Nonlinear Strength Research Articles

Continuum finite element analysis generalizes in vivo trabecular bone microstructural strength measures between two CT scanners with different image resolution

Fragility of trabecular bone (Tb) microstructure is increased in osteoporosis, which is associated with rapid bone loss and enhanced fracture-risk. Accurate assessment of Tb strength using in vivo imaging available in clinical settings will be significant for management of osteoporosis and understanding its pathogenesis. Emerging CT technology, featured with high image resolution, fast scan-speed, and wide clinical access, is a promising alternative for in vivo Tb imaging. However, variation in image resolution among different CT scanners pose a major hurdle in CT-based bone studies. This paper presents nonlinear continuum finite element (FE) methods for computation of Tb strength from in vivo CT imaging and evaluates their generalizability between two scanners with different image resolution. Continuum FE-based measures of Tb strength under different loading conditions were found to be highly reproducible (ICC ≥ 0.93) using ankle images of twenty healthy volunteers acquired on low- and high-resolution CT scanners 44.6 ± 2.7 days apart. FE stress propagation was mostly confined to Tb micro-network (2.3 ± 1.7 MPa) with nominal leakages over the marrow space (0.4 ± 0.5 MPa) complying with the fundamental principle of mechanics at in vivo imaging. In summary, nonlinear continuum FE-based Tb strength measures are reproducible among different CT scanners and suitable for multi-site longitudinal human studies.

Effect of Shear Action on Structural and Electrical Insulation Properties of Polypropylene

Polypropylene undergoes permanent alterations during the processing and manufacture of cables due to shear effects, which in turn affect all of its qualities. There are currently few research papers on the modulation of material structure and many performance parameters by the shear stress field. In this study, we examined the impact of various shear levels on the structural, mechanical, and electrical properties of polypropylene, as well as their relationships. The results indicated that shear strength decreased the material’s viscosity and oxidation resistance. As shear duration increased, crystallinity began to diminish. In the meantime, the crystallinity improved as the shear temperature rose. The thermal elongations of the sheared samples were all about 5%. Short-term shearing boosted the material’s toughness, but as the degree of shear continued to increase, the material’s toughness and rigidity steadily decreased. The storage modulus of the material decreased with increasing shear, the loss peak initially increased and subsequently decreased, the peak position shifted from low to high temperature, and the loss factor was relatively small. In samples sheared for brief periods, an accumulation of space charge and an increase in its nonlinear threshold field strength were observed. With increasing shear time, the material’s space charge accumulation was repressed, the current density initially grew and then reduced, and the nonlinear threshold field strength initially fell and then increased. Under shearing, the electrical strength of the material increased by approximately 2%. In addition, the presence of an antioxidant improved all of the aforementioned features.

The Influence of the Fractal Dimension on the Mechanical Behaviors of the Soil–Rock Mixture: A Case Study from Southwest China

As the typical multi-phase geotechnical material, the particle size distribution of the natural soil–rock mixture (S–RM) has a significant impact on the structural and mechanical properties. The coarse grain content used in the laboratory and simulation tests falls short of accurately describing the particle size distribution feature of the entire material. The main subject of this article is the influence of the fractal dimension on mechanical behaviors based on the fractal theory. The double fractal characteristics were principally discussed along with the typical particle size distribution characteristics of the S–RM in the Three Gorges Reservoir and southwest China. The influence of the various fractal dimensions on the mechanical behaviors of S–RM was then investigated using three groups of large–scale triaxial tests, and the responses of the linear and nonlinear strength indexes were analyzed. The results show that the stress–strain curves of S–RM in the hyperbolic shape are visible under various confining pressure, and the nonlinear strength characteristics can be observed. The coarse grain content exhibits a negative correlation to the average fraction dimension. The difference between the coarse and fine grain fraction dimensions becomes considerably more obvious as the coarse grain content increases, which also increases the error when using the average fractal dimension. The voids between the coarse grains cannot be filled with the fine grains as the grain coarseness grows, resulting in a loose structure and a contact frictional effect, which lowers cohesion and raises the peak friction angle.

