Nonlinear Properties Research Articles

Chaos in gene regulatory networks: Effects of time delays and interaction structure.

In biological system models, gene expression levels are typically described by regulatory feedback mechanisms. Many studies of gene network models focus on dynamical interactions between components, but often overlook time delays. Here we present an extended model for gene regulatory networks with time delayed negative feedback, which is described by delay differential equations. We analyze nonlinear properties of the model in terms of chaos and compare the conditions with the benchmark homogeneous gene regulatory network model. Chaotic dynamics depend strongly on the inclusion of time delays, but the minimum motifs that show chaos differ when both original and extended models are considered. Our results suggest that, for a particular higher order extension of the gene network, it is possible to observe chaotic dynamics in a two-gene system without adding any self-inhibition. This finding can be explained as a result of modification of the original benchmark model induced by previously unmodeled dynamics. We argue that the inclusion of additional parameters in regulatory gene circuit models substantially enhances the likelihood of observing non-periodic dynamics.

Analytical Solution of Non-Linear Oscillator and Thermal Properties of Interacting System of Real Polyatomic Molecules

The study examined the solution of nonlinear oscillator and thermal properties of interacting system of real polyatomic molecules. A nonlinear oscillator potential was substituted into the radial part of the Schrodinger wave equation and solved using the Frobenius method to obtain the energy eigenvalues of the system. The partition function and the energy eigenvalues are used to determine three thermal properties for four polyatomic molecules which showed that added energy is required in the absence of the nonlinear term as the orbital and magnetic quantum numbers are increased and degeneracy completely removed. Other findings also reveal that as the virial coefficients of the four polyatomic molecules vary, the additive property of entropy is observed as well as the enhancement of the mean energy approximately proportional to the volume of the molecules. The four polyatomic molecules under consideration are environmentally impactful and are indispensable to man.

The analysis of the stability of the Cauchy problem in the cylindrical double-layer area

Ceramic protective coats, for instance, on turbine blades, create a double-layer area with various thermophysical properties and they require metal temperature control. In this paper, it is implemented by formulating a Cauchy problem for the equation of thermal conductivity in the metal cylindrical area with a ceramic layer. Due to the ill posed problem, a regularization method was applied consisting in the notation of thermal balance for the ceramic layer. A spectral radius for the equation matrix was taken as the stability measure of the Cauchy problem. Numerical calculations were performed for a varied thickness of the ceramic layer, with consideration of the non-linear thermophysical properties of steel and a ceramic layer (zirconium dioxide). A polynomial was determined which approximates temperature distribution in time for the protective layer. The stability of solutions was compared for undisturbed and disturbed temperature values, and thermophysical parameters with various ceramic layer thickness. The obtained calculation results confirmed the effectiveness of the proposed regularization method in obtaining stable solutions at random data disturbance.

Saturable absorption properties and ultrafast photonics applications of HfS3.

In this Letter, we focus on investigating the ultrafast photonics applications of two-layer HfS3 nanosheets. We prepared two-layer HfS3 nanosheets and carried out experiments to study their nonlinear saturable absorption properties. The results showed that the two-layer HfS3-based saturable absorber exhibited a modulation depth of 16.8%. Additionally, we conducted theoretical calculations using first principles to estimate the structural and electronic band properties of the two-layer HfS3 material. Furthermore, we utilized the two-layer HfS3 materials as SAs in an erbium-doped fiber cavity to generate mode-locked laser pulses. We measured a repetition frequency of 8.74 MHz, a pulse duration of 540 fs, and a signal-to-noise ratio of 77 dB. Overall, our findings demonstrate that the two-layer HfS3 material can serve as a reliable saturable absorber, possessing properties comparable to currently used two-dimensional materials. This expands the application fields of HfS3 materials and highlights their potential for advanced optoelectronic devices.

