Response Regime Research Articles

Finite-size effects in response functions of molecular systems

We consider an electron in a localized potential submitted to a weak external, time-dependent field. In the linear response regime, the response function can be computed using Kubo’s formula. In this paper, we consider the numerical approximation of the response function by means of a truncation to a finite region of space. This is necessarily a singular approximation because of the discreteness of the spectrum of the truncated Hamiltonian, and in practice a regularization (smoothing) has to be used. Our results provide error estimates for the response function past the ionization threshold with respect to both the smoothing parameter and the size of the computational domain.

Pasting and Rheological Properties of Starch Paste/Gels in a Sugar-Acid System.

This study was to investigate the impact of granule size, amylose content, and starch molecular characteristics on pasting and rheological properties of starch paste/gels in neutral (water) and sugar-acid systems. Normal rice starch (RS), waxy rice starch (WRS), normal tapioca starch (TS), and waxy tapioca starch (WTS) representing small-granule starches and intermediate-granule starches respectively, were used in the study. Impacts of granule size, AM content, and their synergistic effects resulted in different starch susceptibility to acid hydrolysis and interactions between starch and sucrose-water, yielding different paste viscosities in both systems. The high molecular weight (Mw¯) and linearity of amylopectin and amylose molecules increased the consistency of starch pastes. RS produced a stronger and more brittle gel than other starch gels in both neutral and sugar-acid systems. The results indicated the impact of the effect of granule size and amylose content on starch gel behaviors. Properties of waxy starch gels were mainly governed by amylopectin molecular characteristics, especially in the sugar-acid system. Adding sugar and acid had minor impacts on starch gel behaviors in the linear viscoelastic (LVE) region but were most evident in the nonlinear response regime of starch gels as shown in the Lissajous curves at large oscillatory strain.

One experiment makes a direct comparison of structural recovery with equilibrium relaxation.

For a molecular glass-former, propylene glycol, we directly compare the equilibrium fluctuations, measured as "structural" relaxation in the regime of linear response, with structural recovery, i.e., field induced physical aging in the limit of a small perturbation. The two distinct correlation functions are derived from a single experiment. Because the relaxation time changes only 2% during structural recovery, no aging model is needed to analyze the results. Although being conceptually different processes, dielectric relaxation and recovery dynamics are observed to be identical for propylene glycol, whereas single-particle dynamics as seen by photon correlation spectroscopy are significantly faster. This confirms the notion that structural recovery and aging are governed by all modes observed by dielectric spectroscopy, i.e., including cross correlations, not only by single-particle dynamics. A comparison with analogous results for other materials suggests that the relation between relaxation and recovery time scales may be material specific rather than universal.

Nonlinear dynamic characteristics of a hysteretic TMD and its application on a tall building

Hysteretic tuned mass damper (HTMD) has shown strong capacity on the vibration control for high-rise buildings. However, the dynamic effect of HTMD has not been thoroughly studied. In this paper, the nonlinear dynamic characteristics of a harmonically excited system equipped with HTMD are investigated firstly with a thorough parametric analysis. The extended incremental harmonic balance method is used to obtain the frequency responses of this nonlinear system. The Floquet theory is adopted to examine the stability of response. Poincare map and bifurcation diagram are employed to study the response regimes and bifurcations near the resonance frequency. Finally, a high-rise building equipped with HTMD is investigated under transverse wind excitation. Standard deviation of response is employed to examine the control effect of HTMD, by comparing to a linear TMD. The obtained results show that a well-designed HTMD can have superior performance in suppressing the vortex-induced vibration, and a more effective energy absorbing capacity than linear TMD.