Application of Orthogonal Functions to Equivalent Linearization Method for MDOF Duffing–Van der Pol Systems under Nonstationary Random Excitations

Many mechanical systems manifest nonlinear behavior under nonstationary random excitations. Neglecting this nonlinearity in the modeling of a dynamic system would result in unacceptable results. However, it is challenging to find exact solutions to nonlinear problems. Therefore, equivalent linearization methods are often used to seek approximate solutions for this kind of problem. To overcome the limitations of the existing equivalent linearization methods, an orthogonal-function-based equivalent linearization method in the time domain is proposed for nonlinear systems subjected to nonstationary random excitations. The proposed method is first applied to a single-degree-of-freedom (SDOF) Duffing–Van der Pol oscillator subjected to stationary and nonstationary excitations to validate its accuracy. Then, its applicability to nonlinear MDOF systems is depicted by a 5DOF Duffing–Van der Pol system subjected to nonstationary excitation, with different levels of system nonlinearity strength considered in the analysis. Results show that the proposed method has the merit of predicting the nonlinear system response with high accuracy and computation efficiency. In addition, it is applicable to any general type of nonstationary random excitation.

Multipole vector solitons in coupled nonlinear Schrödinger equation with saturable nonlinearity

We construct the coupled self-defocusing saturated nonlinear Schrödinger equation and obtain the dipole-dipole, tripole-dipole and dipole-tripole vector soliton solutions by changing the potential function parameters and using the square operator method of power conservation. With the increase of soliton power, the dipole-dipole, tripole-dipole and dipole-tripole vector solitons can all exist. The existence of the three kinds of vector solitons is obviously modulated by the potential function. The existence domain of three kinds of vector solitons, modulated by the potential function, is given in this work. The stability domains of three vector solitons are modulated by the soliton power of each component. The stability regions of three kinds of vector solitons expand with the increase of the power of two-component soliton. With the increase of saturation nonlinear strength, the power values of the tripole-dipole and dipole-tripole vector solitons at the critical points from stable state to unstable state decrease gradually, and yet the power of the soliton at the critical point from the stable state to the unstable state does not change.

Noise-dissipation Correlated Dynamics of a Double-well Bose-Einstein Condensate-reservoir System

Abstract: In this work, we study the dissipative dynamics of a double-well Bose-Einstein condensate (BEC) out-coupled to reservoir at each side of its trap. The sub-system comprises of a simple Bose-Hubbard model, where the interplay of atom-tunneling current and inter-particle interaction are the main quantum features. The contact with two separate heat baths causes dissipation and drives the system into a non-equilibrium state. The system is well described by the Generalized Quantum Heisenberg-Langevin equation. We considered two Markovian dissipative BEC systems based on (i) the mean-field model (MF), where the internal noise has been averaged out and (ii) the noise-correlated model (FDT). Physical quantities, such as population imbalance, coherence and entanglement of the system, are computed for the models. The two-mode BEC phases, such as the quantum tunneling state and the macroscopic quantum-trapping state, evolved into complicated dynamics by controlling the non-linear interaction and dissipation strengths. We found that many important quantum features produced by the noise-correlated FDT model are not captured by the mean-field model. Keywords: Double-well BEC, Dissipation, Noise, Markovian, Non-Markovian, Fixed points. PACS: 03.75 Lm, 03.65 Yz, 03.75 Gg, 05.