Experimental Investigation of Characteristics and Development of Nonlinearity Models for FR1-Range Radio-Frequency Amplifiers

Experimental studies of nonlinear properties of low-power radio-frequency amplifiers similar to those used in 4G/5G mobile communication equipment of the FR1 frequency range are carried out. The measurements of the characteristics of the amplifiers are performed by using the double-frequency testing technique at frequencies of the n7 band (2500–2570 / 2620–2690 MHz), which is allocated in Belarus for 4G mobile communication systems, and the n78 band (3300–3800 MHz), which is planned to be used in Belarus for 5G mobile communications. Based on the results of the measurements of double-frequency characteristics of the amplifiers, their single-tone amplitude characteristics, as well as two-tone characteristics and values of the dynamic range of 3-, 5-, 7-, and 9th order intermodulation in the first harmonic zone, high-order polynomial models of transfer characteristics of the investigated amplifiers are synthesized. The synthesized models are suitable for use in a wide dynamic range of input signals in case of simultaneous modeling of nonlinear effects of all kinds that pose a danger to radio reception in a complex electromagnetic environment created in the frequency bands of mobile (cellular) communications: both “subtle” effects (intermodulation) and “rough” effects (desensitization, cross-modulation). When using the technology of discrete nonlinear analysis of the behavior of radio equipment in a complex electromagnetic environment, the obtained models provide high efficiency of simulation and quantitative analysis of nonlinear processes and radio interference occurring in 4G/5G/6G radio equipment and networks in a complex electromagnetic environment.

A new size-dependent nonlinear model for piezoelectric semiconductor nanofibers by considering the effects of strain gradient and flexoelectricity

Flexotronics induced by the strain gradient and flexoelectricity in a semiconductor with symmetric or asymmetric crystal structures have attracted considerable attention as a promising approach for tunable electronic processes. However, the electric nonlinear properties between the carriers and electric field are ignored in most of related studies. In this study, a new size-dependent nonlinear model is developed to investigate the interaction among the size effects (caused by strain gradient and flexoelectricity), piezo-effects and semiconducting properties in a piezoelectric semiconductor (PS) nanofiber with asymmetric crystal structures. In addition, the Von-Kármán's nonlinear strain is also considered to check the effect of geometric nonlinearity. It is found that the piezo-effect can be enhanced (reduced) by the effect of flexoelectricity (strain gradient) due to a new positive (negative) superimposed increment of electric field under a pair of tensile stress. Besides, the size effect will be weakened by the semiconducting property. The studies will provide guidance for theoretical analysis of size effect in nano PSs and design of flexotronic devices.

An Equivalent Linear Method to Predict Nonlinear Bending Mechanics of Dredging Floating Hose String

Dredging hoses are flexible and are particularly suitable for slurry transportations for mud or sand in dredging projects. To achieve sufficient bending stiffness and to prevent the pipe body from collapsing, this type of hose segment is a composite structure that is embedded with several cord reinforcement layers and steel wires in its rubber layer. To quickly evaluate the nonlinear bending mechanical properties of rubber hoses, this study proposes the equivalent stiffness method of linear superposition, which is verified by test data and numerical results. The results show that the equivalent bending stiffness method proposed in this study is in good agreement with numerical and experimental results. Then, by comparing the calculation results of the hose string, it was demonstrated that the linear stiffness superposition method proposed in this study can also accurately predict the bending mechanical behavior characteristics of string hose, and provide reliable guidance for hose design in practice.

Interfacial failure behavior of longitudinally coupled slab tracks restored by interface adhesives

