Tensor Functions Research Articles

Modelling and simulation of coupled fluid transport and time-dependent fracture in fibre-reinforced hydrogel composites

Physicochemical and mechanical stimuli can trigger fluid transport and inelastic solid deformations in the fracture process of anisotropic hydrogel composites. The underlying mechanisms for the time-dependent deformation and fracture behaviour of hydrogel composites remain elusive and poorly understood. The present work develops an anisotropic poro-visco-hyperelastic-damage model based on the theory of porous media (TPM) to analyse the relationship between the coupled time-dependent behaviours, i.e.visco-hyperelasticity and fluid transport, and the fracture behaviour of hydrogel composites. The visco-hyperelasticity of the polymer networks resulting from the breaking and reforming kinetics of physical bonds is described by introducing internal variables based on the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic parts. The fluid transport through the porous polymer networks is governed by Darcy’s law. A continuum damage model is proposed to describe the mechanical degradation of the anisotropic hydrogel composites, e.g., the cross-link unzipping and chain scission in polymer networks as well as the damage and breaking of embedded nanofibres. An integral-type nonlocal averaging algorithm is employed in the proposed damage model to eliminate the mesh dependence of numerical simulations. Furthermore, an operator split integration algorithm and an exponential mapping algorithm are applied to integrate evolution equations for internal variables and stresses. The resulting exponential tensor function is computed via spectral decompositions. The consistent tangent operators for an implicit finite element procedure are derived in detail in this contribution. Three representative numerical examples are used to validate the proposed model and investigate the mechanisms of the time-dependent fracture behaviour of anisotropic hydrogel composites. The computational results demonstrate that the proposed model can capture the fracture behaviour of hydrogel composites with different fibre orientations.

Weighted generalized tensor functions based on the tensor-product and their applications

There are three weighted decompositions of tensors proposed in this paper, and the corresponding definitions of the weighted generalized tensor functions are given. The Cauchy integral formula of the weighted Moore-Penrose inverse is developed for solving the tensor equations. Besides above, we give the weighted projection tensors to discuss the representations of the weighted generalized power of tensors. Finally, some special tensors are studied which can preserve the structural invariance under the tensor functions defined in this paper.

Quantum Field Theory and its Anomalies for Topological Matter

Topology enters in quantum field theory (qft) in multiple forms: one of the most important, in non-abelian gauge theories, being in the identification of the θ vacuum in QCD. A very relevant aspect of this connection is through the phenomenon of chiral and conformal qft anomalies. It has been realized that a class of materials, comprising topological insulators and Weyl semimetals, also exhibit the phenomenon of anomalies, which are responsible for several exotic phenomena, such as the presence of edge currents, resilient under perturbations and scattering by impurities. Another example comes from the response functions of these materials under thermal and mechanical stresses, that may be performed using correlation functions of stress energy tensors in General Relativity. In this case the conformal anomaly plays an important role. We briefly illustrate some salient features of this correspondence, and the effective action describing the long-range interactions that may account for such topological effects.

The influence of a metal rod inside a spherical Luneberg lens on its characteristics

The paper discusses the option of installing a load-bearing element inside a spherical Luneberg lens (LL). The presence of a metal element inside the LL will increase the structural rigidity of the spherical antenna and thereby expand the scope of use of the LL at various mobile communications and radar facilities with severe operating conditions. The influence of a metal rod inside the main spherical structure on the radiation pattern in two main planes in the linear polarization mode and on the diffraction pattern of the radiation field is estimated. The results of the analysis of the directional characteristics and the diffraction pattern of the LL radiation field were obtained using modeling in the Ansys Electronics Desktop (HFSS Design) working environment, as well as mathematical modeling using the Green tensor function method. At the same time, the obtained mathematical relations can be used in the future to solve the problem of finding the optimal size and position of a metal element in the sphere of LL.

Generalized MBI Algorithm for Designing Sequence Set and Mismatched Filter Bank With Ambiguity Function Constraints

A sequence set with ambiguity function (AF) specifications is frequently required in multi-transmit active sensing systems which exploit waveform diversity. This paper formulates a new model to jointly design sequence set and mismatched filter bank with AF requirements, which is a generalization of the auto-AF and cross-AF adopted in the matched filter scheme to attain lower AF sidelobe levels with an increased degree-of-freedom. The aforementioned designs result in nonconvex and nonlinear high-order polynomial (HOP) optimization problems with HOP constraints. Although the maximum block improvement (MBI) method has exhibited the powerful HOP optimization ability to design a short sequence with slow-time AF, it cannot tackle HOP constraints and involves high-complexity tensor operations. To address these issues, we develop a generalized MBI method for the HOP constrained optimization formulations. In addition, the proposed algorithm significantly reduces the computational complexity via designing an equivalent polynomial function for the original multi-linear tensor function. Numerical results demonstrate the excellent performance of our design solutions.

