Relaxing Medium Research Articles

Beclomethasone dipropionate, formoterol fumarate and glycopyrronium bromide: Synergy of triple combination therapy on human airway smooth muscle ex vivo.

Combining inhaled corticosteroids (ICSs), long-acting β2 -adrenoceptor agonists (LABAs) and long-acting muscarinic antagonists (LAMAs) is recommended to treat severe forms of asthma and chronic obstructive pulmonary disease (COPD). Clinical benefits have been demonstrated for ICS/LABA/LAMA combinations. This study characterized the interaction between the ICS beclomethasone dipropionate, the LABA formoterol fumarate and the LAMA glycopyrronium bromide in human airways. Human passively sensitized airways and bronchi from COPD donors were stimulated with histamine or carbachol. Tissues were incubated overnight with beclomethasone and then treated with formoterol and glycopyrronium, alone or in triple combination. The interaction was assessed by using Bliss Independence and Unified Theory theorems. Beclomethasone/formoterol/glycopyrronium combination synergistically relaxed medium bronchi and small airways. Beclomethasone/formoterol/glycopyrronium combination at 100:6:12.5 combination ratio was a balanced drug mixture leading to very strong synergistic effect on relaxation of medium bronchi (Combination Index: from 0.042 to 0.96) and middle to very strong synergy in small airways (Combination Index: from 0.018 to 0.310). The synergy was related with the activation of intracellular glucocorticoid receptors and Gsα subunit G-protein of β2 -adrenoceptors, leading to the modulation of cyclic AMP-dependent PKA pathway. Triple beclomethasone/formoterol/glycopyrronium combination induces synergistic bronchorelaxant effect in medium and small human airways, at least in ex vivo experiments. Further research is needed to confirm these findings in clinical studies in patients with asthma or COPD.

How frictional response during solute solvation controls solute rotation in naturally abundant deep eutectic solvent (NADES)? A case study with amino acid derivative containing DES

We explored frictional response of a room temperature naturally abundant deep eutectic solvent made of betaine, urea and water ([Bet:Ure:Wat (11.7:12:1 weight ratio)]) via temperature dependent measurements of solute-centered dynamics, and characterized the coupling between the relaxation rates and medium friction. Time-resolved fluorescence studies with this medium at different temperatures revealed fractional viscosity dependencies for solute rotation and solvation rates, suggesting strong temporal heterogeneity in the medium. Intriguingly, such a substantial viscosity decoupling was found to occur at a temperature ~90–130 K above the measured glass transition temperature (Tg~218 K) of this amino acid derivative containing DES. Estimated activation energies from dynamic fluorescence anisotropies of hydrophobic and hydrophilic solutes were nearly half (~30 kJ mol−1) of that estimated from temperature dependent viscosity measurements (~57 kJ mol−1). Both rotational and solvation energy relaxations for these solutes were found strongly non-exponential yet the friction that controlled solute's rotation in this biodegradable deep eutectic solvent did not fully map the resistance that medium particles experienced while solvating the solute. This is new, and contrasting to results found for several complex systems that include ionic deep eutectics, ionic liquids, and confined water. This observation should be reexamined via more sophisticated measurements. Temperature dependent densities and refractive indices were measured to understand the dipolar solvation response in this medium, particularly the correctness of the missing components estimated from a well-known approximate method developed for conventional room temperature polar solvents.

Microstructure-related Stoneley waves and their effect on the scattering properties of a 2D Cauchy/relaxed-micromorphic interface

In this paper we set up the full two-dimensional plane wave solution for scattering from an interface separating a classical Cauchy medium from a relaxed micromorphic medium. Both media are assumed to be isotropic and semi-infinite to ease the semi-analytical implementation of the associated boundary value problem.Generalized macroscopic boundary conditions are presented (continuity of macroscopic displacement, continuity of generalized tractions and, eventually, additional conditions involving purely microstructural constraints), which allow for the effective description of the scattering properties of an interface between a homogeneous solid and a mechanical metamaterial. The associated “generalized energy flux” is introduced so as to quantify the energy which is transmitted at the interface via a simple scalar, macroscopic quantity.Two cases are considered in which the left homogeneous medium is “stiffer” and “softer” than the right metamaterial and the transmission coefficient is obtained as a function of the frequency and of the direction of propagation of the incident wave. We show that the contrast of the macroscopic stiffnesses of the two media, together with the type of boundary conditions, strongly influence the onset of Stoneley (or evanescent) waves at the interface. This allows for the tailoring of the scattering properties of the interface at both low and high frequencies, ranging from zones of complete transmission to zones of zero transmission well beyond the band-gap region.

