Thermal Nonlinearity Research Articles

A high constancy and noise suppression voltage shift generator in SEIR-based BIST circuit for ADC linearity test

—The built-in self-test (BIST) circuit is designed to be highly integrated with ADC under test and tests the static linearity based on the stimulus error identification and removal (SEIR) method. A novel level shift generator is proposed for high-precision ADC testing to break the resolution limitation caused by thermal noise and non-linearity. The double sampling operation realized by the chopper circuits cancels the sampling kT/C noise, and the circuit further reduces the amplifier's thermal noise by reducing the noise bandwidth. Besides, this paper presents a new method to achieve a highly linearity-constant voltage shift by applying the negative-C technique. Implemented in 180 nm CMOS process, the simulation results show that the noise power of the voltage shift is reduced by 10 dB, and the constancy of voltage shift is only 3.7 ppm over the entire ADC input range. Benefitting from the noise and linearity performance enhancement, this BIST circuit can test 18-bit ADC to 18-bit accuracy level with one-tenth sampling points.

Dynamic verification of an optimisation algorithm for power dispatch of integrated energy systems

The urgent need to achieve net-zero carbon emissions by 2050 has led to a growing focus on innovative approaches to producing, storing, and consuming energy. Integrated energy systems (IES) have emerged as a promising solution, capitalising on synergies between energy networks and enhancing efficiency. Such a holistic approach enables the integration of renewable energy sources and flexibility provision from one energy network to another, reducing emissions while facilitating strategies for operational optimisation of energy systems. However, emphasis has been mostly made on steady-state methodologies, with a dynamic verification of the optimal solutions not given sufficient attention. To contribute towards bridging this research gap, a methodology to verify the outcomes of an optimisation algorithm is presented in this paper. The methodology has been applied to assess the operation of a civic building in the UK dedicated to health services. This has been done making use of real energy demand data. Optimisation is aimed at improving power dispatch of the energy system by minimising operational costs and carbon emissions. To quantify potential discrepancies in power flows and operational costs obtained from the optimisation, a dynamic model of the IES that better captures real-world system operation is employed. By incorporating slow transients of thermal systems, control loops, and non-linearity of components in the dynamic model, often overlooked in traditional optimisation modules, the methodology provides a more accurate assessment of energy consumption and operational costs. The effectiveness of the methodology is assessed through model-in-the-loop co-simulations between MATLAB/Simulink and Apros alongside a series of scenarios. Results indicate significant discrepancies in power flows and operational costs between the optimisation and the dynamic model. These findings illustrate potential limitations of conventional operational optimisation modules in addressing real-world complexities, emphasising the significance of dynamic verification methods for informed energy management and decision-planning.

Thermal response of nematicons in a parabolic potential

The thermal response of nematicons in a parabolic potential has been numerically studied. Single-peak nematicons exist only in the absence of thermal response coefficients. Because focusing reorientational nonlinearity is dominant in this case. In the presence of thermal response, the competition between focusing reorientational and defocusing thermal nonlinearities leads to the transformation of single-peak to double-peak nematicons. In this domain, the defocusing thermal nonlinearity is greater than the focusing reorientational nonlinearity, resulting in double-peak nematicons. The energy landscape experienced by the light beam within the medium is modified by the competing nonlinearities. The presence of both focusing reorientational and defocusing thermal nonlinearities creates multiple maxima in the energy landscape, allowing for the stabilization of double-peak nematicons as equilibrium states. When a parabolic potential is present, periodic oscillations can be obtained in nematicon. For small values of thermal response coefficients, double-peak nematicons having periodic oscillations are obtained. The thermal response coefficients have significant impacts on the wavelength of the oscillations of double-peak nematicon. The wavelength has been found to increase with increasing thermal response coefficients. Large values of the thermal response coefficients result in a double-peak nematicon with no oscillations. The linear stability analysis shows that single-peak nematicons and double-peak nematicons having periodic oscillations are stable, while double-peak nematicon with a non-oscillatory nature is unstable.

Control-oriented thermal model and load identification for circulating cooling water system in precision process applications

With the increasing precision in machining and measurement, there is a growing demand for improved temperature stability in cooling water systems used in industrial processes. Accurate thermal models and load states are essential for developing efficient controllers to enhance temperature performance. This paper focuses on the development of thermal models for various components of circulating water systems in precision water-cooling processes. It presents a control-oriented thermal model framework that segregates the water circulation cycles and defines system inputs and processes. A novel identification algorithm is proposed to address thermal inertia and cyclic nonlinearity by extracting the cyclic period and cycle change rate. The algorithm can simultaneously estimate the state–space model and unmeasurable load disturbances. A validation experimental setup was constructed, and the results demonstrate that, for different flow scenarios, the estimated load and thermal model parameters align well, with correlations exceeding 0.85 and error ratios close to 10%. Additionally, the circulating water output temperature can be accurately predicted. The fitting degrees surpass 84% within five cycles, with correlations exceeding 0.97 and error standard deviations below 0.22 °C.