Longitudinally coupled slab tracks (LCSTs), one of the most popular slab track types, have experienced severe damage like interfacial debonding and gapping over the past few years. Although adhesives have been used to restore the separated interfaces of LCSTs, the high-temperature environment still poses a great challenge to the repaired tracks. Therefore, this paper presents a numerical investigation on the interfacial failure behavior of LCSTs restored by interface adhesives under high-temperature load. Firstly, the constitutive relationships and the damage behavior of the original and the restored interfaces between the track slabs and mortar layers was modelled based on the cohesive zone theory. Secondly, a finite element model of the LCST was established in which the nonlinear mechanical properties of the interfaces and the materials, as well as the nonlinear distribution of track temperature were considered. Last but not least, damage evolution law of interfaces restored by adhesives, the effects of adhesive-use area, and the performance of adhesives on interfacial debonding and gapping under high-temperature loads were studied. The following conclusions are drawn: (1) After adopting the adhesive, the maximum vertical displacement of track slabs can be reduced by 35.2%. (2) An adhesive-use depth above 500 mm on both sides of the lateral path is recommended to lower the height of interfacial gaps to below 1 mm. (3) In addition to using adhesives, keeping the T-shaped joints in a good condition also plays a crucial role in mitigating interfacial gapping. (4) The distribution of the interfacial damage index D on the lateral path of the track shows a significant asymmetry when adhesives are only used on one side of the lateral path.

Fourth-grade nanofluid model with dissipative and nonlinear radiative properties transported peristaltically via a flexible diverging duct holding a porous media under the influence of concentration and heat convection in an induced magnetic field

The major goal of this work is to give a thorough examination of the effect of double diffusion convection (DDC) in addition to a generated magnetic field on peristaltic movement of fourth-grade nanofluid across a vertical sophisticated asymmetrical microchannel using a nondeformable porous media as a basis for intricate pumping systems inspired by biological processes for hazardous waste. The mathematical formulas pertaining to flow, heat/mass transfer under the influence of viscous dissipation, nonlinear heat radiation, and Joule heating were developed using Buongiorno’s framework for nanofluids with combining the thermophoresis and Brownian motion characteristics. Mathematical analysis has been conducted under the suppositions of an extended wavelength and a relatively small Reynolds number. Magnetic field induced axially, density of current, magnetic force function, thermal characteristics, nanoparticles proportion gradient, an additional stress tensor, pressure gradient, and stream function are all given explicit formulas. The constructed function (ND Solve function) within the Wolfram software (Mathematica) is employed to computationally resolve the ensuing system of coupled nonlinear differential equations. Numerical and pictorial evidence is presented to highlight the significance of different physiological characteristics of flow volumes. Further, contour visualizations and circulation bolus have been used to highlight the trapping phenomena, one of among the most noteworthy peristaltic motion occurrences. The main results showed that, despite the dissolvent concentration and the volume percentage of nanoparticles having the opposite effects, the resistance of a substance to heat is shown to climb as the Soret and Dufour numbers rise. At larger levels of the electromagnetic Reynolds number, Strommer’s number, electric field parameter, and thermal Grashof number, stronger axial induced magnetic fields (IMFs) are also provided.

Weak error analysis for the stochastic Allen–Cahn equation

We prove strong rate resp. weak rate O(τ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {O}}}(\ au )$$\\end{document} for a structure preserving temporal discretization (with τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} the step size) of the stochastic Allen–Cahn equation with additive resp. multiplicative colored noise in d=1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=1,2,3$$\\end{document} dimensions. Direct variational arguments exploit the one-sided Lipschitz property of the cubic nonlinearity in the first setting to settle first order strong rate. It is the same property which allows for uniform bounds for the derivatives of the solution of the related Kolmogorov equation, and then leads to weak rate O(τ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal {O}}}(\ au )$$\\end{document} in the presence of multiplicative noise. Hence, we obtain twice the rate of convergence known for the strong error in the presence of multiplicative noise.

Dual Role of Beam Polarization and Power in Nematic Liquid Crystals: A Comprehensive Study of TE- and TM-Beam Interactions.

