Exponential Nonlinearity Research Articles

The coupling effects of pore structure and rock mineralogy on the pre-Darcy behaviors in tight sandstone and shale

The pore structure and mineral composition play a crucial role in controlling the water flow behaviors of low-permeability media, which is characterized by threshold pressure gradient (TPG) and nonlinear flow curve. To figure out the coupling effects of these two factors on pre-Darcy flow regimes, water flow experiments were conducted on four tight sandstones, three shales and one fractured shale. The results indicate that both the TPG and pseudo threshold pressure gradient (PTPG) decrease with an increase in total porosity and macropores porosity. The variation of the nonlinear exponent (n) with total porosity and macropore porosity can be described by an exponential function with three parameters. The clay minerals and brittle minerals exert completely opposite influence on the variation of pre-Darcy flow parameters (PTPG, TPG and n). Both TPG/PTPG and n increase with increasing clay content while reduce with increase in the brittle minerals content. Theoretical analyses based on the disjoining pressure demonstrate that immovable water and electro-viscous effect are mainly responsible for water flow deviating from Darcy's law in tight sandstone and shale. Calculation results show that the proportion of immovable water of intact samples ranges from 23.46% to 89.73%, the movable water content ranges from 10.27%–76.54%. The pre-Darcy flow parameters exponentially increase with increase in immovable water content while exponentially decrease with increasing proportion of movable water. For the shale sample used in this work, the immovable water and electro-viscous effect contributing to the pre-Darcy flow account for 81.11%–90.35% and 9.58%–18.51%, respectively. The different flow regimes are controlled by the pore diameter and the thickness of water with shear fluidity. If the diameter of interconnected pores is larger than 10 μm, the Darcy flow regime dominates. When the diameter of minor pore throat of the flow channels are less than 33.82 nm for sandstones and 37.68 nm for shales, the movement of water in this flow channel would generate the TPG.

Chaotic RF Generator for Sub-1-GHz Chaos-Based Communication Systems: Mathematical Modeling and Experimental Validation

In this paper, we have studied, designed and realized a single-transistor chaotic generator with a smooth power spectrum of about −35 dBm in frequency bandwidth up to 1 GHz. The chaos generator model is described by a continuous-time six-dimensional autonomous system assuming an exponential nonlinearity. Chaotic behavior is characterized by bifurcation diagrams, Lyapunov exponents, phase portraits of the attractors and spectra of the oscillations, using both numerical and circuit simulations. Advanced Design System (ADS)-based simulations were carried out to support the theoretical analysis, and to validate the mathematical model. The simulations are carried out using real transistor parameters and taking into account the properties of the substrate, the influence of the board topology and the characteristics of the layout material. This simulation method known as EM/Circuit Co-Simulation allows the simulation results to approach as closely as possible to those of the experiments. In the light of the positive simulation results, the proposed structure is realized to demonstrate its feasibility, and to confirm the numerical results. The prototype is manufactured and mounted on a breadboard using the surface-mount devices and BFP193 bipolar junction transistor. After realizing the generator, we pushed it further towards perfection, through the proposal and realization of a broadband amplifier, in order to gain more bandwidth to improve the spectral characteristic of the generator, which makes it promising for many communication applications such as spread spectrum communication, direct chaotic communication, etc.

Lie group classification of the nonlinear transmission line model and exact traveling wave solutions

A nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor's voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor's voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the \(\tanh\)-method of the governing nonlinear problem.

Study of the structural properties and temperature-dependent hopping conductivity mechanism to the analysis of nonlinearity exponent in Nd0.7−xCexSr0.3MnO3 manganites

Study of the structural properties and temperature-dependent hopping conductivity mechanism to the analysis of nonlinearity exponent in Nd0.7−xCexSr0.3MnO3 manganites

A novel hyperchaotic map and its application in fast video encryption

By the combined feedback of exponential, cubic and sinusoidal nonlinearity, a hyperchaotic map is constructed, which has the distinct features as providing two unipolar hyperchaotic sequences and large area of hyperchaotic orbit. A fast video encryption algorithm that adopted the permutation-diffusion-permutation strategy was developed consequently based on the hyperchaotic system. Each frame image obtained from the video stream is encrypted by the algorithm in real time. To accelerate the encryption, the frame image are encrypted in parallel. Experiment results and security analysis confirm the good security, robustness, and effectiveness of the encryption algorithm.

Levodopa-dependent differences in the non-oscillatory activity of the subthalamic nucleus.