ON DIFFUSE INSTABILITY OF ORTHOTROPIC VISCOPLASTIC PLATES

Elastic strain is covered by the effective medium homogenization method inside a representative volume element (RVE). It has an incremental quasi rate-independent (QRI) form obtained by the endochronic concept of thermodynamic time. The rate dependence takes place by means of stress rate dependent value of the initial yield stress. Free meso rotations and constrained micro rotations within a representative volume element (RVE) are assumed. A comparison between QRI and J2 diffuse instability equations is presented for orthotropic materials. A new QRI nonlinear evolution equation for orthotropic materials is derived by tensor function representation with Spencer-Boehler structural tensors.

Exact static spherical symmetric soliton-like solutions to the scalar and electromagnetic nonlinear induction field equations in general relativity

In this paper, we have obtained exact static spherical symmetric soliton-like solutions to the electromagnetic and scalar nonlinear induction field equations taking into account the own gravitational field of the elementary. The results show that the metric tensor functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of elementary particles has a finite value. The importance of the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions have been proved.

Formulation of a Basic Constitutive Model for Fine - Grained Soils Using the Hypoplastic Framework

Abstract A hypoplastic approach to constitutive modelling was developed by Kolymbas 1996 considering a non-linear tensor function in the form of strain and stress rate. However, the implicit formulation of the hypoplastic model with indirect material parameters severely limits its applicability to real-world geotechnical problems. In many cases, the numerical analysis of geotechnical problems relies on simple elastoplastic constitutive models that cannot model a wide range of soil response aspects. One promising paradigm of constitutive modelling in geotechnics is hypoplasticity, but many of the hypoplastic models belong to advanced models. In the article, we present the simple hypoplastic model as an alternative to the widely used Mohr-Coulomb elastoplastic model.

Bulk contributions to the Casimir interaction of Dirac materials

Exploiting methods of Quantum Field Theory we compute the bulk polarization tensor and bulk dielectric functions for Dirac materials in the presence of a mass gap, chemical potential, and finite temperature. Using these results (and neglecting eventual boundary effects), we study the Casimir interaction of Dirac materials. We describe in detail the characteristic features of the dielectric functions and their influence on the Casimir pressure.

Olfactory Function and Diffusion Tensor Imaging as Markers of Mild Cognitive Impairment in Early Stages of Parkinson's Disease.

Parkinson's disease (PD) is a neurodegenerative disorder that is typified by motor signs and symptoms but can also lead to significant cognitive impairment and dementia Parkinson's Disease Dementia (PDD). While dementia is considered a nonmotor feature of PD that typically occurs later, individuals with PD may experience mild cognitive impairment (PD-MCI) earlier in the disease course. Olfactory deficit (OD) is considered another nonmotor symptom of PD and often presents even before the motor signs and diagnosis of PD. We examined potential links among cognitive impairment, olfactory functioning, and white matter integrity of olfactory brain regions in persons with early-stage PD. Cognitive tests were used to establish groups with PD-MCI and with normal cognition (PD-NC). Olfactory functioning was examined using the University of Pennsylvania Smell Identification Test (UPSIT) while the white matter integrity of the anterior olfactory structures (AOS) was examined using magnetic resonance imaging (MRI) diffusion tensor imaging (DTI) analysis. Those with PD-MCI demonstrated poorer olfactory functioning and abnormalities based on all DTI parameters in the AOS, relative to PD-NC individuals. OD and microstructural changes in the AOS of individuals with PD may serve as additional biological markers of PD-MCI.

Ascending–descending and direct–inverse cascades of Reynolds stresses in turbulent Couette flow

The interaction between small- and large-scale structures and the coexisting bottom-up and top-down processes are studied in a turbulent plane Couette flow, where space-filling longitudinal rolls appear at relatively low values of the Reynolds number $Re$ . A direct numerical simulation database at $Re_\tau =101$ is built to replicate the highest $Re$ considered in recent experimental work by Kawata & Alfredsson (Phys. Rev. Lett., vol. 120, 2018, 244501). Our study is based on the exact budget equations for the second-order structure function tensor $\left \langle {\delta u_i \delta u_j} \right \rangle$ , i.e. the anisotropic generalized Kolmogorov equations (AGKE). The AGKE study production, redistribution, transport and dissipation of every Reynolds stress tensor component, considering simultaneously the physical space and the space of scales, and properly define the concept of scale in the inhomogeneous wall-normal direction. We show how the large-scale energy-containing motions are involved in the production and redistribution of the turbulent fluctuations. Both bottom-up and top-down interactions occur, and the same is true for direct and inverse cascading. The wall-parallel components $\left \langle {\delta u \delta u} \right \rangle$ and $\left \langle {\delta w \delta w} \right \rangle$ show that both small and large near-wall scales feed the large scales away from the wall. The wall-normal component $\left \langle {\delta v \delta v} \right \rangle$ is different, and shows a dominant top-down dynamics, being produced via pressure-strain redistribution away from the wall and transferred towards near-wall larger scales via an inverse cascade. The off-diagonal component shows a top-down interaction, with both direct and inverse cascades, albeit the latter takes place within a limited range of scales.