Optical spatial solitons are self-guided wave packets that maintain their transverse profile due to the self-focusing effect of light. In nematic liquid crystals (NLC), such light beams, called nematicons, can be induced by two principal mechanisms: light-induced reorientation of the elongated molecules and thermal changes in the refractive index caused by partial light absorption. This paper presents a detailed investigation of the propagation dynamics of light beams in nematic liquid crystals (NLCs) doped with Sudan Blue dye. Building on the foundational understanding of reorientational and thermal solitons in NLCs and the effective breaking of the action-reaction principle in spatial solitons, this study examines the interaction of infrared (IR) and visible beams in a [-4-(trans-4'-exylcyclohexyl)isothiocyanatobenzene] (6CHBT) NLC. Our experimental results highlight the intricate interplay of beam polarizations, power levels, and the nonlinear properties of NLCs, offering new insights into photonics and nonlinear optics in liquid crystals.

A new denoising approach based on mode decomposition applied to the stock market time series: 2LE-CEEMDAN.

Time series, including noise, non-linearity, and non-stationary properties, are frequently used in prediction problems. Due to these inherent characteristics of time series data, forecasting based on this data type is a highly challenging problem. In many studies within the literature, high-frequency components are commonly excluded from time series data. However, these high-frequency components can contain valuable information, and their removal may adversely impact the prediction performance of models. In this study, a novel method called Two-Level Entropy Ratio-Based Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (2LE-CEEMDAN) is proposed for the first time to effectively denoise time series data. Financial time series with high noise levels are utilized to validate the effectiveness of the proposed method. The 2LE-CEEMDAN-LSTM-SVR model is introduced to predict the next day's closing value of stock market indices within the scope of financial time series. This model comprises two main components: denoising and forecasting. In the denoising section, the proposed 2LE-CEEMDAN method eliminates noise in financial time series, resulting in denoised intrinsic mode functions (IMFs). In the forecasting part, the next-day value of the indices is estimated by training on the denoised IMFs obtained. Two different artificial intelligence methods, Long Short-Term Memory (LSTM) and Support Vector Regression (SVR), are utilized during the training process. The IMF, characterized by more linear characteristics than the denoised IMFs, is trained using the SVR, while the others are trained using the LSTM method. The final prediction result of the 2LE-CEEMDAN-LSTM-SVR model is obtained by integrating the prediction results of each IMF. Experimental results demonstrate that the proposed 2LE-CEEMDAN denoising method positively influences the model's prediction performance, and the 2LE-CEEMDAN-LSTM-SVR model outperforms other prediction models in the existing literature.

Image quality in CT thorax: effect of altering reconstruction algorithm and tube load.

Non-linear properties of iterative reconstruction (IR) algorithms can alter image texture. We evaluated the effect of a model-based IR algorithm (advanced modelled iterative reconstruction; ADMIRE) and dose on computed tomography thorax image quality. Dual-source scanner data were acquired at 20, 45 and 65 reference mAs in 20 patients. Images reconstructed with filtered back projection (FBP) and ADMIRE Strengths 3-5 were assessed independently by six radiologists and analysed using an ordinal logistic regression model. For all image criteria studied, the effects of tube load 20 mAs and all ADMIRE strengths were significant (p<0.001) when compared to reference categories 65 mAs and FBP. Increase in tube load from 45 to 65 mAs showed image quality improvement in three of six criteria. Replacing FBP with ADMIRE significantly improves perceived image quality for all criteria studied, potentially permitting a dose reduction of almost 70% without loss in image quality.

Introducing Optical Nonlinearity in PDMS Using Organic Solvent Swelling

The feasibility of introducing optical nonlinearity in poly-dimethyl siloxane (PDMS) using organic solvent swelling was investigated. The third-order nonlinear refraction and absorption properties of the individual materials, as well as the PDMS/solvent compounds after swelling were characterized. The well-established Z-scan technique served as characterization method for the nonlinear properties under picosecond pulsed laser excitation at a 532 nm wavelength. These experiments included investigations on the organic solvents nitrobenzene, 2,6-lutidine, and toluene, which showed inherent optical nonlinearity. We showed that nitrobenzene, one of the most well-known nonlinear optical materials, has proven suboptimal in this context due to its limited swelling effect in PDMS and comparatively high (non)linear absorption, resulting in undesirable thermal effects and potential photo-induced damage in the composite material. Toluene and 2,6-lutidine not only exhibited lower absorption compared to nitrobenzene but also show a more pronounced swelling effect in PDMS. The incorporation of toluene caused a weight change of up to 116% of PDMS, resulting in substantial nonlinear optical effects, reflected in the nonlinear refractive index of the PDMS/toluene composite n2=3.1×10−15 cm2/W.