Thresholds between modulational stability, rogue waves and soliton regimes in saturable nonlinear media

We study a third-order nonlinear Schrödinger equation for saturable nonlinear media, which can represent either optical pulse propagation in 1D nonlinear waveguide arrays or electron dynamics in one-dimensional lattices. Here, we describe how stable uniform solutions can evolve into regimes in which they are localized and the influence of saturation on this transition. We observed regular and chaotic-like breathing dynamics as intermediate regimes, which have their domain of existence significantly altered by the saturation parameter. Critical nonlinear strengths separating the existing regimes are shown in phase diagrams, evidencing the role played by saturation. Numerical data and analytical approach show the nonlinear strength above which uniform solutions become breather solutions increasing with the saturation parameter. In the regular breathing regime, we reveal the breathing frequency for media with saturable nonlinearity displaying faster growth as it moves away from the critical point of uniform solutions. Furthermore, critical nonlinear strength separating the regimes of regular and chaotic-like breather solutions exhibits a decreasing behavior as the saturation parameter increases. The latter ones present clear signatures of emerging rogue waves, such as peaks showing long-tailed statistics. Thresholds of this regime are increased by the saturable nonlinearity. Thus, the regime of localized solutions, which we have shown to be well-described by bright soliton-like structures, becomes less accessible with increasing saturation.

On the Quantization of AB Phase in Nonlinear Systems.

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of π at the critical nonlinearity at which the Dirac cone appears and disappears (thus yielding π-quantization of the AB phase so long as the nonlinear Dirac cone exists), whereas for all other powers of nonlinearity, the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel using a new numerical model based on generalized nonlinear unified strength theory

It is proposed a new numerical model based on the generalized nonlinear unified strength theory (GNUST). Based on the modified continuous multi-segment plastic flow rule, the proposed model considers how confining stresses influence plastic flow on the premise of ensuring the continuity of plastic flow. In a finite-difference code, the proposed numerical model was successfully implemented, and it was validated by simulating the stress distribution in an elastoplastic ring subjected to circumferential pressure in the plane strain state, and the role of the constitutive parameters was investigated. Finally, two rock tunneling projects were analyzed using the proposed numerical model: excavation plastic zone (EPZ) distribution in a deep-buried diversion tunnel and construction displacements in a shallow-buried highway tunnel. The numerical results obtained with the proposed numerical model based on the GNUST criterion agreed well with those from on-site measurements, emphasizing the significance of the intermediate principal stress. The empirical formula for determining the parameter b has been verified by practical engineering, ensuring the application of the numerical model even without triaxial test data. Thus, the proposed numerical model has good applicability to practical rock engineering and can provide guidance and reference for similar rock projects.

Study of SHG and LE-O Susceptibilities of InAs Crystal: Linear Absorption Taken into Account

We applied a model involving two coupled anharmonic oscillators (electronic and ionic) to estimate the Second Harmonic Generation (SHG) and Linear Electro-Optic (LE-O) susceptibilities of InAs crystal. The crystal of InAs belongs to III-V group compounds owing cubic zinc-blende-type structure. Linear absorption is considered for the selected spectral region 1250 nm – 390 nm. So, the contribution of the imaginary part of the involved complex linear ionic susceptibility to the resultant SHG and LE-O susceptibilities is taken into account and hence the absolute value of complex-linear ionic susceptibility is used in place of the complex-linear ionic susceptibility in the computation of SHG and LE-O coefficients. All of the four constants (nonlinear strength factors), appearing in the model, are determined with the help of experimental data of SHG susceptibility measured in the selected region of 1076 nm-535 nm. Application of such calculated nonlinear strength factors in the concerned modelled expressions, SHG and LE-O susceptibility coefficients are computed as a function of frequency to illustrate the dispersion in the region of 1250 nm –390 nm.