Electric field influenced coordinate jump of the guiding centre and magnetotransport

ABSTRACT Our studies formulate a classical theory to study the influence of in-plane electric field on electron-impurity scattering process and magnetotransport in a two-dimensional space, in the presence of a strong out-of-plane magnetic field. Our studies connect classical scattering and quantum Landau Level broadening, as will be reviewed in this report. We derived an electric current formula in agreement with the current derived from the Drude theory under a strong magnetic field. Our electric current formula is derived microscopically from the migration of the guiding centres at strong magnetic field regime . The electron-impurity scattering under electromagnetic field not only shifts the guiding centre coordinates X and Y, but also changes cyclotron radius R. The change of cyclotron radius R compensates the change of the electric potential energy during the scattering process. The broadening of cyclotron radius is a classical manifestation of Landau Levels broadening. Our conductivity derived from our current formula in the linear response regime results in the same as the current derived from Kubo current fluctuation theory, providing a special case of the fluctuation-dissipation theorem.

Allelic correlation is a marker of trade-offs between barriers to transmission of expression variability and signal responsiveness in genetic networks.

Genetic networks should respond to signals but prevent the transmission of spontaneous fluctuations. Limited data from mammalian cells suggest that noise transmission is uncommon, but systematic claims about noise transmission have been limited by the inability to directly measure it. Here, we build a mathematical framework modeling allelic correlation and noise transmission, showing that allelic correlation and noise transmission correspond across model parameters and network architectures. Limiting noise transmission comes with the trade-off of being unresponsive to signals, and within responsive regimes, there is a further trade-off between response time and basal noise transmission. Analysis of allele-specific single-cell RNA-sequencing data revealed that genes encoding upstream factors in signaling pathways and cell-type-specific factors have higher allelic correlation than downstream factors, suggesting they are more subject to regulation. Overall, our findings suggest that some noise transmission must result from signal responsiveness, but it can be minimized by trading off for a slower response. A record of this paper's transparent peer review process is included in the supplemental information.

Temperature response to periodic modulation in internal heating convection

Thermal convection in nature and industrial applications usually encounters time-varying internal heating (IH); however, the effect of temporal modulation on temperature responses and heat fluxes of the system has been rarely explored. Here, we numerically studied the IH convection with a temporally periodic heating source. We conducted direct numerical simulations over Rayleigh number (Ra) range 105≤Ra≤109 at fixed Prandtl number Pr = 1 with dimensionless modulation frequency 4×10−5≤f≤10−1 and amplitude fixed at Ω = 1. We first find that the introduction of periodic modulation has a slight effect on the heat transport over the individual plates and flow strength except for the lowest Ra. We then focus on the characteristics of the amplitude A and phase lag Δϕ of the globally averaged temperature response to the periodic modulation. Three regimes of the phase response are identified: (i) in-phase regime, where synchronous response is found at small frequencies with the vanished phase lag Δϕ and A keeping at constant value; (ii) transition regime, where both Δϕ and A decrease with increasing f for moderate frequencies; and (iii) half anti-phase regime, where Δϕ attains the minimal value −π/2. We also find that the transition behavior between three regimes can be well described using the normalization of the Ra-dependent critical frequency with the scaling Ra−0.30. To explain the regime transition, we further theoretically deduce an analytical solution for A and Δϕ, which agrees well with the numerical results. This solution can explain why fRa0.30 gives a good description of the transition behavior. Our present findings provide a fundamental understanding of the underlying mechanism of temporal modulation on IH systems and have substantial implications for the investigation of convective system with periodic heating source.

Impatiens glandulifera (Balsaminaceae) in Ukraine: its current distribution, ecological and coenotic features

