Instability Domain Research Articles

Charge transport in DNA model with vibrational and rotational coupling motions

The dynamics of the Peyrard-Bishop model for vibrational motion of DNA dynamics, which has been extended by taking into account the rotational motion for the nucleotides (Silva et al., J. Biol. Phys. 34, 511–519, 2018) is studied. We report on the presence of the modulational instability (MI) of a plane wave for charge migration in DNA and the generation of soliton-like excitations in DNA nucleotides. We show that the original differential-difference equation for the DNA dynamics can be reduced in the continuum approximation to a set of three coupled nonlinear equations. The linear stability analysis of continuous wave solutions of the coupled systems is performed and the growth rate of instability is found numerically. Numerical simulations show the validity of the analytical approach with the generation of wave packets provided that the wave numbers fall in the instability domain.

Three-dimensional processing maps and microstructural evolution of a CNT-reinforced Al-Cu-Mg nanocomposite

The determination of the optimum processing window of a material at elevated temperatures is essential for metal forming. Such an “ideal” processing window could be characterized by the workability parameters of power dissipation efficiency, Ziegler's instability criteria, and the presence of favorable microstructures. The purpose of the present study is to develop three-dimensional (3D) processing maps of a 2.0wt% carbon nanotube (CNT) reinforced 2024Al nanocomposite and to manifest continuous changes of power dissipation efficiency and flow instability domains involving key processing parameters of temperature, strain rate, and strain via isothermal compressive tests. The optimal hot working parameters of the 2024Al base alloy and the 2.0wt% CNT/2024Al nanocomposite were identified to be at higher temperatures and lower strain rates, with a moderately smaller processing window for the nanocomposite due to the strengthening effect of CNTs and microstructural complexities. Instability occurred at higher strain rates and lower temperatures for both base alloy and nanocomposite. In the stable domain dynamic recrystallization was observed to occur, and the fraction of recrystallized grains increased with increasing deformation temperature, along with the presence of more random textures.

Parametric resonance and jump analysis of a beam subjected to periodic mass transition

In this paper, the dynamic stability of a simply supported beam excited by the transition of circulating masses is investigated by preserving nonlinear terms in the analysis. The intermittent loading across the beam results in a time-varying periodic equation. The effects of convective mass acceleration besides large deformation beam theory are both considered in the derivation of governing equations which is performed through adopting a variable-mass-system approach. In order to deal with the coupling between longitudinal and transversal deflections, the inextensibility assumption is implicitly introduced into the Hamiltonian formulation to reduce the model order. An appropriate interpretation is presented in order to maintain this approximation reasonable. Different semi-analytical methods are implemented to find the domains of stability and instability of the problem in a parameter space. By accounting the non-autonomous form of the governing equations, a qualitative change in behavior due to nonlinear terms is demonstrated which has not been addressed in previous studies.

The interaction between cytosine methylation and processes of DNA replication and repair shape the mutational landscape of cancer genomes.

Methylated cytosines (5mCs) are frequently mutated in the genome. However, no studies have yet comprehensively analysed mutation–methylation associations across cancer types. Here we analyse 916 cancer genomes, together with tissue type-specific methylation and replication timing data. We describe a strong mutation–methylation association across colorectal cancer subtypes, most interestingly in samples with microsatellite instability (MSI) or Polymerase epsilon (POLE) exonuclease domain mutations. By analysing genomic regions with differential mismatch repair (MMR) efficiency, we suggest a possible role for MMR in the correction of 5mC deamination events, potentially accounting for the high rate of 5mC mutation accumulation in MSI tumours. Additionally, we propose that mutant POLE asserts a mutator phenotype specifically at 5mCs, and we find coding mutation hotspots in POLE-mutant cancers at highly-methylated CpGs in the tumour-suppressor genes APC and TP53. Finally, using multivariable regression models, we demonstrate that different cancers exhibit distinct mutation–methylation associations, with DNA repair influencing such associations in certain cancer genomes. Taken together, we find differential associations with methylation that are vital for accurately predicting expected mutation loads across cancer types. Our findings reveal links between methylation and common mutation and repair processes, with these mechanisms defining a key part of the mutational landscape of cancer genomes.