Nonlinear study of indolamines: A hidden property that might have possible implications in neurodegeneration

Indolamines (e.g., serotonin and melatonin) are tryptophan-derived class of neurotransmitters and neuromodulators that play crucial roles in mood regulation, sleep-wake cycles, and gastrointestinal functions. These biogenic amines exert their effects by binding to specific receptors in the central nervous system, influencing neuronal activity and signalling cascades. Indolamines are vital in maintaining homeostasis, and imbalances in their levels have been implicated in various neurological and psychiatric disorders. Hence, in the present study, we have investigated the nonlinear properties of indolamines under a continuous wave (CW) and pulsed laser excitation using the closed-aperture (CA) Z-scan technique. The CA Z-scan is a cost-effective and sensitive analytical tool for investigating nonlinear properties. It is observed that indolamines show negative refractive and positive absorptive nonlinearity under in vitro physiological conditions. The origin of nonlinearity is ascribed to the thermo-optical effect governed by the saturated atomic absorption and molecular orientation mechanisms under CW and pulsed laser excitation, respectively. The strength of nonlinearity is found to vary linearly with the concentration of indolamines. Overall, serotonin possesses stronger nonlinearity than melatonin. The maximum nonlinearity (refractive index (n2) & absorption coefficient (β)) for melatonin under CW and pulsed laser excitations are (-1.266 × 10−12 m2W−1 and -1.883 × 10−17 m2W−1) & (8.046 × 10−8 mW−1 and 1.516 × 10−13 mW−1), respectively. Meanwhile, the maximum n2 and β under pulsed laser excitation for serotonin are obtained as -3.195 × 10−17 m2W−1 and 6.149 × 10−12 mW−1, respectively. The outcome of the results may be utilized in understanding processes mediated by indolamines and designing therapeutic interventions.

Nanosecond-pulse fiber laser mode-locked with polyaniline saturable absorber

We prove that mode-locking of an Erbium-doped fiber laser (EDFL) with a Polyaniline (PANI) saturable absorber (SA) can produce nanosecond pulses at repetition rate of 962 kHz in the elongated ring cavity. The SA is fabricated by embedding a PANI into PVA. The conducting polymer-based SA exhibits a good optical nonlinear property with a modulation depth of 2.3%. The laser operated in nanosecond regime due to the saturable absorption of the PANI PVA SA instead of nonlinear polarization evolution. A clean single pulse is observed, and the pulse train exhibits low jitter. It operated at 1530.8 nm with a pulse duration of 228 ns and a maximum pulse energy of 3.1 nJ. Due to its extremely large chirp property, the proposed laser is suited for application in the chirped-pulse amplification systems.

Three-Four Photon Transition Mn(II) Complex Monitoring Lysosome-Related ATP in Real Time via Fluorescence Lifetime Imaging.

Currently, in situ monitoring of the adenosine triphosphate (ATP) level in lysosomes is critical to understand their involvement in various biological processes, but it remains difficult due to the interferences of limited targeting and low resolution of fluorescent probes. Herein, we report a classic Mn(II) probe (FX2-MnCl2) with near-infrared (NIR) nonlinear (NLO) properties, accompanied by three-four photon transition and fivefold fluorescence enhancement in the presence of ATP. FX2-MnCl2 combines with ATP through dual recognition sites of diethoxy and manganese ions to reflect slightly fluorescence lifetime change. Through the synergy of multiphoton fluorescence imaging (MP-FI) and multiphoton fluorescence lifetime imaging microscopy (MP-FLIM), it is further demonstrated that FX2-MnCl2 displays lysosome-specific targeting behavior, which can monitor lysosome-related ATP migration under NIR laser light. This work provides a novel multiphoton transformation fluorescence complex, which might be a potential candidate as a simple and straightforward biomarker of lysosome ATP in vitro for clinical diagnosis.