Federated learning based nonlinear two-stage framework for full-reference image quality assessment: An application for biometric

The non-linearity in medical image processing is a critical issue. Because the privacy of the medical image and loss of data is a major concern in recent years. Federated learning is a most advanced form of machine learning in which, rather than transmitting data to local server, a machine learning (ML) algorithm is installed to various devices to train on the information. The parameters from the separate modules will then be transferred to a master ML/ (deep learning) DL model for global training. The research of Image Quality Assessment (IQA) aims to simulate the process of human perception of image quality and construct an objective image quality model as consistent as possible with subjective assessment. The existing IQA methods can be roughly divided into traditional methods and deep learning methods. Traditional methods are knowledge-driven, using prior knowledge or assumptions about the human visual system (HVS) to heuristically design image quality index. Deep learning methods are data-driven, using a large amount of annotated data to learn the mapping from the image to its visual quality end-to-end. To effectively integrate traditional methods into deep networks and investigate the knowledge (model)-driven deep learning methods are the current mainstream trends in IQA research. In this paper, we take the contrary direction and improve traditional methods guided by the cue from deep learning methods. The main works include: 1. the employment of activation function ensure the nonlinear approximation ability of the neural network, here we first extend the two-stage framework widely used in the field of full-reference image quality assessment and propose a nonlinear two-stage framework. 2. Within this framework, we revisit the Edge Strength SIMlarity (ESSIM) algorithm that we previously published in IEEE Signal Processing Letters, and proposed the Nonlinear Edge Strength SIMlarity (NESSIM) algorithm. Experiments on public databases show that NESSIM can obtain good assessment results in traditional methods. • Improve traditional methods guided by the cue from deep learning methods. • Employment of activation function ensure the nonlinear approximation ability of the neural network. • Propose a nonlinear two-stage framework • Proposed the Nonlinear Edge Strength SIMlarity (NESSIM) algorithm.

Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation

We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the Schrödinger equation with small potential and the nonlinear Schrödinger equation (NLSE) with weak nonlinearity. For the Schrödinger equation with small potential characterized by a dimensionless parameter ε ∈ ( 0 , 1 ] \varepsilon \in (0, 1] , we employ the unitary flow property of the (second-order) time-splitting Fourier pseudospectral (TSFP) method in L 2 L^2 -norm to prove a uniform error bound at time t ε = t / ε t_\varepsilon =t/\varepsilon as C ( t ) C ~ ( T ) ( h m + τ 2 ) C(t)\widetilde {C}(T)(h^m +\tau ^2) up to t ε ≤ T ε = T / ε t_\varepsilon \leq T_\varepsilon = T/\varepsilon for any T > 0 T>0 and uniformly for ε ∈ ( 0 , 1 ] \varepsilon \in (0,1] , while h h is the mesh size, τ \tau is the time step, m ≥ 2 m \ge 2 and C ~ ( T ) \tilde {C}(T) (the local error bound) depend on the regularity of the exact solution, and C ( t ) = C 0 + C 1 t C(t) =C_0+C_1t grows at most linearly with respect to t t with C 0 C_0 and C 1 C_1 two positive constants independent of T T , ε \varepsilon , h h and τ \tau . Then by introducing a new technique of regularity compensation oscillation (RCO) in which the high frequency modes are controlled by regularity and the low frequency modes are analyzed by phase cancellation and energy method, an improved uniform (w.r.t ε \varepsilon ) error bound at O ( h m − 1 + ε τ 2 ) O(h^{m-1} + \varepsilon \tau ^2) is established in H 1 H^1 -norm for the long-time dynamics up to the time at O ( 1 / ε ) O(1/\varepsilon ) of the Schrödinger equation with O ( ε ) O(\varepsilon ) -potential with m ≥ 3 m \geq 3 . Moreover, the RCO technique is extended to prove an improved uniform error bound at O ( h m − 1 + ε 2 τ 2 ) O(h^{m-1} + \varepsilon ^2\tau ^2) in H 1 H^1 -norm for the long-time dynamics up to the time at O ( 1 / ε 2 ) O(1/\varepsilon ^2) of the cubic NLSE with O ( ε 2 ) O(\varepsilon ^2) -nonlinearity strength. Extensions to the first-order and fourth-order time-splitting methods are discussed. Numerical results are reported to validate our error estimates and to demonstrate that they are sharp.