Domains of pulsational instability of low-frequency modes in rotating upper main sequence stars

We determine instability domains on the Hertzsprung–Russell diagram for rotating main sequence stars with masses of 2–20 M⊙. The effects of the Coriolis force are treated wihin the traditional approximation. High-order g modes with harmonic degrees ℓ up to 4 and mixed gravity–Rossby modes with |m| up to 4 are considered. We include the effects of rotation in wider instability strips for a given ℓ compared to the non-rotating case and in an extension of the pulsational instability to hotter and more massive models. We present results for a fixed value of the initial rotation velocity as well as for a fixed ratio of the angular rotation frequency to its critical value. Moreover, we check how the initial hydrogen abundance, metallicity, overshooting from the convective core and opacity affect the pulsational instability domains. The effect of rotation on the period spacing is also discussed.

Temporal instability of charged viscoelastic liquid jets under an axial electric field

A three-dimensional temporal linear instability analysis is performed for charged viscoelastic liquid jets moving in an inviscid gas under an axial electric field; the analytical dimensionless dispersion relation is derived in this paper. The viscoelastic fluid described by the Oldroyd-B model is intended to be a Taylor–Melcher leaky dielectric, while the ambient gas is treated as perfectly dielectric. Results show that two local growth rate maxima exist in the axisymmetric mode, and the instability domain can be simply connected or can consist of two separate regions separated by a stable area, depending mainly upon the axial electric field intensity and two viscoelastic parameters considered here, i.e. the time constant ratio and residual stress tension. It is found that the radial electric field has dual effects on the axisymmetric instability and it enhances the asymmetric instability, while the axial electric field affects the asymmetric mode non-monotonically versus different surface charge, and inhibits the axisymmetric mode. The competition between the axisymmetric and asymmetric instabilities reveals that the axial electric field will promote the predominance of asymmetric instability over the axisymmetric mode, which causes the bending motion in most experimental observations. An energy budget is also applied to explain the variation trend in the temporal growth rate versus different radial and axial electric fields.

Rayleigh-Taylor instability in thin liquid films subjected to harmonic vibration

The dynamics of the Rayleigh-Taylor instability of a two-dimensional thin liquid film placed on the underside of a planar substrate subjected to either normal or tangential harmonic forcing is investigated here in the framework of a set of long-wave evolution equations accounting for inertial effects derived earlier by Bestehorn, Han, and Oron [“Nonlinear pattern formation in thin liquid films under external vibrations,” Phys. Rev. E 88, 023025 (2013)]. In the case of tangential vibration, the linear stability analysis of the time-periodic base state with a flat interface shows the existence of the domain of wavenumbers where the film is unstable. In the case of normal vibration, the linear stability analysis of the quiescent base state reveals that the instability threshold of the system is depicted by a combination of distinct thresholds separate for the Rayleigh-Taylor and Faraday instabilities. The nonlinear dynamics of the film interface in the case of the static substrate results in film rupture. However, in the presence of the substrate vibration in the lateral direction, the film interface saturates in certain domains in the parameter space via the mechanism of advection induced by forcing, so that the continuity of the film interface is preserved even in the domains of linear instability while undergoing the time-periodic harmonic evolution. On the other hand, sufficiently strong forcing introduces a new inertial mode of rupture. In the case of the normal vibration, the film evolution may exhibit time-periodic, harmonic or subharmonic saturated waves apart of rupture. The enhancement of the frequency or amplitude of the substrate forcing promotes the destabilization of the system and a tendency to film rupture at the nonlinear stage of its evolution. A possibility of saturation of the Rayleigh-Taylor instability by either normal or unidirectional tangential forcing in three dimensions is also demonstrated.