Abstract Data on the spontaneous distribution (529 sites) of Impatiens glandulifera in the territory of Ukraine have been collected and studied comprehensively. I. glandulifera invades plant communities of the Phragmito-Magnocaricetea class (1 alliance), Salicetea purpureae (1 association), Alnetea glutinosae (1 association), Robinietea (2 associations), and Epilobietea angustifolii (2 associations). The species phytoindicative assessment, which considered 12 ecological factors, revealed that in its secondary distribution range I. glandulifera shows charactericstics of a stenotopic hygromesophyte, subacidophile and is a semi-eutrophic species. In the studied areas, the environmental niche of I. glandulifera is limited mainly by soil water response (Hd) and saline (Sl) regimes, and soil carbonate content. A thermal regime (Tm) response of the species to an increase in the average annual air temperature by 1, 2, and 30С has been predicted. A temperature increase of 20С could, lead to a critical shift in the values of soil acidity (Rc) and salinity regimes (Sl) that might cause a decline of the species’ potential niches in the studied area. The obtained data have the potential to be useful in limiting the spread of I. glandulifera into new territories and reducing its transforming effect in plant communities of river valley corridors.

Vortex-induced vibration of a circular cylinder with nonlinear restoring forces at low-Reynolds number

The numerical simulation of two-dimensional flows around an elastically-mounted circular cylinder on a linear/quadratic spring configuration at low-Reynolds number (Re) is conducted in order to study the vortex-induced vibration (VIV) of the system. The extent of Re used in this study range from 50 to 150 inclusive. The data obtained from the numerical simulations are used to investigate the impact of the nonlinearity in the spring configuration on the VIV response of the dynamical system. The equivalent natural frequency for a circular cylinder supported elastically on a linear/quadratic spring is derived and found to depend on the square root of the maximum amplitude of the transverse displacement. The range of Re associated with the initial branch of the response is increased (extended) and the upper and lower branches are suppressed (almost disappearing when the hardening nonlinearity is sufficiently strong) for an elastically-mounted cylinder on a linear/quadratic spring configuration compared to that for the same cylinder supported elastically on a linear spring. The detailed characteristics (e.g., vortex shedding modes, amplitude and oscillation frequency of the transverse displacement, etc.) of the lock-in range and the transition out of this range for the VIV system as a function of increasing Re is studied using power spectrum, phase portrait and dynamical mode decomposition analysis. The information obtained from the analysis is synthesized in order to investigate the different physical mechanisms and phenomena appearing in the VIV system and how these are linked to the underlying vortex shedding and amplitude response regimes (initial branch, upper branch, desynchronization branch) of the dynamics of the fixed (stationary) and elastically-mounted cylinder.

Relation between fluctuations and efficiency at maximum power for small heat engines

We study the ratio between the variances of work output and heat input, $\eta^{(2)}$, for a class of four-stroke heat engines which covers various typical cycles. Recent studies on the upper and lower bounds of $\eta^{(2)}$ are based on the quasistatic limit and the linear response regime, respectively. We extend these relations to the finite-time regime within the endoreversible approximation. We consider the ratio $\eta_{\text{MP}}^{(2)}$ at maximum power and find that the square of the Curzon-Ahlborn efficiency, $\eta_{\text{CA}}^2$, gives a good estimate of $\eta_{\text{MP}}^{(2)}$ for the class of heat engines considered, i.e., $\eta_{\text{MP}}^{(2)} \simeq \eta_{\text{CA}}^2$. This resembles the situation where the Curzon-Ahlborn efficiency gives a good estimate of the efficiency at maximum power for various kinds of finite-time heat engines. Taking an overdamped Brownian particle in a harmonic potential as an example, we can realize such endoreversible small heat engines and give an expression of the cumulants of work output and heat input. The approximate relation $\eta_{\text{MP}}^{(2)} \simeq \eta_{\text{CA}}^2$ is verified by numerical simulations. This relation also suggests a trade-off between the efficiency and the stability of finite-time heat engines at maximum power.