Piecewise parabolic method for propagation of shear shock waves in relaxing soft solids: One-dimensional case.

Shear shock waves can be generated spontaneously deep within the brain during a traumatic injury. This recently observed behavior could be a primary mechanism for the generation of traumatic brain injuries. However, shear shock wave physics and its numerical modeling are relatively unstudied. Existing numerical solvers used in biomechanics are not designed for the extremely large Mach numbers (greater than 1) observed in the brain. Furthermore, soft solids, such as the brain, have a complex nonclassical viscoleastic response, which must be accurately modeled to capture the nonlinear wave behavior. Here, we develop a 1D inviscid velocity-stress-like system to model the propagation of shear shock waves in a homogeneous medium. Then a generalized Maxwell body is used to model a relaxing medium that can describe experimentally determined attenuation laws. Finally, the resulting system is solved numerically with the piecewise parabolic method, a high-order finite volume method. The nonlinear and the relaxing components of this method are validated with theoretical predictions. Comparisons between numerical solutions obtained for the proposed model and the experiments of plane shear shock wave propagation based on high frame-rate ultrasound imaging and tracking are shown to be in excellent agreement.

Intense Pulses in Relaxing Media with Limited “Memory Time,” Power-Law and Nonanalytic Nonlinearities

Processes that accompany propagation of time-limited pulsed signals in a relaxing medium are investigated for the case of a nonlinear medium with power-law (quadratic or cubic) nonlinearity or nonanalytic nonlinearity (modular or quadratically cubic one). Instead of ordinary integro-differential equations with exponential or fractional-power kernels, a simplified model of a medium with finite “memory time” is used. Such a medium “remembers” its prehistory within a limited time interval, and the corresponding kernel of the integral term is nonzero only within a finite interval. For this model, the problem is reduced to solving a difference-differential equation, which considerably reduces the amount of calculations, as compared to the initial integral equation. The processes that accompany evolution of pulses, namely, the formation of compression and rarefaction shock fronts and the appearance of triangular and trapezoidal nonlinear structures, are described. Effect of relaxation time on these processes is revealed.

Simulation of Self-sustained Relaxation of a Two-dimensional Metastable Medium by Means of a Traveling Wave

The traveling wave mode of self-sustained relaxation of a metastable medium, such as combustion and annealing of radiation-induced defects in solids, is studied. The mechanism of self-sustained relaxation and propagation of the traveling wave is a positive thermal-concentration feedback and heat transfer. The thermal-concentration feedback develops because the relaxation rate depends strongly on temperature, and the energy of the metastable state transforms into thermal energy in the process of relaxation. Hence, the relaxation leads to an increase in the medium temperature and, consequently, to further support of the relaxation. In this work, traveling waves are considered, and their features are investigated by computer simulation. The shape and speed of the traveling wave are investigated as a function of the medium properties, and the way of its initiation. We examined the shapes of wavefronts as they propagate on a plane, and observed two different regimes of traveling wave propagation. Sometimes the front of the traveling wave spreads as a whole and velocity of propagation is perpendicular to the wavefront. Sometimes small perturbations arise on the wavefront, and then grow by virtue of relaxation along the front, thus, the new area of the relaxed medium has the form of a narrow strip that propagates along the line of the front and maintains a constant width in the direction perpendicular to the front. We observe the appearance of one or more small perturbations, which arise in a symmetric way. The influence of boundaries on the traveling waves was also investigated.