Study on hot deformation behavior and intrinsic workability of 6063 aluminum alloys using 3D processing map

Hot deformation in 6063 aluminum alloys was investigated by hot compression testing over the temperature range of 573–723 K with strain rates of 0.01–10 s−1 using a Gleeble 3500 thermal-mechanical simulator. Based on the experimental results, constitutive equations compensated with strain were developed to model the hot deformation behavior. The intrinsic workability was further analyzed by establishing three-dimensional processing maps. These maps were constructed based on dynamic materials model to delineate variations in power dissipation efficiency and flow instability domains. Combined with microstructure observation, recommended processing domains are predicated to be within the temperatures range of 673–723 K and strain rates range of 0.01–0.1 s−1. Under such conditions, the main softening mechanism is dynamic recrystallization. The results from these processing maps agree well with microstructure observation.

Constitutive behavior and processing maps of low-expansion GH909 superalloy

The hot deformation behavior of GH909 superalloy was studied systematically using isothermal hot compression tests in a temperature range of 960 to 1040°C and at strain rates from 0.02 to 10 s−1 with a height reduction as large as 70%. The relations considering flow stress, temperature, and strain rate were evaluated via power-law, hyperbolic sine, and exponential constitutive equations under different strain conditions. An exponential equation was found to be the most appropriate for process modeling. The processing maps for the superalloy were constructed for strains of 0.2, 0.4, 0.6, and 0.8 on the basis of the dynamic material model, and a total processing map that includes all the investigated strains was proposed. Metallurgical instabilities in the instability domain mainly located at higher strain rates manifested as adiabatic shear bands and cracking. The stability domain occurred at 960–1040°C and at strain rates less than 0.2 s−1; these conditions are recommended for optimum hot working of GH909 superalloy.

Optimized method for solving the inverse problem for a triangular plasmonic waveguide using a response of scanning heterodyne microscope

A method proposed previously to solve the inverse problem for triangular plasmonic waveguides using a TE-polarized response of scanning differential heterodyne microscope has been optimized. The use of the phase contrast of microscope response at two wavelengths as initial data made it possible to reduce significantly the solution error and eliminate the instability domains of initial data, in which the solution error dramatically increased. It is demonstrated that the accuracy of determining the waveguide parameters significantly improves in comparison with the case where the amplitude and phase contrast of response at one wavelength are used as initial data. It is shown that the solution of the inverse problem can be further optimized using contrasts of amplitude responses as additional initial data. The dependences of the error of inverse problem solution on the error in determining the initial data are calculated.

A Comparative Study of Constitutive and Neural Network Models for Flow Behavior of Mg-5.9Zn-1.6Zr-1.6Nd-0.9Y Alloy and Processing Maps

Isothermal and constant strain rate compression tests of as-homogenized Mg-5.9Zn-1.6Zr-1.6Nd-0.9Y alloy were performed by using Gleeble-3800 thermo-mechanical simulator at temperature between 523 and 723 K and strain rate range from 0.001 to 1 s−1, respectively. The deformation behavior of the alloy at elevated temperature was investigated. A strain-dependent constitutive model based on the Arrhenius model and back-propagation neural network (BPNN) model of the flow stress was established. The predictability of the two models was evaluated by average absolute relative error (AARE) and correlation coefficient (R c), respectively. The results show that the BPNN model has more accurate predictability than strain-dependent constitutive model. Processing maps are obtained according to the principles of the dynamic materials modeling and microstructures of the compressed samples. The microstructure of the samples was observed by optical microscope and electron backscattered diffraction. Processing maps show that the instability domain is at a strain rate of range of 0.015-1 s−1 and a temperature between 523 and 623 K. The alloy has good workability at 630-700 K and 0.008-0.1 s−1, wherein dynamic recrystallization occurs.