Response regimes in the fluid–structure interaction of wall turbulence over a compliant coating

The interaction between a turbulent boundary layer flow and compliant surfaces is investigated experimentally. Three viscoelastic coatings with different material stiffnesses are used to identify the general surface response to the turbulent flow conditions. For the softest coating, the global force measurements show two obvious regimes of interaction with an indicated transition at $U_b/C_t\sim 3.5$ , where $U_b$ is the bulk flow velocity and $C_t$ is the coating shear velocity. The one-way coupled regime shows friction values comparable to those of the rigid wall, while the two-way coupled regime indicate a significant increase in fluid friction. Within the one-way coupled regime for $U_b/C_t>1.2$ , the flow measurements show a low level of two-way coupling represented by the change of the velocity profile as well as the increase in the Reynolds stresses in the near-wall region. This is supported by the surface deformation measurements. Initially, the turbulent flow structures induce only an imprint on the coating surface, while a change in surface response occurs when the surface wave propagation velocity $c_w$ equals the shear wave velocity of the coating $C_t$ (i.e. $c_w/C_t\sim 1$ ). Above $U_b/C_t>1.2$ , a growth in wavelength is observed with increasing flow velocity, most probably due to the surface wave formation generated downstream the pressure features of the flow. The surface response is stable and correlates with the high-intensity turbulent pressure fluctuations in the turbulent boundary layer, with a wave propagation velocity $c_w\sim 0.7\unicode{x2013}0.8$ $U_b$ . Within the two-way coupled regime, additional fluid motions and a downward shift in the logarithmic region of the velocity profile are observed due to substantial surface deformation and confirm the frictional drag increase. Another type of surface response is initiated by phase-lag instability in combination with surface undulations that start to protrude the viscous sublayer, where the propagation velocity of surface wave trains is $c_w\sim 0.17\unicode{x2013}0.18$ $U_b$ .

Vibration suppression of a linear oscillator by a chain of nonlinear vibration absorbers with geometrically nonlinear damping

Nonlinear energy sink (NES) is a lightweight vibration absorber that is coupled to linear primary structure for passive vibration mitigation. In this work, we aim to investigate the effects of geometrically nonlinear damping on the capacity of multiple-degree-of-freedom (MDOF) NES to mitigate forced responses of the impulsively and harmonically loaded linear oscillator (LO). For the system under applied shock excitation, extensive simulation results show that the internal use of nonlinear damping enables the MDOF NES to rapidly and effectively absorb, transfer and dissipate the shock-induced energy for a broad range of initially imparted energies, particularly for the high or very high energy levels. The effectiveness of the optimized MDOF NES is further improved since the large-amplitude oscillations of the LO are reduced to a sufficiently low level during initial regime of motion. When the LO is subjected to harmonic excitations, the analytical study is performed to obtain the slow invariant manifold (SIM) by means of complexification-averaging (CX-A) method. The complex geometry of SIM reveals the energy transfer paths when the system reaches steady state. The global system behavior (strongly modulated response or periodic oscillation regimes) is analytically predicted by the singular points and ordinary equilibrium points, and a close match is achieved between theoretical analysis and numerical results. It is found that the proposed MDOF NES with nonlinear damping can eliminate the upper closed high-amplitude isolated branch, and the frequency bandwidth of multiple steady-state responses also decreases, the robustness and capacity of vibration attenuation by the proposed NES is dramatically enhanced. The findings in this work facilitate the design and broad applications in diverse engineering fields for the protection and safe operation of mechanical structures.

Targeted energy transfer in a vibro-impact cubic NES: Description of regimes and optimal design

In this study, we address the response regimes of a novel Nonlinear Energy Sink (NES) that couples both cubic and impact nonlinearities. In a non-smooth condition, the conventional multiple scales method is considered with impact condition. By identifying the occurrence of the collision, the asymptotic analysis of the equivalent cubic NES model and Vibro-Impact (VI) NES model can illustrate the fixed point of the Vibro-Impact Cubic (VIC) NES. Three types of VIC NES are described as a function of clearance length. The role of clearance length on the response regimes is provided, offering solid criteria for optimal design. Combined with the simulation results, our experimental observations prove the restraint effect of impact on the robustness of the Strongly Modulated Response (SMR).