Asymptotic homogenization approach for anisotropic micropolar modeling of periodic Cauchy materials

A micropolar-based asymptotic homogenization approach for the analysis of composite materials with periodic microstructure is proposed. The upscaling relations, conceived to determine the macro-descriptors (macro displacement and the micropolar rotation fields) as a function of the micro displacement field, are consistently derived in the asymptotic framework. In particular, the micropolar rotation field is expressed in terms of the microscopical infinitesimal rotation tensor and perturbation functions. The micro displacement field is, in turn, obtained by choosing a third order approximation of the asymptotic expansion, in which the macroscopic fields are expressed as a third order polynomial expansion. It follows that the macro descriptors are directly related to both perturbation functions and micropolar two-dimensional deformation modes. Furthermore, a properly conceived energy equivalence between the macroscopic point and a microscopic representative portion of the periodic composite material is introduced to derive the consistent overall micropolar constitutive tensors. It is pointed out that these constitutive tensors are not affected by the choice of the periodic cell. Moreover, in the case of vanishing microstructure the internal-length-scale-dependent constitutive tensors tend to zero, as expected. Finally, the capabilities of the proposed approach are shown through some illustrative examples.

Robust Multi-Frame Super-Resolution Based on Adaptive Half-Quadratic Function and Local Structure Tensor Weighted BTV.

It is difficult to improve image resolution in hardware due to the limitations of technology and too high costs, but most application fields need high resolution images, so super-resolution technology has been produced. This paper mainly uses information redundancy to realize multi-frame super-resolution. In recent years, many researchers have proposed a variety of multi-frame super-resolution methods, but it is very difficult to preserve the image edge and texture details and remove the influence of noise effectively in practical applications. In this paper, a minimum variance method is proposed to select the low resolution images with appropriate quality quickly for super-resolution. The half-quadratic function is used as the loss function to minimize the observation error between the estimated high resolution image and low-resolution images. The function parameter is determined adaptively according to observation errors of each low-resolution image. The combination of a local structure tensor and Bilateral Total Variation (BTV) as image prior knowledge preserves the details of the image and suppresses the noise simultaneously. The experimental results on synthetic data and real data show that our proposed method can better preserve the details of the image than the existing methods.

Two shear driven flow regimes in microfluidic nematic devices: Tumbling and laminar

The purpose of this study is to show how the tangential component of the shear stress (SS) σzx applied to the boundary of the microsized nematic channel containing a temperature gradient ∇T effects the character of director field n̂ evolution to its stationary orientation n̂st. Calculations based on extension of the classical Ericksen-Leslie theory, supplemented by thermomechanical correction of the stress tensor and Rayleigh dissipation function, with accounting the entropy balance equation, show that due to coupling among the SS σzx,∇T, and ∇n̂ in confined hybrid aligned nematic (HAN) channel the horizontal nematic flow v may be excited. Calculations also show that there is a difference in the evolution of n̂ to its stationary orientation n̂st, in the “laminar” case of confined nematic phase, composed of 4-cyano-4′-pentylbiphenyl(5CB) molecules, when -γ2/γ1>1, and in the “tumbling” case of confined nematic phase, composed of 4-cyano-4′-octylbiphenyl(8CB) molecules, when -γ2/γ1<1, respectively. It has been also shown the possible way how to set up a temperature difference ΔT=Tup-Tlw across the HAN microfluidic channel, initially equal to zero, under the action of σzx applied to the boundary of the HAN channel.

