critical Fermi surface in two spatial dimensions. The theory describes the onset of Ising order in a Fermi liquid, and closely related theories apply to other cases with critical Fermi surfaces. We employ random couplings in flavor space between the fermions and the bosonic order parameter, but there is no spatial randomness: consequently, the $G$-$\Sigma$ path integral of the theory is expressed in terms of fields bilocal in spacetime. The critical exponents of the large $N$ saddle-point are the same as in the well-studied non-random RPA theory; in particular, the entropy density vanishes in the limit of zero temperature. We present a full numerical solution of the large $N$ saddle-point equations, and the results agree with the critical behavior obtained analytically. Following analyses of Sachdev-Ye-Kitaev models, we describe scaling operators which descend from fermion bilinears around the Fermi surface. This leads to a systematic consideration of the role of time reparameterization symmetry, and the scaling of the Cooper pairing and $2k_F$ operators which can determine associated instabilities of the critical Fermi surface. We find no violations of scaling from time reparameterizations. We also consider the same model but with spatially random couplings: this provides a systematic large $N$ theory of a marginal Fermi liquid with Planckian transport.

Late-time approaches to the Hubble tension deforming H(z), worsen the growth tension

ABSTRACT Many late-time approaches for the solution of the Hubble tension use late time smooth deformations of the Hubble expansion rate H(z) of the Planck18/ΛCDM best fit to match the locally measured value of H0 while effectively keeping the comoving distance to the last scattering surface and Ω0mh2 fixed to maintain consistency with Planck CMB measurements. A well-known problem of these approaches is that they worsen the fit to low z distance probes. Here, we show that another problem of these approaches is that they worsen the level of the Ω0m − σ8 growth tension. We use the generic class of CPL parametrizations corresponding to evolving dark energy equation of state parameter $w(z)=w_0+w_1\frac{z}{1+z}$ with local measurements H0 prior and identify the pairs (w0, w1) that satisfy this condition. This is a generic class of smooth deformations of H(z) that are designed to address the Hubble tension. We show that for these models the growth tension between dynamical probe data and CMB constraints is worse than the corresponding tension of the standard Planck18/ΛCDM model. We justify this feature using a full numerical solution of the growth equation and fit to the data, as well as by using an approximate analytic approach. The problem does not affect recent proposed solutions of the Hubble crisis involving a SnIa intrinsic luminosity transition at zt ≃ 0.01.

Analysis of cone penetration in brittle liquefiable soils

The paper presents a comprehensive set of simulations of the cone penetration test with pore pressure measurements (CPTu test) in brittle, potentially liquefiable, soils using advanced numerical techniques. The large displacements and large deformations involved in the cone penetration problem are tackled using the Particle Finite Element Method, especially adapted for the analysis of coupled geotechnical problems (G-PFEM). A non-local regularization technique is adopted to prevent the pathological mesh dependence associated with continuum analysis of softening materials. Brittle soil behaviour is described using the CASM constitutive model. Undrained CPTu tests are simulated for a range of soils with different degree of brittleness. Effects of permeability, partial drainage and cone roughness are also explored. The results of the analyses are assessed in terms of the interpretation and classification procedures usually applied in practice. In addition, advantage is taken of the availability of a full numerical solution to explore aspects of soil response during penetration that are not possible when only global CPTu observations are available. The full set of numerical analyses have been able to capture the essential features of the problem and to provide useful insights into the effects of brittleness on the mechanisms and results of the CPTu test.