Dipole dynamics of an interacting bosonic mixture

We unravel the coupled dipole dynamics of a two-species Bose-Einstein condensate with tunable interspecies interaction. We produce a degenerate mixture of $^{41}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ in an optical trap and we study the dipole oscillations of both atomic species in the linear response regime. Varying the interspecies interaction from the weakly to the strongly attractive side, we measure the frequencies and the composition of the two dipole eigenmodes. For sufficiently strong interactions, even beyond the mean-field collapse, we find that the frequency of the low-energy eigenmode is determined only by the bare trap frequencies and the species population imbalance. The experimental results are well reproduced by numerical simulations based on two coupled Gross-Pitaevskii equations. Our findings provide a detailed picture of the dipole excitations in asymmetric bosonic mixtures.

From very low to high fields: The dielectric behavior of the liquid crystal 5CB

The liquid crystal 4-cyano-4′-pentylbiphenyl (5CB) is investigated regarding its nonlinear dielectric behavior as reflected in the dependence of the static dielectric constant εs on the magnitude of the electric field. The initial flow-induced homogeneous orientation of nematic domains can be erased by moderate electric fields, yielding states with little to no preferred orientation. Such samples are then subjected to ac and dc electric fields of various amplitudes, covering more than four orders of magnitude, between <10 V cm−1 to 220 kV cm−1. Their regime of linear dielectric response, i.e., field invariant static permittivity, is limited to fields <10 V cm−1, equivalent to a voltage <50 mVrms across a 50 μm thick sample. The Piekara factor, which gauges the sensitivity of εs to E2, is a factor of 108 times larger at low fields than its counterpart at elevated fields, where the nematic domains are highly aligned in homeotropic orientation. After removing the electric field, the nematic system returns to a state with little residual alignment, as judged by the dielectric constant settling near the value of the orientational average, 〈ε〉 = (ε|| + 2ε⊥)/3, and not far from that of the isotropic phase, εiso. The structural recovery associated with a field induced change in alignment is slow compared with dipole reorientation. For a different nematogen, itraconazole, no such extreme sensitivity to electric fields is found.

Assessment of spatio-temporal patterns of water quality in a tropical river by multivariate statistical analysis and water quality index methods

Rivers are facing seasonal as well as long-term changes in their hydro-ecological regime in response to multiple stressors that have affected water quality as well as flow volumes. Ramganga is an important tributary of the Ganga River that provides freshwater to the people of Uttar Pradesh and Uttarakhand. In recent years, industrial discharges, agricultural and municipal wastes and wastewater releases have severely polluted the river throughout its stretch. The contamination index (CI) values at Moradabad in the pre-monsoon, monsoon and post-monsoon seasons were 0.78, 0.86, 0.76-not contaminated, at Bareilly 1.68, 1.65, 1.22-slightly contaminated, at Dabri 2.32, 2.34, 1.76-slightly contaminated while the pollution index (PI) values at Moradabad were 1.76, 2.23, 1.43-slightly contaminated, at Bareilly 4.29, 4.49, 3.95-severely contaminated and at Dabri 13.06, 12.21, 9.49- severely contaminated. The pollutants responsible for high pollution are NH3+, PO4-3, SO4-2, NO2-+NO3- which primarily come from agricultural run-off as the farmers use phosphate, ammonium and sulphate fertilizers and pesticides. The land use type along the banks of the Ramganga in Bareilly and Dabri is primarily dominated by agricultural lands. Hence, the increased CI and PI values at Bareilly and Dabri clearly indicate high agricultural pollution.

Giant Second-Order Nonlinear Hall Effect in Twisted Bilayer Graphene.

