Nonconservative Field Research Articles

Allen-Cahn Equation for Modeling Temporal Evolution of Non-Conserved Field Variables in Cancer Cell Migration

Allen-Cahn Equation for Modeling Temporal Evolution of Non-Conserved Field Variables in Cancer Cell Migration

From noise on the sites to noise on the links: Discretizing the conserved Kardar-Parisi-Zhang equationin real space.

Numerical analysis of conserved field dynamics has been generally performed with pseudospectral methods. Finite differences integration, the common procedure for nonconserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work we present a method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents α,β, and z in d=1 and in d=2. To illustrate the potentiality of the method, we further consider the cKPZ equationon different kinds of nonstandard lattices and on the random Euclidean graph. This is a unique numerical study of conserved field dynamics on an irregular topology, paving the way for a broad spectrum of possible applications.

Ordering kinetics in the active Ising model.

We undertake a numerical study of the ordering kinetics in the two-dimensional (2D) active Ising model (AIM), a discrete flocking model with a conserved density field coupled to a nonconserved magnetization field. We find that for a quench into the liquid-gas coexistence region and in the ordered liquid region, the characteristic length scale of both the density and magnetization domains follows the Lifshitz-Cahn-Allen growth law, R(t)∼t^{1/2}, consistent with the growth law of passive systems with scalar order parameter and nonconserved dynamics. The system morphology is analyzed with the two-point correlation function and its Fourier transform, the structure factor, which conforms to the well-known Porod's law, a manifestation of the coarsening of compact domains with smooth boundaries. We also find the domain growth exponent unaffected by different noise strengths and self-propulsion velocities of the active particles. However, transverse diffusion is found to play the most significant role in the growth kinetics of the AIM. We extract the same growth exponent by solving the hydrodynamic equationsof the AIM.

Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws

It is well known that [Formula: see text]-contact geometry is a suitable framework to deal with non-conservative field theories. In this paper, we study some relations between solutions of the [Formula: see text]-contact Euler–Lagrange equations, symmetries, dissipation laws and Newtonoid vector fields. We review the [Formula: see text]-contact Euler–Lagrange equations written in terms of [Formula: see text]-vector fields and sections and provide new results relating the solutions in both approaches. We also study different kinds of symmetries depending on the structures they preserve: natural (preserving the Lagrangian function), dynamical (preserving the solutions), and [Formula: see text]-contact (preserving the underlying geometric structures) symmetries. For some of these symmetries, we provide Noether-like theorems relating symmetries and dissipation laws. We also analyze the relation between [Formula: see text]-contact symmetries and Newtonoid vector fields. Throughout the paper, we will use the damped vibrating string as our main illustrative example.

Assessing the impacts of soil and water conservation practices on soil physicochemical properties in contrasting slope landscapes of Southern Ethiopia

In Ethiopia in general and in the study area, soil erosion, which is the main cause of land degradation, is a significant environmental and agricultural problem. The efficiency of various land management strategies used over time to reduce their detrimental effects on soil quality and health has been questioned. The purpose of this study was to determine the efficacy of soil and water management methods applied to the Offa District of the Wolaita Zone in southern Ethiopia. A total of 36 composite and core soil samples were taken from the topographies of both conserved and non-conserved fields from the top 20 cm soil depth. The collected soil data were examined using analysis of variance (ANOVA), and the mean values of the treatments were separated using the Fisher multiple range test. The results revealed that the physical and chemical properties of soil (pH, Organic carbon, Total nitrogen, Available phosphorus, Cation exchange capacity (CEC), exchangeable basic cations (Ca2+, Mg2+, K+, and Na+), Soil texture, and Bulk density showed a significance difference (p < 0.05) between the measures of soil and water conservation (SWC). The treated soils of Fanya juu, stone bund, and soil bund had the highest soil pH (6.56, 6.56, and 6.11), organic carbon (1.80, 1.62, and 1.76 %), total nitrogen (0.18, 0.16, and 0.17 %), accessible phosphorus (2.72, 2.77, and 1.94 ppm), and all exchangeable basic cations showed higher amount than untreated. The results showed that the implemented SWC structures had high value in restoring and preserving soil nutrients and improving the productive capacity of the soil. This study confirmed the effectiveness of SWC practices in improving soil quality. To achieve soil quality, it's essential to maintain awareness and use of the latest technology. It is strongly advised to highlight the urgent need for SWC training, public awareness, and government support.