The study of local field potentials (LFP) recorded from the basal ganglia of patients with movement disorders led to significant advancement in the understanding the pathophysiology of Parkinson's disease (PD). The possibility of investigating possible changes in the activity of the brain caused by the levodopa administration may provide a useful tool to evaluate the influence or the side-effects of the treatment from patient to patient. The analysis was carried out through a systematic analysis of the fractal component of the subthalamic local field potentials (STN-LFP) that may reveal, with respect to the classical power spectrum analysis, novel important information about the dynamic modulation caused by the drug intake. Indeed, so far, much of what is known about that is related to the presence of a spectral peak in the beta frequency band then attenuated after the levodopa administration. The nonlinear power-law exponent goes beyond this feature, exploring differences that reflect the fractal (scale-free) behavior of the PD brain dynamics. Here, in order to demonstrate that the presence or absence of the peak has no effect on the computation of the power-law exponent, we used simulated LFP recordings. After that, we performed the fractal analysis in shorts epochs of STN LFPs recordings ( N=24 patients, 12 females and 12 males) before and after Levodopa administration. We found no differences in the nonlinear power-law exponent for simulated data, reinforcing the idea that the parameter was not influenced by the attenuation of the hallmark peak for PD patients. As regard real LFP time series, we found that pharmacological treatment for PD differently altered LFP power of non-oscillatory activity, as well as changed the level of fractal exponent in specific frequency bands. Particularly we observed an increase of the fractal exponent in condition of post-levodopa with significant differences related to the response to levodopa in Parkinson's disease. Clinical Relevance- This study points out a potentially novel non-oscillatory biomarker which could reflect intrinsic properties of complex biological systems thus constituting a potential target parameter for novel and alternative neuroprosthetic applications.

On a Fractional Parabolic Equation with Regularized Hyper-Bessel Operator and Exponential Nonlinearities

Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. More specifically, we examine the existence and uniqueness of mild solutions in Hilbert scale-spaces which are constructed by a uniformly elliptic symmetry operator on a smooth bounded domain. Our main argument is based on the Banach principle argument. In order to achieve the necessary and sufficient requirements of this argument, we have smoothly combined the application of the Fourier series supportively represented by Mittag-Leffler functions, with Hilbert spaces and Sobolev embeddings. Because of the presence of the fractional operator, we face many challenges in handling proper integrals which appear in the representation of mild solutions. Besides, the source term of an exponential type also causes trouble for us when deriving the desired results. Therefore, powerful embeddings are used to limit the growth of nonlinearity.

The Ground State Solutions for Kirchhoff-Schrödinger Type Equations with Singular Exponential Nonlinearities in ℝN

The Ground State Solutions for Kirchhoff-Schrödinger Type Equations with Singular Exponential Nonlinearities in ℝN

Ground state solutions for a Kirchhoff‐type elliptic system involving critical exponential growth nonlinearities

The aim of this paper is to study the ground state solution for a Kirchhoff‐type elliptic system without the Ambrosetti–Rabinowitz condition.

A spectral analysis of the nonlinear Schrödinger equation in the co-exploding frame

The nonlinear Schrödinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon identifying the self-similar solutions in the so-called “co-exploding frame”, a dynamical systems analysis of their stability is natural, yet is complicated by the mixed Hamiltonian-dissipative character of the relevant frame. In the present work, we study the spectral picture of the relevant linearized problem. We examine the point spectrum of 3 eigenvalue pairs associated with translation, U(1) and conformal invariances, as well as the continuous spectrum. We find that two eigenvalues become positive, yet are attributed to symmetries and are thus not associated with instabilities. In addition to a vanishing eigenvalue, 3 more are found to be negative and real, while the continuous spectrum is nearly vertical and on the left-half (spectral) plane. The eigenfunctions and eigenvalues are approximated both asymptotically and numerically, with good agreement between the two approaches. The non-Hamiltonian nature of the co-exploding system results in the 3 eigenvalue pairs failing to be equal-and-opposite by an exponentially small amount. A projection method is used to evaluate this small correction, and at the same time explains the subtle effects of finite boundaries and their role in the observed weak eigenvalue oscillations.

Nonlinear elasticity, yielding, and entropy in amorphous solids.

The holographic duality has proven successful in linking seemingly unrelated problems in physics. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, including strong similarities between the rheology of amorphous solids, effective field theories for elasticity, and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of nonlinear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the nonlinear elastic exponent, the yielding strain/stress, and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path toward understanding the complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.

Symplectic Algorithms for Stable Manifolds in Control Theory

In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm includes two key aspects. The first one is to prove a precise estimate for radius of convergence and the errors of local approximate stable manifolds. The second one is to extend the local approximate stable manifolds to larger ones by symplectic algorithms which have better long-time behaviors than general-purpose schemes. Our approach avoids the case of divergence of the iterative sequence of approximate stable manifolds, and reduces the computation cost. We illustrate the effectiveness of the algorithm by an optimal control problem with exponential nonlinearity.