Two-dimensional lattice soliton and pattern formation in a cold Rydberg atomic gas with nonlocal self-defocusing Kerr nonlinearity

We propose a Rydberg-dressed atomic gas under the condition of electromagnetically induced transparency (EIT) to realize two-dimensional (2D) optical lattices and achieve nonlocal giant Kerr nonlinearity. We obtain the formation of stable 2D bright lattice solitons that result by the balance of diffraction with negative effective mass and nonlocal self-defocusing Kerr nonlinearity. Moreover, extended optical pattern formations are observed based on the modulation instability (MI). It is interesting to note that the solitons and patterns obtained are strongly influenced by the depth of the potential, the degree of nonlocality, and the strength of the Kerr nonlinearity. The results of our work provide a route for versatile control of laser patterns and solitons, which may have potential applications in optical communications and information processing.

Temporal trapping: a route to strong coupling and deterministic optical quantum computation

The realization of deterministic photon–photon gates is a central goal in optical quantum computation and engineering. A longstanding challenge is that optical nonlinearities in scalable, room-temperature material platforms are too weak to achieve the required strong coupling, due to the critical loss-confinement trade-off in existing photonic structures. In this work, we introduce a spatio-temporal confinement method, dispersion-engineered temporal trapping, to circumvent the trade-off, enabling a route to all-optical strong coupling. Temporal confinement is imposed by an auxiliary trap pulse via cross-phase modulation, which, combined with the spatial confinement of a waveguide, creates a “flying cavity” that enhances the nonlinear interaction strength by at least an order of magnitude. Numerical simulations confirm that temporal trapping confines the multimode nonlinear dynamics to a single-mode subspace, enabling high-fidelity deterministic quantum gate operations. With realistic dispersion engineering and loss figures, we show that temporally trapped ultrashort pulses could achieve strong coupling on near-term nonlinear nanophotonic platforms. Our results highlight the potential of ultrafast nonlinear optics to become the first scalable, high-bandwidth, and room-temperature platform that achieves strong coupling, opening a path to quantum computing, simulation, and light sources.

Impulse mitigation in nonlinear composite-based woodpile phononic crystals

In this work, we study the mitigation of stress waves in composite-based woodpile phononic crystals composed of heterogeneous cylindrical rods, whose bending mode exhibits local resonant behavior that strongly interferes with external perturbation. Impulse excitation in this system is transformed into several modulated wave patterns depending on resonant frequencies and their mechanical properties. Thus, these mechanisms have been a candidate for novel methods of shock mitigation without relying on material dissipation. Here, we suggest the mechanical system consisting of the unit cell's composite configuration as an approach for more efficient shock attenuation. To efficiently analyze the nonlinear wave dynamics of the proposed systems, we present an extended discrete element model (DEM) resulting from a combination of an analytic beam theory with the discretization model. We numerically and experimentally demonstrate extreme dispersive waves for shock mitigation by adjusting the weighted composition ratio of the heterogeneous cylinder. Using the verified DEM, we also investigate the strong attenuation performance of incident impulse in disorder-induced systems with different nonlinear strengths. We, thus, expect that these composite-based mechanical systems could be used to design tunable modulation energy transport and efficient impact protector devices.

Topological characteristics of gap closing points in nonlinear Weyl semimetals

In this work we explore the effects of nonlinearity on three-dimensional topological phases. Of particular interest are the so-called Weyl semimetals, known for their Weyl nodes, i.e., point-like topological charges which always exist in pairs and demonstrate remarkable robustness against general perturbations. It is found that the presence of onsite nonlinearity causes each of these Weyl nodes to break down into nodal lines and nodal surfaces at two different energies while preserving its topological charge. Depending on the system considered, additional nodal lines may further emerge at high nonlinearity strength. We propose two different ways to probe the observed nodal structures. First, the use of an adiabatic pumping process allows the detection of the nodal lines and surfaces arising from the original Weyl nodes. Second, an Aharonov-Bohm interference experiment is particularly fruitful to capture additional nodal lines that emerge at high nonlinearity.