In the second-order response regime, the Hall voltage can be nonzero without time-reversal symmetry breaking but inversion symmetry breaking. Multiple mechanisms contribute to the nonlinear Hall effect. The disorder-related contributions can enter the NLHE in the leading role, but experimental investigations are scarce, especially the exploration of the contributions from different disorder sources. Here, we report a giant nonlinear response in twisted bilayer graphene, dominated by disorder-induced skew scattering. The magnitude and direction of the second-order nonlinearity can be effectively tuned by the gate voltage. A peak value of the second-order Hall conductivity reaching 8.76 μm SV^{-1} is observed close to the full filling of the moiré band, four order larger than the intrinsic contribution detected in WTe_{2}. The scaling shows that the giant second-order nonlinear Hall effect in twisted bilayer graphene stems from the collaboration of the static (impurities) and dynamic (phonons) disorders. It is mainly determined by the impurity skew scattering at 1.7K. The phonon skew scattering, however, has a much larger coupling coefficient, and becomes comparable to the impurity contribution as the temperature rises. Our observations provide a comprehensive experimental understanding of the disorder-related mechanisms in the nonlinear Hall effect.

Ultrafast Excitonic Response in Two-Dimensional Hybrid Perovskites Driven by Intense Midinfrared Pulses.

Two-dimensional organic-inorganic hybrid perovskites (2DHPs) are natural quantum-well-like materials, in which strong quantum and dielectric confinement effects due to the organic spacers give rise to tightly bound excitons with large binding energy. To examine the mutual interactions between the organic spacer cations and the inorganic charge-residing octahedral framework in 2DHPs, here we perform femtosecond pump-probe spectroscopy by direct vibrational pumping of the organic spacers, followed by a visible-to-ultraviolet probe covering their excitonic resonances. Measurements on prototypical lead-bromide based 2DHP compounds, (BA)_{2}PbBr_{4} and (BA)_{2}(FA)Pb_{2}Br_{7} (BA^{+}=butylammonium; FA^{+}=formamidinium), reveal two distinct regimes of the temporal response. The first regime is dominated by a pump-induced transient expansion of the organic spacer layers that reduces the exciton oscillator strength, whereas the second regime arises from pump-induced lattice heating effects primarily associated with a spectral shift of the exciton energy. In addition, vibrational excitation enhances the biexciton emission, which we attribute to a stronger intralayer exciton confinement as well as vibrationally induced exciton detrapping from defect states. Our study provides fundamental insights regarding the impact of organic spacers on excitons in 2DHPs, as well as the excited-state dynamics and vibrational energy dissipation in these structurally diverse materials.

Negative resistance and heat dissipation in superconducting wires in an ac magnetic field

A superconducting wire embedded into an alternating magnetic field H∝cos(ωt) can manifest negative resistance. At high enough frequencies ω≳1/τ, where τ is the characteristic time of magnetic relaxation, this effect becomes prominent. As a result, the energy obtained by the wire from a source of magnetic field (external coil) is transformed into the electromotive force which reduces the external voltage required to keep the transport current in the wire. We show that negative resistance appears in line with the out-of-phase regime of the ac magnetic response, and both are related with the crucial inhibition of the vortex dynamics by zero-field (annihilation) lines. We also find a universal (independent of frequency) expression for the mean voltage in a wire.

Analysis and Measurement of Noise Suppression in a Nonlinear Regenerative Amplifier

This paper analyzes the ability to suppress in-band noise power of a regenerative amplifier (RA) operating in the nonlinear regime in response to a continuous wave (CW) input tone. As opposed to the linear regime where a CW tone and the noise floor experience the same transfer function, it is shown that the non-linear saturation behavior of an RA yields different transfer characteristics between a CW tone and noise, ultimately leading to an improvement in the output carrier-to-noise ratio (CNR). This is all thanks to the high gain, narrow bandwidth, and the compressive third-order nonlinearity of the RA. This non-linear noise suppression is first analyzed mathematically using single tones in the frequency domain to represent the signal and the noise. Then, simulation of an RA circuit model is shown to be in excellent agreement with the analytical results. Lastly, a discrete RA has been implemented to experimentally verify the noise-suppression phenomenon. The measurement results clearly demonstrate noise suppression and show an output CNR improvement of up to 3 dB. Potential applications of the RA with noise suppression are also discussed.