Subharmonic resonant excitation of edge waves by breaking surface waves

Abstract. Parametric excitation of edge waves with a frequency 2 times less than the frequency of surface waves propagating perpendicular to the inclined bottom is investigated in laboratory experiments. The domain of instability on the plane of surface wave parameters (amplitude–frequency) is found. The subcritical instability is observed in the system of parametrically excited edge waves. It is shown that breaking of surface waves initiates turbulent effects and can suppress the parametric generation of edge waves.

Hot Deformation Behavior and Intrinsic Workability of Carbon Nanotube-Aluminum Reinforced ZA27 Composites

Using a controlled thermal simulator system, hybrid carbon nanotube-aluminum reinforced ZA27 composites were subjected to hot compression testing in the temperature range of 473-523 K with strain rates of 0.01-10 s−1. Based on experimental results, a developed-flow stress model was established using a constitutive equation coupled with strain to describe strain softening arising from dynamic recrystallization. The intrinsic workability was further investigated by constructing three-dimensional (3D) processing maps aided by optical observations of microstructures. The 3D processing maps were constructed based on a dynamic model of materials to delineate variations in the efficiency of power dissipation and flow instability domains. The instability domains exhibited adiabatic shear band and flow localization, which need to be prevented during hot processing. The recommended domain is predicated to be within the temperature range 550-590 K and strain rate range 0.01-0.35 s−1. In this state, the main softening mechanism is dynamic recrystallization. The results from processing maps agree well with the microstructure observations.

Processing maps and microstructural evolution of Al–Cu–Li alloy during hot deformation

The hot deformation behavior of Al–Cu–Li alloy was investigated by hot compression tests in the temperature range of 340–500 °C with strain rate of 0.001–10.000 s−1. Based on the dynamic materials model (DMM), processing maps of the test alloy were developed for optimizing hot processing parameters. The optimum parameters of hot deformation for Al–Cu–Li alloy are at temperature of 400–430 °C and strain rate of about 0.100 s−1, with efficiency of power dissipation of around 30%. The microstructural manifestation of the alloy deformed in instability domains is flow localization, and dynamic softening first occurs in flow localizations structure. In stable domains, dynamic recovery (DRV) and dynamic recrystallization (DRX) are the main microstructural evolution mechanism. DRX is gradually strengthened with the increase in deformation temperature and the decrease in strain rate. During hot deformation, the DRX mechanism of Al–Cu–Li alloy is dominated by continuous DRX (CDRX). A DRX model of Al–Cu–Li alloy is proposed based on the microstructural evolution process of the test alloy.

Effect of niobium addition on hot deformation behaviors of medium carbon ultra-high strength steels

The hot deformation behaviors of two medium carbon ultra-high strength steels with different niobium contents were investigated by using Zener-Hollmom parameter and processing map, and the effect of niobium addition on the hot deformation behavior of medium carbon steel was determined. The hot compression tests were conducted on a Gleeble-3500 thermo-mechanical simulator deformed at temperatures from 850 to 1 200 °C and strain rates from 0.001 to 1 s−1. The processing maps of two test steels were built at a true strain of 0.7 based on dynamic materials model (DMM). There are two peak efficiency domains and two flow instability regions in both test steels. However, the peak efficiency domains of Nb-bearing steel move to higher temperature due to the inhibition of dynamic recrystallization (DRX), and the instability domains of Nb-bearing steel are enlarged due to the precipitation of Nb-containing particles during hot deformation. The optimum process parameters of Nb-bearing and Nb-free steels for industrial production were determined according to the processing map and the microstructural observation.