Nonautonomous k-contact field theories

This paper provides a new geometric framework to describe non-conservative field theories with explicit dependence on the space–time coordinates by combining the k-cosymplectic and k-contact formulations. This geometric framework, the k-cocontact geometry, permits the development of Hamiltonian and Lagrangian formalisms for these field theories. We also compare this new formulation in the autonomous case with the previous k-contact formalism. To illustrate the theory, we study the nonlinear damped wave equation with external time-dependent forcing.

Analysis of Selected Soil Properties in Relation to Soil and Water Conservation Practices in Sibiya Arera, Soro District, South Central Ethiopia.

Soil erosion by water is a severe and continuous ecological problem in the south central highlands of Ethiopia. Limited use of soil and water conservation technologies by farmers is one of the major causes that have resulted in accelerated soil erosion. Within this context, significant attention has been given to soil and water conservation practices. This study was conducted to investigate the effects of soil and water conservation practices on soil physicochemical properties after being practiced continuously for up to 10 years. The physicochemical properties of soil of landscape with physical soil and water conservation structures without biological conservation measures and physical soil and water conservation structures combined with biological conservation measures were compared with soil of landscape without soil and water conservation practices. The result of analysis disclosed that soil and water conservation interventions (both with biological and without biological measures) significantly increased the soil pH, soil organic carbon, total nitrogen, and available phosphorus content than the soil of landscape without soil and water conservation practices. The results of the analysis also showed that the mean value of cation exchange capacity and exchangeable bases (K+, Na+, Ca2 +, and Mg2 +) of the soil under nonconserved farm field was significantly lower as compared to the soil of adequately managed farm fields. The findings of this study clarified that there was significant variation in soil properties. This variation could be due to uneven transport of soil particles by runoff. Therefore, soil conservation structures supported with biological measures improves the soil's physicochemical properties.

Multicontact formulation for non-conservative field theories

A new geometric structure inspired by multisymplectic and contact geometries, which we call multicontact structure, is developed to describe non-conservative classical field theories. Using the differential forms that define this multicontact structure as well as other geometric elements that are derived from them while assuming certain conditions, we can introduce, on the multicontact manifolds, the variational field equations which are stated using sections, multivector fields, and Ehresmann connections on the adequate fiber bundles. Furthermore, it is shown how this multicontact framework can be adapted to the jet bundle description of classical field theories; the field equations are stated in the Lagrangian and the Hamiltonian formalisms both in the regular and the singular cases.

Direct Measurement of the Electric Field Induced by a Transcranial Magnetic Stimulator

This work proposes a simple method to carry out in lab a direct measurement of the primary solenoidal electric field that transcranial magnetic stimulation coils generate in the brain. This method avoids indirect estimation of this electric field from measurements of magnetic fields, and at the same time, overcomes the difficulty posed by the presence of a dominant conservative electric field, also produced by the coil. This conservative electric field, which is removed in practice by human tissue, is eliminated in the proposed measurement method by using a simple setup that does not require the introduction of the measurement probe inside a conducting solution resembling the human tissue. The proposed measurement method allows for measuring the primary solenoidal electric field in front of the coil in the air. This method has been validated by comparing the results of electromagnetic simulation with the measurement of the magnetic field and the non-conservative electric field produced by a commercial transcranial magnetic stimulation coil.

Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential

In this paper, we investigate optimal control problems for a nonlinear state system which constitutes a version of the Caginalp phase field system modeling nonisothermal phase transitions with a nonconserved order parameter that takes thermal memory into account. The state system, which is a first-order approximation of a thermodynamically consistent system, is inspired by the theories developed by Green and Naghdi. It consists of two nonlinearly coupled partial differential equations that govern the phase dynamics and the universal balance law for internal energy, written in terms of the phase variable and the so-called thermal displacement, i.e., a primitive with respect to time of temperature. We extend recent results obtained for optimal control problems in which the free energy governing the phase transition was differentiable (i.e., of regular or logarithmic type) to the nonsmooth case of a double obstacle potential. As is well known, in this nondifferentiable case standard methods to establish the existence of appropriate Lagrange multipliers fail. This difficulty is overcome utilizing of the so-called deep quench approach. Namely, the double obstacle potential is approximated by a family of (differentiable) logarithmic ones for which the existence of optimal controls and first-order necessary conditions of optimality in terms of the adjoint state variables and a variational inequality are known. By proving appropriate bounds for the adjoint states of the approximating systems, we can pass to the limit in the corresponding first-order necessary conditions, thereby establishing meaningful first-order necessary optimality conditions also for the case of the double obstacle potential.

Energy and Matter Supply for Active Droplets

AbstractChemically active droplets provide simple models for cell‐like systems that can grow and divide. Such active droplet systems are driven away from thermodynamic equilibrium and turn over chemically, which corresponds to a simple metabolism. Two scenarios of nonequilibrium driving are considered. First, droplets are driven via the system boundaries by external reservoirs that supply nutrient and remove waste (boundary‐driven). Second, droplets are driven by a chemical energy provided by a fuel in the bulk (bulk‐driven). For both scenarios, the conservation of energy and matter as well as the balance of entropy are discussed. Conserved and nonconserved fields are used to analyse the nonequilibrium steady states of active droplets. Using an effective droplet model, droplet stability and instabilities leading to droplet division are explored. This work reveals that droplet division occurs quite generally in active droplet systems. The results suggest that life‐like processes such as metabolism and division can emerge in simple nonequilibrium systems that combine the physics of phase separation and chemical reactions.

Generalized nonconservative gravitational field equations from Herglotz action principle

We formulate a nonconservative gravitational theory based on the Herglotz variational principle in a tensorial covariant form. The model presented here may be seen as an improvement of the theory proposed in [ et al., Phys. Rev. D 95, 101501 (2017)], whose resulting field equations are meaningful just in particular coordinate systems. The new theory we report in this work is free from such a restriction. In comparison to the standard general relativity, both theories based on the Herglotz principle contain an extra vector field, the Herglotz field, but the new theory is formulated by taking advantage of the restricted equivalence between Lagrangian functions in the scope of the Herglotz action principle. The more restricted class of equivalent Lagrangian functions, in comparison with the Hamilton variational principle, is the key point to finding a Lagrangian that generates a new alternative gravitational theory in a covariant form. Once the equations that govern the dynamics of the gravitational field are obtained, a few simple cosmological models are investigated. It is found that the Herglotz vector field reduces to a single function that, under certain conditions, plays the role of the cosmological constant in general relativity, turning unnecessary the introduction of dark energy to explain the accelerated expansion of the Universe. The linearized version of the theory is also investigated and it is verified that the theory shows a dissipative character regarding the propagation of gravitational perturbations. From observational data, in both scenarios, the magnitude of the Herglotz field is estimated.

Scaling of the entropy production rate in a φ^{4} model of active matter.

In active φ^{4} field theories the nonequilibrium terms play an important role in describing active phase separation; however, they are irrelevant, in the renormalization group sense, at the critical point. Their irrelevance makes the critical exponents the same as those of the Ising universality class. Despite their irrelevance, they contribute to a nontrivial scaling of the entropy production rate at criticality. We consider the nonequilibrium dynamics of a nonconserved scalar field φ (Model A) driven out-of-equilibrium by a persistent noise that is correlated on a finite timescale τ, as in the case of active baths. We perform the computation of the density of entropy production rate σ and we study its scaling near the critical point. We find that similar to the case of active Model A, and although the nonlinearities responsible for nonvanishing entropy production rates in the two models are quite different, the irrelevant parameter τ makes the critical dynamics irreversible.