Dark solitons in liquid crystals with competing re-orientational and thermal nonlocal nonlinearities

The properties of dark solitons in liquid crystals with competing nonlinearities are investigated by the model proposed by Jung. Under the condition of the rectangular response function, the relationship between the width of the dark soliton and the parameters of the medium is obtained by the variational method. It is found that the width of the dark solitons first decreases and then increases with the increment of the orientational nonlocality, the width of the soliton increases monotonously with the increase of the thermal nonlocality, and the width of the soliton decreases monotonously with the increase of the thermal nonlinearity coefficient. It is also found that the width of dark solitons is more sensitive to the orientational nonlocality than the other parameters. In addition, the width of the soliton increases monotonously with the grayness of the solitons. The analytical results are consistent with the numerical simulations that are obtained by the split-step Fourier algorithm.

Nonlinear dynamics of cavity optomechanical-thermal systems.

Cavity optomechanics is concerned with the interaction between optical cavities and mechanical resonators. Here, we present systematic research on the dynamic behaviors of cavity optomechanical systems incorporating the influence of thermal nonlinearity. A dimensionless theoretical model was established to describe the system and numerical simulations were performed to study the dynamic behaviors. We theoretically identify the staircase effect, which can abruptly alter the system parameters when adiabatically sweeping the pump laser frequency across the optical cavity resonance and driving the mechanical resonator into oscillation. Moreover, we found bistability effects in several detuning intervals when sweeping the laser forward and backward. Both effects are analyzed theoretically and the roots lie in the thermal instability between averaged cavity energy and laser detuning. Our study shows the dynamic behaviors in an optomechanical-thermal system and provides guidance in leveraging the systems for applications in optical frequency comb, phonon laser, etc.

Stabilization of a Rao–Nakra Sandwich Beam System by Coleman–Gurtin’s Thermal Law and Nonlinear Damping of Variable-Exponent Type

In this paper, we explore the asymptotic behavior of solutions in a thermoplastic Rao–Nakra (sandwich beam) beam equation featuring nonlinear damping with a variable exponent. The heat conduction in this context adheres to Coleman–Gurtin’s thermal law, encompassing linear damping, Fourier, and Gurtin–Pipkin’s laws as specific instances. By employing the multiplier approach, we establish general energy decay results, with exponential decay as a particular manifestation. These findings extend and generalize previous decay results concerning the Rao–Nakra sandwich beam equations.

Synthesis, Growth, Photoluminescence, Thermal, and Third-Order Nonlinear Optical Properties of Glycine Methyl Ester Hydrochloride Single Crystal for Opto-Electronic Applications

Synthesis, Growth, Photoluminescence, Thermal, and Third-Order Nonlinear Optical Properties of Glycine Methyl Ester Hydrochloride Single Crystal for Opto-Electronic Applications

Two-dimensional modulation instability and higher-order soliton clusters in nematic liquid crystals with competing re-orientational and thermal nonlocal nonlinearities

We investigate two-dimensional modulation instability (MI) and higher-order soliton clusters in nematic liquid crystals with competing re-orientational and thermal nonlocal nonlinearities. With linear-stability analysis, we show nonlocality can suppress effectively MI of two-dimensional plane wave. By employing variational (Lagrangian) approach, bifurcated solutions of higher-order solitons, i.e., Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) soliton clusters are obtained analytically. Propagation dynamics of both upper and lower branches of solitons are demonstrated numerically. Properties, such as stable propagation distance and mode transformation between HG and LG modes are also discussed in detail.

Solid and hollow whispering gallery mode resonators for all optical switch

Whispering-gallery-modes resonators (WGMR) are effective switching devices when either coated or filled with non-linear material. We present examples of all-optical switching of hybrid WGM using polyfluorene, a methacrylate azobenzene and an acrylate derivates. We have studied the Kerr non-linear effect and thermal nonlinearities in a such hybrid systems.