Pulsational instabilities in hot pre-horizontal branch stars

The ϵ mechanism is a self-excitation mechanism of pulsations which acts on the regions where nuclear burning takes place. It has been shown that the ϵ mechanism can excite pulsations in models of hot helium-core flash, and that the pulsations of LS IV-14· 116, a He-enriched hot subdwarf star, could be explained that way. We aim to study the ϵmechanism effects on models of hot pre-horizontal branch stars and determine, if possible, a domain of instability in the log g — log T eff plane. We compute non-adiabatic non-radial pulsations on such stellar models, adopting different values of initial chemical abundances and mass of the hydrogen envelope at the time of the main helium flash. We find an instability domain of long-period (400 s ≲ P ≲ 2500 s) g -modes for models with 22000K ≲ Teff ≲ 50000K and 4.67 ≲ log g ≲ 6.15.

Low frequency modes and instability analysis in non-thermal dusty magnetoplasma considering dust charge fluctuation and polarization force

The effect of non-thermal ion population on self-gravitational instability of magnetized dusty plasma considering electrons are in Maxwell-Boltzmann distribution has been investigated. The dust dynamics is described including polarization force, thermal velocity, and charge fluctuation dust. The modified general dispersion relation has been derived including non-thermal ion population, polarization force, and dust charge fluctuation for self-gravitating dusty plasma system, using the normal mode analysis method. The obtained general dispersion relation is discussed in parallel and perpendicular modes of propagation. The population of non-thermal ion, polarization force and dust charge fluctuation affect the self-gravitational instability criteria in both the modes of propagation while the magnetic field affects the instability criterion only in perpendicular mode of propagation. The domains of instability has been discussed analytically to signify the importance of considered parameters. The stability of the self-gravitating dusty plasma system has been analyzed using Routh-Hurwitz stability criterion. Numerical calculations have been performed to analyze the effects of non-thermal ion population, polarization force, and dust charge fluctuation on the growth rate of self-gravitational instability. The results of the present work can be useful in self-gravitating dusty plasma found in space and the interstellar medium such as the interstellar molecular clouds where non-thermally distributed ions are the species of the plasma matter.

Instability of an oscillator moving along a thin ring on a viscoelastic foundation

The stability of an oscillator uniformly moving along a thin ring that is connected to an immovable axis by a distributed viscoelastic foundation has been studied. The dynamic reaction of the ring to the oscillator is represented by a frequency and velocity dependent equivalent stiffness. The characteristic equation for the vibration of the oscillator is obtained. It is shown that this equation can have roots with a positive real part, which imply the exponential increase of the amplitude of the oscillator’s vibration in time, i.e. instability. The critical velocity after which instability can occur is determined. With the help of the D-decomposition method, the instability domains are found in the space of the system parameters. Parametric study of the stability domains is carried out.

Dynamic stability of a viscoelastic plate

The paper considers the problem of stability of a viscoelastic plate subjected to intermittent load. A differential equation was designed, which describes the dynamic stability of the plate stressed by permanent and alternating loads across the plate’s plane. A solution in the form of a series with separated variables has been examined. Linear differential equations of the third order were obtained for the time function. A critical frequency equation was obtained as well. The major domains of dynamic instability were investigated. Another analysis was dedicated to the way the position of the prime instability domain is affected by relaxation time as well as correlation between long-term and instantaneous moduli of elasticity.

Thermodynamic and morphological characterization of Turing patterns in non-isothermal reaction-diffusion systems.

The effect of temperature on the bifurcation diagram and Turing instability domain under non isothermal conditions is studied in the reversible Gray-Scott model. After adding the energy balance to the cubic autocatalytic model, the thermostat temperature and heat transfer coefficient are used as control parameters in the Turing pattern formation. The patterns obtained in the domain of the thermal parameter are characterized by quantifying the overall entropy generation rate and two topological indices; Shannon entropy and Minkowski functionals. The results show that it is possible to induce transitions between Turing patterns of different morphologies by regulating the temperature, and that these transitions take place at a lower entropy generation value compared to other parameters, such as kinetic constants and reactant fluxes. Finally, a correlation between entropy generation and topological indices shows that a difference between direct and inverse patterns is mainly morphological and not energetic.