Singular solutions to [formula omitted]-Hessian equations with fast-growing nonlinearities

We study a class of elliptic problems, involving a k-Hessian and a very fast-growing nonlinearity, on a unit ball. We prove the existence of a radial singular solution and obtain its exact asymptotic behavior in a neighborhood of the origin. Furthermore, we study the multiplicity of regular solutions and bifurcation diagrams. An essential ingredient of this study is analyzing the number of intersection points between the singular and regular solutions for rescaled problems. In the particular case of the exponential nonlinearity, we obtain the convergence of regular solutions to the singular and analyze the intersection number depending on the parameter k and the dimension d.

The ground state solution for biharmonic Kirchhoff–Schrödinger equations with singular exponential nonlinearities in $${\mathbb {R}}^{4}$$

The ground state solution for biharmonic Kirchhoff–Schrödinger equations with singular exponential nonlinearities in $${\mathbb {R}}^{4}$$

Existence of Positive Solutions for (N, p)-Laplace Equation with Exponential Nonlinearity Term and Convection Term in Dimension $${\mathbb {N}}$$

Existence of Positive Solutions for (N, p)-Laplace Equation with Exponential Nonlinearity Term and Convection Term in Dimension $${\mathbb {N}}$$

Groundstates for magnetic Choquard equations with critical exponential growth

This paper is dedicated to show the existence of ground state solution for a magnetic Choquard equation with critical exponential growth. By introducing a Moser type function involving magnetic potential and applying analytical techniques, we surmount the obstacles brought from the magnetic potential which makes it a complex-valued problem and the critical exponential growth nonlinearity which makes it difficult to show the non-vanishing of Cerami sequence. Our methods can be applied to related magnetic elliptic equations.

Planar Schrödinger-Poisson system with critical exponential growth in the zero mass case

In this paper, we develop new proof techniques and analytical methods to prove the existence of ground state solutions for the following planar Schrödinger-Poisson system with zero mass{−Δu+ϕu=f(u),x∈R2,Δϕ=2πu2,x∈R2, where f∈C(R,R) has the critical exponential growth at infinity and there is no monotonicity restriction on f(u)/u3. In particular, by using delicate estimates we obtain a desired upper bound for the Mountain Pass level just with the optimal asymptotic condition κ=liminf|t|→∞t2F(t)eα0t2>0 to restore the compactness in the presence of critical exponential growth, which significantly improves analogous assumptions on asymptotic behavior of t2F(t)eα0t2 or tf(t)eα0t2 at infinity in the previous works. Moreover, we use a different approach from the one of Du and Weth (2017) [21] dealing with the power nonlinearities to establish the Pohozaev type identity, which not only allows critical exponential growth nonlinearities, but also deals with the non-autonomous case containing a linear term V(x)u in the first equation, both of which are not covered in the existing literature. To our knowledge, there has not been any work in the literature on the subject, even for the simpler equation: −Δu=f(u) in R2.

Quasilinear Choquard equations involving N‐Laplacian and critical exponential nonlinearity

In the present paper, we study a class of quasilinear Choquard equations involving ‐Laplacian and the nonlinearity with the critical exponential growth. We discuss the existence of positive solutions of such equations.

The dynamical behavior for a famous class of evolution equations with double exponential nonlinearities

An analytical investigation for a famous class of evolution equations with double exponential nonlinearities that has vast applications in many nonlinear sciences is presented. These equations include the Tzitzéica Equation (TE), Dodd-Bullough-Mikhailov Equation (DBME), Tzitzéica-Dodd-Bullough-Mikhailov equation (TDBME) and the Peyrard Bishop DNA Equation (PB-DNA-E). Furthermore, the Kudryashov method for constructing exponential function solutions has been employed to reveal various sets of traveling wave solutions with different geometrical structures to the identified models. We also give the graphical illustrations of certain solutions to further analyze the results.

How Long Can the MJO be Predicted During the Combined Phases of ENSO and QBO?

AbstractThe predictability limit of the Madden‐Julian Oscillation (MJO) in the El Niño and La Niña boreal winters (November‐February) is investigated using observational data and historical run outputs of CMIP models. The MJO predictability is computed by the nonlinear local Lyapunov exponents approach for various MJO indices obtained from bandpass‐filtered (30–80 days) outgoing longwave radiation, 850‐hPa zonal wind, and 200‐hPa zonal wind data. The result shows that the MJO predictability during La Niña winters is enhanced by up to 8 days compared to El Niño winters. Enhanced convection of the MJO phases 2–4 with persistence propagation during La Niña winters leads to higher predictability, as compared with those for El Niño winters. The highest (lowest) predictability of the MJO shows 39 (31) days during La Niña/EQBO (El Niño/EQBO) winters. The longer persistence of the MJO during La Niña/EQBO winters leads to higher predictability.