Locally One-Dimensional Difference Schemes for Parabolic Equations in Media Possessing Memory

Many processes in complex systems are nonlocal and possess long-term memory. Such problems are encountered in the theory of wave propagation in relaxing media [1, p. 86], whose equation of state is distinguished by a noninstantaneous dependence of the pressure p(t) on the density ρ(t); the value of p at a time t is determined by the value of the density ρ at all preceding times; i.e., the medium has memory. Similar problems are also encountered in mechanics of polymers and in the theory of moisture transfer in soil [2]; the same equation arises in the theory of solitary waves [3] and is also called the linearized alternative Korteweg–de Vries equation, or the linearized Benjamin–Bona–Mahony equation. One of such problems was studied in [4]. In the present paper, a locally one-dimensional scheme for parabolic equations with a nonlocal source, where the solution depends on the time t at all preceding times, is considered.

Plane nonlinear shear waves in relaxing media.

Model equations with cubic nonlinearity are developed for a plane shear wave of finite amplitude in a relaxing medium. The evolution equation for progressive waves is solved analytically for a jump in stress that propagates into an undisturbed medium. Weak-shock theory is used to determine the amplitude and location of the shock when the solution predicts a multivalued waveform. The solution is similar to that obtained by Polyakova, Soluyan, and Khokhlov [Sov. Phys. Acoust. 8, 78-82 (1962)] for a compressional wave with quadratic nonlinearity in a relaxing fluid. Numerical simulations illustrate the effect of relaxation on shock formation in an initially sinusoidal shear wave. The minimum source amplitude required for an initially sinusoidal waveform to develop shocks in a relaxing medium is determined as a function of the dispersion and relaxation time. Limiting forms of the evolution equation are considered, and analytical solutions incorporating weak-shock theory are presented in the high-frequency limit. A Duffing-type model for a nonlinear shear-wave resonator is developed and investigated.

Simulation of plastic deformation and destruction in the process of chip formation

Metal cutting is a complex process in which several mechanisms are at work simultaneously. The mathematical modelling allows carrying out research into the optimization of machining conditions. This work examines the simulation of chip formation during the process of cutting. The studies demonstrated that the chip formation process, taking into account the plastic deformation and destruction of metal in the local zone, is most appropriately represented by a rheological model in the form of a series connection of elasticductile- plastic relaxing medium of Ishlinskiy (reflecting the process of primary deformation of metal from the cut off layer) and the medium of Voigt with two elastic-dissipative elements (representing the process of deformation and frictions from the convergent shaving). The attained complex rheological model served as the basis for constructing a representative dynamic model for the chip formation process. The key factors that govern the chip formation have been taken into account, such as tool vibration frequency and amplitude, depth of cut, feed rate.

The N-loop soliton solutions for [formula omitted]-dimensional Vakhnenko equation

A (2+1)-dimensional Vakhnenko equation is investigated, which describes high-frequent wave propagations in relaxing medium. The N-loop soliton solutions for the equation are calculated by applying the improved Hirota method and the variable transformations. The N-loop soliton solutions can be expressed explicitly. Furthermore, the interaction patterns are graphically observed for the N-loop soliton solutions. The dynamical interactions among the N-solitons (N≥2) are elastic.

Exact solutions of an integro-differential equation with quadratically cubic nonlinearity

Exact solutions of a nonlinear integro-differential equation with quadratically cubic nonlinear term are found. The equation governs, in particular, stationary shock wave propagation in relaxing media. For the exponential kernel the shapes of both compression and rarefaction shocks having a finite width of the front are calculated. For media with limited “memorizing time” the difference relation permitting the construction of wave profile by the mapping method is derived. The initial equation is rather general. It governs the evolution of nonlinear waves in real distributed systems, for example, in biological tissues, structurally inhomogeneous media and in some meta-materials.

Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE) as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE), by a change of independent variables. The VPE has anN-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprisesN-loop-like solitons. Aspects of the inverse scattering transform (IST) method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads toN-soliton solutions andM-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

Dynamic simulation of chip formation in the process of cutting

This work examines the simulation of chip formation during the process of cutting. An analysis of complex rheological models enabled a set of assumptions to be considered, thereby substantiating a hypothesis relating to the chip formation process. The studies demonstrated that the chip formation process, taking into account the plastic deformation and destruction of metal in the local zone, is most appropriately represented by a rheological model in the form of a series connection of elastic-ductile-plastic relaxing medium of Ishlinskiy (reflecting the process of primary deformation of metal from the cut off layer) and the medium of Voigt with two elastic-dissipative elements (representing the process of deformation and frictions from the convergent shaving). The attained complex rheological model served as the basis for constructing a representative dynamic model for chip formation process.

Barothropic relaxing media under pressure perturbations: Nonlinear dynamics

In this paper, we delve into the dynamics of a barothropic relaxing medium under pressure perturbations originating from blast wave explosions in the milieu. Analyzing the problem within the viewpoint of the Lyakhov formalism of geodynamic systems, we derive a complex-valued nonlinear evolution equation which models the wave propagation of the pressure perturbations within the barothropic medium. As a result, we find that the previous system can be circularly polarized and hence support traveling rotating pressure excitations which profiles strongly depend upon their angular momenta. In the wake of these results, we address some physical implications of the findings alongside their potential applications.

Plane nonlinear shear waves in relaxing media

Plane nonlinear shear waves in relaxing media

Deformation models under intense dynamic loading (Review)

This paper considers currently available models of irreversible deformation processes of materials under dynamic, in particular shock-wave, loading. The models can be divided into three groups: (1) macroscopic (continuum) models—traditional models of continuum mechanics, primarily classical models of elastic-plastic deformation, their various generalizations to the case of dynamic processes and models of viscoelastic relaxation media; (2) microstructural models based on the description of microstructural mechanisms of irreversible deformation (usually, the concept of the kinetics of a dislocation ensemble); (3) atomistic molecular dynamics models and calculations. A special category includes the most promising (from the point of view of the author) multilevel models which combine the advantages of each of these approaches and consider deformation mechanisms of various levels. Examples of calculations using such models are presented.

Еволюцiя хвильових полiв у блокових релаксуючих середовищах

Еволюцiя хвильових полiв у блокових релаксуючих середовищах

Head-on collisions of localized pressure excitations in derivative cubic relaxing media: dynamical structure survey

In the wake of the recent derivation of the new cubic nonlinear evolution equation of high-frequency pressure perturbations of a barothropic medium under relaxation (Kuetche V K et al 2014 J. Math. Phys. 55 052702), we closely investigate the head-on collisions of some typical localized waveguide excitations, which are solutions to the previous system. From the viewpoint of Hirotaʼs formalism, we delve into the structural scattering features of the interacting waves mentioned above. As a result, we find that there might exist some ‘characteristic’ amplitude ratio of the interacting waves at which the scattering changes its features. Accordingly, we provide an illustration of the previous result within the depiction of the interactions between three single soliton solutions alongside the phase-shift of each particle. Following these depictions, we address some physical implications of the results as well as the different potential applications.

Хвильові локалізовані структури в релаксуючих середовищах з флуктуаціями

Хвильові локалізовані структури в релаксуючих середовищах з флуктуаціями

On Stationary Solutions of the Reduced Gardner–Ostrovsky Equation

The detailed analysis of stationary solutions of the reduced Gardner–Ostrovsky (GO) equation is presented. The GO equation is the popular model for the description of large-amplitude internal oceanic waves affected by Earth’s rotation. Its reduced version in which the small-scale dispersion is neglected is used when very long internal waves are considered. The equation is also applicable to other types of nonlinear waves in various media (plasma, optical media, relaxing media, etc.) when the large-scale dispersion plays a dominant role in comparison with the small-scale dispersion. Balancing the nonlinear effect such dispersion gives rise to existence of stationary waves, both periodic and non-periodic. It is shown that only smooth periodic waves make physical sense. Systematic analysis of stationary solutions to the GO equation and their categorisation is presented.