State-Spatial Viewpoint of Stress in Thermally Postbuckled and Nonlinearly Bent FG Saturated Poroelastic Circular Plates

A dimensionless discrete state-space mathematical model is proposed for stress analysis of an axially-symmetric saturated poroelastic circular plate being loaded by temperature rise of one of the flat faces. Computation of stress by means of this model is free from a need for differentiation. The curves of thermal postbuckling, thermal nonlinear bending, radial stress, circumferential stress and resultant radial force have been achieved by means of six state-space variables and differential quadrature procedure. The effects of loading temperature, boundary conditions, porosity, pore distribution and fluid pore pressure on the thermal post buckling and nonlinear bending phenomena have been investigated. The critical postbuckling thermal load has been determined by means of a numerical algorithm that does not converge to trivial solution because it starts from a relatively great numerical thermal load. Contrary to the governing equation in usual form, the governing equations in state space together with the state equations equalize the number of the governing assembled difference equations and that of the unknowns, and eventually do not require to apply the so-called auxiliary extra boundary conditions at the nodes adjacent to the boundary nodes. As another advantage, in state-spatial viewpoint, there is not any necessity for computing the coefficients of derivatives with order higher than unity.

Six-wave interaction with double wavefront reversal in multimode waveguides with Kerr and thermal nonlinearities

Spatial selectivity of six-wave radiation converters, which perform double wavefront conjugation of a signal wave in long multimode waveguides with both Kerr and thermal nonlinearities, is studied. Waveguides with infinitely conductive surfaces, with a parabolic refractive index profile, were used. It is shown that the spatial structure of the first pump wave does not affect the quality of doubled wavefront conjugation in a waveguide with Kerr nonlinearity, but only slightly affects the quality of doubled wavefront conjugation in a waveguide with thermal nonlinearity. A decrease in the radius of the second Gaussian pump wave on the back face of the waveguide leads to an improvement in the quality of the doubled wavefront reversal both in the case of six-wave interaction in the Kerr and thermal nonlinearities. In a parabolic waveguide, when the zero mode of the waveguide is excited by pump waves at a constant frequency of the second pump wave, an increase in the frequency of the first pump wave worsens the quality of the double wavefront conjugation.

Thermally nonlinear analysis of propagating cracks under generalized thermal shock

In this paper, the thermally nonlinear response of stationary and moving cracks in isotropic media subjected to a hyperbolic thermal shock in the framework of the eXtended Finite Element Method (XFEM) is examined. For this purpose, the thermally nonlinear fully coupled Lord-Shulman (LS) model is considered as governing equations. In addition, two cases of material properties, temperature-dependent (TD) and temperature-independent (TID), are assumed. The geometry, including a predefined crack, is modeled using the XFEM for spatial discretization. For modeling the dynamic crack growth within the XFEM, the Maximum Tangential Stress (MTS) criterion is modified based on the stress field near the tip of a growing crack to calculate the dynamic crack growth angle. Besides, the nonlinear form of the Newmark integration scheme is implemented for the numerical integration in the time domain. Finally, a method based on one of the Barnet-Lothe tensors for isotropic materials is employed to extract the stress intensity factors (SIFs). In the provided examples, the effects of thermal nonlinearity, the temperature-dependency of material properties, and the LS relaxation time on the crack propagation path are explored.

Four-wave mixing on thermal and resonant nonlinearities with feedback for object and signal waves

Background. The need to create highly efficient four-wave radiation converters in order to use them in adaptive optics systems, for real-time processing of complex spatio-temporal fields, in interferometry, quantum cryptography, etc. requires along with the use of traditional methods to increase the efficiency of such converters by increasing the interaction length, radiation power density, effective value of the nonlinear susceptibility of the development of new methods. One of these methods is a method based on the imposition of feedback on one or more interacting waves. Aim. The influence of feedback on the amplitude reflection coefficient of the degenerate four-wave radiation converter on thermal and resonant nonlinearities has been considered. Methods. The amplitude reflection coefficient of a degenerate four-wave radiation converter on thermal and resonant nonlinearities in the presence of feedback for both object and signal waves has been analyzed by a numerical method based on the multiple passage of the signal and object waves of the nonlinear layer in the ring resonator. Results. It was shown, that the difference in the reflection coefficients in the presence and absence of feedback for both object and signal waves increase monotonically with a growth in the pumping waves intensity and does not depend on the parameter characterizing the relationship between thermal and resonant nonlinearities at the approximation of a small reflection coefficient. Conclusion. The range of values of the absorption coefficient in which the imposition of feedback for both object and signal waves leads to an increase in the efficiency of the four-wave radiation converter has been established.

Current Measurement Offset Error Compensation for IFOC Induction Motor Drives

In vector control, the accuracy of the current measurement is crucial for ensuring good control performance. However, current measurement offset error is caused by various reasons in the current sensors, the op-amplifiers, and the A/D conversion circuits, such as thermal drift and nonlinearity. The measurement offset error results in undesired current ripples, which deteriorates the speed and torque control performance of the vector-controlled drive systems. This paper proposes the PI-type observer-based current offset error compensation method for the induction motor (IM). The proposed PI-type observer can estimate the DC offset error during the motor operation, which is designed in the stationary reference frame. This study analyzes the effect of the parameter mismatch and confirms the robustness of the parameter mismatch. Simulation and experimental results are provided to verify the performance of the current measurement offset error compensation method.