Resonant Band Hybridization in Alloyed Transition Metal Dichalcogenide Heterobilayers.

Bandstructure engineering using alloying is widely utilized for achieving optimized performance in modern semiconductor devices. While alloying has been studied in monolayer transition metal dichalcogenides, its application in van der Waals heterostructures built from atomically thin layers is largely unexplored. Here, heterobilayers made from monolayers of WSe2 (or MoSe2) and MoxW1 - xSe2 alloy are fabricated and nontrivial tuning of the resultant bandstructure is observed as a function of concentration x. This evolution is monitored by measuring the energy of photoluminescence (PL) of the interlayer exciton (IX) composed of an electron and hole residing in different monolayers. In MoxW1 - xSe2/WSe2, a strong IX energy shift of ≈100 meV is observed for x varied from 1 to 0.6. However, for x < 0.6 this shift saturates and the IX PL energy asymptotically approaches that of the indirect bandgap in bilayer WSe2. This observation is theoretically interpreted as the strong variation of the conduction band K valley for x > 0.6, with IX PL arising from the K - K transition, while for x < 0.6, the bandstructure hybridization becomes prevalent leading to the dominating momentum-indirect K - Q transition. This bandstructure hybridization is accompanied with strong modification of IX PL dynamics and nonlinear exciton properties. This work provides foundation for bandstructure engineering in van der Waals heterostructures highlighting the importance of hybridization effects and opening a way to devices with accurately tailored electronicproperties.

Tunable third‐order NLO properties of acene derivatives with molecular structural modification

AbstractThe substitution of heteroatoms and the expansion of π‐conjugated units have significant effects on the photoelectric properties of polycyclic aromatic hydrocarbons (PAHs). In this study, based on the experimental molecule PBC, 10 acene derivatives containing the pyrrole group were designed by three strategies: (1) changing the connection position of the pyrrole group, (2) exchanging the position of the N atom, and (3) increasing the length of the π‐linker. Density functional theory (DFT) was used to optimize the molecular geometric structure. Time‐dependent density functional theory (TD‐DFT) was used to calculate the relevant parameters of the excited states. The results show that both of the pyrrole group and the N atom in the para‐position, and the addition of the π‐linker can reduce the energy gap, cause redshift of the linear absorption peak, and increase the two photon absorption (TPA) cross‐section. The analyses of the charge density difference (CDD) and the charge‐transfer matrix (CTM) proved that the electron transfer is mainly concentrated in the π‐linker. Moreover, the participation of the multi‐ring skeleton on both sides decreases gradually with the increase of the length of the π‐linker. The length of the π‐linker changes the dominant transition channel and intramolecular charge‐transfer (ICT) characteristics of TPA, thus affecting the transition dipole moments and nonlinear absorption properties. The second hyperpolarizability of the designed molecule PBI5‐p5 is also significantly superior to that of similar materials reported. It is expected that the above molecular design strategies and comprehensive analysis of nonlinear optical (NLO) properties could provide theoretical support for the research on acene derivatives.

A set of fully nonlinear mild slope equations

A set of time-dependent fully nonlinear mild slope equations is established in terms of velocity vector at still water level and free surface elevation, which is derived from the Euler equations without approximation in nonlinearity and only with the potential flow assumption adopted for bottom slope terms. Apart from the fully nonlinear property, the model is also different from previous nonlinear mild slope equations by adopting the velocity expression accurate to the first-order in bottom slope, which allows the new expressions of higher-order bottom slope terms to be established and the fully nonlinear terms related to bottom slope to be included in the equations. The model can be reduced to the classical mild slope equation for linear waves and the fully nonlinear Boussinesq equations for nonlinear waves. The advantages of the present model are validated against the related laboratory experimental results and demonstrated by comparison with the numerical results of other relevant models.