Anisotropic optical properties of Cu2ZnSn(SxSe1−x)4 solid solutions: First-principles calculations with TB-mBJ+U

The main aim of this work is to determine and explain the relationships between optoelectronic properties and the sulfur anion content in Cu2ZnSn(SxSe1−x)4 solid solution. Band gap and absorption coefficient are of primary interest to the engineers and scientists researcher worked in optoelectronic field. Herein, the electronic and optical properties are calculated based on 128 conventional atoms within lattice parameters obtained at 300 K by using the FP-LAPW method combined with quasi-harmonic Debye model. The composition dependent band gaps of CZTSSe solid solutions are investigated by TB-mBJ+U. As results, all materials are semiconductors with a direct band gap ranging from 0.614 to 0.99 eV. The band gap variation increases as a function of sulfur anion content and showed a positive deviation from Vegard's law with a very small downward bowing parameter of + 0.079 eV. The density of state (DOS) calculations indicate that the energy bands of VBM involve Cu_d/anion(S/Se)_p hybridized antibonding-like states. Based on band alignment, the Ec offset between CZTS and CZTSe is larger than the Ev offset. These results are reported previously in other work and are confirmed in this study. Our work included a systematic comparison of the influence of S/(S+Se) atomic ratios on optical quantities. The dielectric function tensors show remarkable anisotropy. In addition, the static dielectric constants are found to decrease with sulfur anion content. The CZTSSe is proved to be suitable for good solar cells with high absorption coefficient (> 104 cm−1). Such deep optical studies would be helpful for future optoelectronic applications of these compounds with different S/(S+Se) atomic ratios.

Squeeze Flow of Stress Power Law Fluids

In this paper, we studied the squeeze flow between circular disks of a new class of fluids defined by an implicit relation referred to as stress power law fluids. The constitutive response of these fluids was written expressing the symmetric part of the velocity gradient as a tensorial function of the Cauchy stress. We assumed that the aspect ratio between the gap separating the disks and the radius was small so that a lubrication expansion could be adopted. We wrote the general problem and looked for a solution that could be written in terms of the small aspect ratio parameter. We obtained a sequence of problems that could be solved iteratively at each order, and we focused on the leading and first order, deriving explicit expressions for the velocity field, stress, and pressure.

One-loop Kubo estimations of the shear and bulk viscous coefficients for hot and magnetized bosonic and fermionic systems

The expressions of the shear viscosity and the bulk viscosity components in the presence of an arbitrary external magnetic field for a system of hot charged scalar bosons (spin 0) as well as for a system of hot charged Dirac fermions (spin $\frac{1}{2}$) have been derived by employing the one-loop Kubo formalism. This is done by explicitly evaluating the thermomagnetic spectral functions of the energy-momentum tensors using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In the present work, a rich quantum field theoretical structure in the expressions of the viscous coefficients in nonzero magnetic field are found, which are different from their respective expressions obtained earlier via kinetic-theory-based calculations; though, in the absence of a magnetic field, the one-loop Kubo and the kinetic-theory-based expressions for the viscosities are known to be identical. We have identified that Kubo and kinetic-theory-based results of viscosity components follow a similar kind of temperature and magnetic field dependency. The relaxation time and the synchrotron frequency in the kinetic theory formalism are realized to be connected, respectively, with the thermal width of propagator and the transitions among the Landau levels of the charged particles in the Kubo formalism. We believe that the connection of the latter quantities is quite new and probably the present work is the first time addressing this interpretation along with the new expressions of viscosity components, not seen in existing works.

Bounds on Regge growth of flat space scattering from bounds on chaos

We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the ‘causally scattering configuration’ in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than s2 in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.

Narrative review of epilepsy: getting the most out of your neuroimaging.

Neuroimaging represents an important step in the evaluation of pediatric epilepsy. The crucial role of brain imaging in the diagnosis, follow-up and presurgical assessment of patients with epilepsy is noted and has to be familiar to all neuroradiologists and trainees approaching pediatric brain imaging. Morphological qualitative imaging shows the majority of cerebral lesions/alterations underlying focal epilepsy and can highlight some features which are useful in the differential diagnosis of the different types of epilepsy. Recent advances in MRI acquisitions including diffusion-weighted imaging (DWI), post-acquisition image processing techniques, and quantification of imaging data are increasing the accuracy of lesion detection during the last decades. Functional MRI (fMRI) can be really useful and helps to identify cortical eloquent areas that are essential for language, motor function, and memory, and diffusion tensor imaging (DTI) can reveal white matter tracts that are vital for these functions, thus reducing the risk of epilepsy surgery causing new morbidities. Also positron emission tomography (PET), single photon emission computed tomography (SPECT), simultaneous electroencephalogram (EEG) and fMRI, and electrical and magnetic source imaging can be used to assess the exact localization of epileptic foci and help in the design of intracranial EEG recording strategies. The main role of these “hybrid” techniques is to obtain quantitative and qualitative informations, a necessary step to evaluate and demonstrate the complex relationship between abnormal structural and functional data and to manage a “patient-tailored” surgical approach in epileptic patients.

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Based on the Cayley-Hamilton theorem and fixed-point method, we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional (3D) inner-product space, which avoids introducing the generating function and Taylor series expansion. The proof is also extended to any finite-dimensional inner-product space.