Nonlinear dispersion properties of metamaterial beams hosting nonlinear resonators and stop band optimization

The nonlinear dispersion properties of a metamaterial beam embedding nonlinear resonators are investigated. The metamaterial beam incorporates a distributed array of local resonators exhibiting softening or hardening cubic nonlinearity. The nonlinear dynamic behavior of the metamaterial beam is first investigated asymptotically via the method of multiple scales, which yields the closed-form nonlinear dispersion functions with the associated stop bands and the nonlinear dispersive waves as a combination of acoustic and optical bending waves. The effects of the resonators nonlinearity and the hosting beam nonlinear bending curvature on the stop bands are investigated in terms of sensitivity with respect to the strength and type of resonators nonlinearity. A full multi-variable optimization is carried out to study the nonlinear stop band size variations with respect to the resonators nonlinearity and the acoustic/optical wave amplitudes. The results show how the exploitation of the nonlinearities offers great possibilities to enlarge the size of the stop bands compared to the corresponding linear case and, hence, greatly enhance the energy absorption bandwidth.

A micro-macro constitutive model for compressive failure of rock by using 4D lattice spring model

In this work, a micro-macro mechanics-based constitutive model is developed to describe the compressive failure process of rock. A micromechanics model is first developed based on the conceptual model of a micro cracked spring bond, where two micro parameters with clearly geometric meanings are introduced. By using the micromechanics model, it is possible to reproduce the whole nonlinear failure process of the rock under compressive loading, however, it fails to predict the reasonable quantitative relation between the crack initiation stress (σCI) and the direct tensile strength (DTS) that is commonly observed in laboratory tests. Therefore, a macroscopic failure criterion is introduced to determine the failure state of the spring bond instead of the spring deformation used in the micromechanics model. The numerical results indicate that the 4D-LSM with the micro-macro constitutive model can not only fully reproduce the whole nonlinear behavior of rock under different confining pressures, but also reproduce the quantitative relation between σCI and the DTS and the overall macroscopic nonlinear failure strength criterion defined by Hoek and Brown. The micro-macro constitutive model not only provides a feasible solution for better describing the complex nonlinear compressive failure process of rock but helps to better understand the internal failure mechanism of rock.

Enhancement of synchronization bandwidth in an arch beam

Synchronization in microstructures has been widely investigated because of its rich dynamics and promising applications. Most investigations are devoted to revealing the basic features or enhancing the application performance in oscillator with hardening nonlinearity. However, few theoretical and experimental studies have been conducted on synchronization with softening nonlinearity, which easily occurs in imperfect manufacturing. In this paper, we built up a phase feedback loop with an arch beam that exhibits softening effect subjected to a synchronization perturbation. Theoretical analysis and experimental verification are applied to explore the effects of the feedback phase delay and nonlinearity on the synchronization bandwidth. The optimal phase delay for best synchronization bandwidth is determined and the significant enhancement of nonlinearity on the synchronization bandwidth is observed. An practical approach of manipulating the nonlinearity strength is proposed by tuning the ratio of the applied ac voltage VAC to DC voltage VDC. The presented foundings provide novel strategies to enhance the synchronization bandwidth in nonlinear oscillator with softening effects.

The peripheral vortex biome of confined quantum fluids and its influence on vortex dipole annihilation

The self-annihilation of a pair of oppositely charged optical vortices (vortex dipole) in a quantum fluid is hindered by nonlinearity and promoted by radial confinement, resulting in rich life-cycle dynamics of such pairs. The competing effects generate a biome of peripheral vortices that can directly interact with the original pair to produce a sequence of surrogation events. Numerical simulation is used to elucidate the role of the vortex biome as a function of nonlinearity strength and the initial spacing between the engineered vortices. The results apply directly to other nonlinear quantum fluids as well and may be useful in the control of complex condensates in which vortex dynamics produce topologically protected phases.