Interplay of reorientational and thermal solitons: unveiling the dynamic coexistence and enhanced nonlinear response in nematic liquid crystals

Spatial solitons in nematic liquid crystals (NLC) are optical beams that maintain their transverse profile due to the self-focusing effect of light. The mechanism leading to the formation of solitons can be either light-induced reorientation of the elongated molecules or thermal changes in the refractive index induced by a light beam. The specific optical properties of nematic liquid crystals cause the reorientational and thermal solitons to coexist in NLC, and their mutual competition can lead to a reduction or enhancement of the overall nonlinear response of the NLC. The study of the interplay between reorientational and thermal solitons allows a better understanding of the conditions under which the solitons can coexist, compete, or enhance each other. Here, we show that the simultaneous existence of both soliton types can lead to a more robust and versatile nonlinear response and can be used in competitive and synergistic configurations by carefully controlling the temperature, intensity, and polarization of the propagating light. As a result of our experimental findings, it may be possible to shape the nature of the interplay between reorientational and thermal solitons and better understand the behavior of reorientational solitons under varying thermal conditions. Furthermore, understanding this mutual interplay may provide insights into the potential of advanced NLC-based photonic devices that exploit the joint effect of reorientational and thermal nonlinearities.

Closed Form Expressions for Nonlinear Analysis of FG-GPLRC Beam Under Thermal Loading: Thermal Postbuckling and Nonlinear Bending

Considering that the exact solution for thermal buckling and post-buckling of the graphene platelets (GPLs)-reinforced composite beam in exposure to temperature changes has not been so far addressed, this problem is investigated in this research. The governing equations of the beam under thermal buckling load were acquired using the principle of virtual work, first-order shear deformation theory, and von Kármán strain field. The effective properties of the materials were then determined using the Halpin–Tsai model and rule of mixtures. Three coupled nonlinear equations are established and solved directly. Results are obtained for beams with clamped and simply supported edges. After validating the results, the effects of changing the GPLs distribution pattern and weight fraction changes on the critical thermal buckling load were evaluated. It is highlighted that for beams with simply supported edges and asymmetric distribution of material properties, the response is not of the bifurcation type.

Propagation dynamics of hybrid-order Poincaré beams in thermal nonlocal media

We study the propagation dynamics of hybrid-order Poincaré (HOP) beams, consisting of two coaxially propagating, orthogonal circularly polarized beams with different topological charges, in a nonlocal medium with thermal nonlinearity. By numerically observing the evolution of beamwidth, isosurface and light intensity with propagation distance, we verify that a HOP soliton with a certain beamwidth ratio can exist only at a proper power ratio. At a fixed propagation distance, the rotation of polarization component of the HOP breather can be controlled linearly by the input power. The polarization of HOP beams is observed as a function of the propagation distance, and the evolution regularity of the polarized rotation angle and ellipticity angle of HOP soliton and HOP breather is summarized.

Platicon stability in hot cavities.

Stability of platicons in hot cavities with normal group velocity dispersion at the interplay of Kerr and thermal nonlinearities was addressed numerically. The stability analysis was performed for different ranges of pump amplitude, thermal nonlinearity coefficient, and thermal relaxation time. It was revealed that for the positive thermal effect (i.e., the directions of the nonlinear and thermal resonance shifts are the same), the high-energy wide platicons are stable, while the negative thermal coefficient provides the stability of narrow platicons.

Thermal nonlinearity and all-optical switching of synthesized Azo-Cl compound

Azo-Cl compound is synthesized and fully characterized via NMR and mass spectroscopies. The Azo-Cl compound thermal properties, theoretical chemical shifts, chemical structure, electron absorption spectrum, frontier molecular orbitals, the atomic dipole moment, corrected Hirshfeld charge analysis and electrostatic molecular potential of the Azo-Cl compound are studied in details. The Azo-Cl compound nonlinear refractive index (NLRI) is estimated via diffraction patterns (DPs) and the Z-scan, using low power continuous wave (cw) laser beam. The all-optical switching (AOS) property is recognized in the Azo-Cl compound using two laser beams. We found that the value of the NLRI of sample calculated by the diffraction patterns is greater than the value calculated by the Z-scan, due to the use of different input powers in both cases. The experimental results proved that the sample showed a high NLRI in the range of 10−7 calculated by the Z-scan method under low input power of 5 mW, which indicates that the Azo-Cl compound is a good candidate to be used in optical device applications.