Self-controlled wave solutions to the Tzitzeica-type nonlinear models in mathematical physics

Quantum field theory and solid-state physics phenomena are interpreted using the Tzitzeica-Dodd-Bullough model and nonlinear optics and electromagnetic waves are studied through the Dodd-Bullough-Mikhailov equation. The nonlinear Cahn-Allen model is important for describing the evolution of non-conserved order fields during anti-period sphere coarsening and the phase separation reaction–diffusion processes in multicomponent alloy structures. In this article, we have assessed the advanced and broad-spectrum solitary wave solutions to the stated models and studied the effects of wave speed as well as physical coordinates on the wave profiles and affirmed that waveform varies with the change of the free parameters associated to them. The soliton solutions are extracted by balancing the exponents of the highest-order linear and nonlinear terms. To thoroughly analyze the wave characteristic of the closed-form solutions, different standard wave profiles including kink, bell-shaped soliton, anti-peakon, periodic, quasi-periodic, complex singular, and several general solitons are depicted. Both Painlevé and traveling wave transformation play important roles in converting the equations into nonlinear differential equations. The solutions formulated in this probe are further generic, wide-spectral and some are distinctive which have not been established in the former studies.

Review of Cases of Integrability in Dynamics of Lower- and Multidimensional Rigid Body in a Nonconservative Field of Forces

Study of the dynamics of a multidimensional solid depends on the force-field structure. As reference results, we consider the equations of motion of low-dimensional solids in the field of a medium-drag force. Then it becomes possible to generalize the dynamic part of equations to the case of the motion of a solid, which is multidimensional in a similarly constructed force field, and to obtain the full list of transcendental first integrals. The obtained results are of importance in the sense that there is a nonconservative moment in the system, whereas it is the potential force field that was used previously.

A phase-field approach for portlandite carbonation and application to self-healing cementitious materials

A conceptual phase-field model is proposed for simulating complex microstructural evolutions during the self-healing process of cementitious materials. This model specifically considers carbonation healing mechanisms activated by means of dissolution of soluble {hbox {Ca(OH)}_{2}} mineral and precipitation of the {hbox {CaCO}_{3}} self-healing product. The system is described by a set of conservative and non-conservative field variables based on a thermodynamic analysis of the precipitation process and realised numerically using the finite element method (FEM). As a novel concept for modeling self-healing of cementitious materials, the evolution of multiple interfaces was investigated and demonstrated on a simple experimental test case of a self-healing mechanism consisting of carbonating calcium hydroxide. Parametric studies were performed to numerically investigate the effect of chemo-physical conditions. Two representative practical examples of cementitious materials were numerically implemented. It is demonstrated that the simulated evolution of the crack morphology is in good qualitative agreement with the experimental data.

Non-conservative gravitational fields around spinning spherical objects (and the absence of gravitomagnetic fields) as revealed by the Kerr metric

Non-conservative gravitational fields around spinning spherical objects (and the absence of gravitomagnetic fields) as revealed by the Kerr metric

Systems with dissipation with a finite number of degrees of freedom: analysis and integrability. I. Primordial problem from dynamics of a multidimensional rigid body in a nonconservative field of forces

Systems with dissipation with a finite number of degrees of freedom: analysis and integrability. I. Primordial problem from dynamics of a multidimensional rigid body in a nonconservative field of forces

Systems with dissipation with five degrees of freedom: analysis and integrability. I. Primordial problem from dynamics of a multidimensional rigid body in a nonconservative field of forces

Systems with dissipation with five degrees of freedom: analysis and integrability. I. Primordial problem from dynamics of a multidimensional rigid body in a nonconservative field of forces

Skinner–Rusk formalism for k-contact systems

In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of k-contact Hamiltonian systems, which is based on the k-symplectic formulation of field theories as well as on contact geometry. In this work we present the Skinner–Rusk unified setting for these kinds of theories, which encompasses both the Lagrangian and Hamiltonian formalisms into a single picture. This unified framework is specially useful when dealing with singular systems, since: (i) it incorporates in a natural way the second-order condition for the solutions of field equations, (ii) it allows to implement the Lagrangian and Hamiltonian constraint algorithms in a unique simple way, and (iii) it gives the Legendre transformation, so that the Lagrangian and the Hamiltonian formalisms are obtained straightforwardly. We apply this description to several interesting physical examples: the damped vibrating string, the telegrapher's equations, and Maxwell's equations with dissipation terms.