Assumption Of Linear Response Research Articles

Update of SO2 emission inventory in the Megacity of Chongqing, China by inverse modeling

Chongqing, a metropolitan with over 32 million residents in southwest China, has suffered from SO2 pollution since 1980s. The emission inventory is an important tool to evaluate the SO2 pollution and to design the effective emission reduction policies. The present work developed a scheme to update the obsolescent SO2 emission inventory in Chongqing obtained from Multi-resolution Emission Inventory for China in 2008 (MEIC2008). The updated emission inventory was estimated by integrating the a priori knowledge of the baseline emissions and the current observations based on Bayesian inference, in which the source-receptor sensitivities were calculated by the Decoupled Direct Method in Three Dimensions in the Community Multiscale Air Quality Modeling System (CMAQ DDM-3D). An analytical solution of the Bayesian theorem was derived based on the linear response assumption and applied to estimate the actual SO2 emissions. The updated emission inventory was comparable with the most recent MEIC emission inventory in 2016 and 2017, and was in line with the decline trend of SO2 emissions in Chongqing in the last decade. The adjustment of the emissions improved the accuracy in predicting SO2 concentrations with the developed method.

Nernst coefficient measurements in two-dimensional materials

The discovery of two-dimensional (2D) ferromagnets and antiferromagnets with topologically nontrivial electronic band structures makes the study of the Nernst effect in 2D materials of great importance and interest. To measure the Nernst coefficient of 2D materials, the detection of the temperature gradient is crucial. Although the micro-fabricated metal wires provide a simple but accurate way for temperature detection, a linear-response assumption that the temperature gradient is a constant is still necessary and has been widely used to evaluate the temperature gradient. However, with the existence of substrates, this assumption cannot be precise. In this study, we clearly show that the temperature gradient strongly depends on the distance from the heater by both thermoelectric transport and thermoreflectance measurements. Fortunately, both measurements show that the temperature gradient can be well described by a linear function of the distance from the heater. This linearity is further confirmed by comparing the measured Nernst coefficient to the value calculated from the generalized Mott’s formula. Our results demonstrate a precise way to measure the Nernst coefficient of 2D materials and would be helpful for future studies.

Investigation of the Failure of Marcus Theory for Hydrated Electron Reactions.

Reactions of the hydrated electron with a wide variety of substrates have been found to exhibit unusually similar activation energies in a manner incompatible with Marcus electron transfer theory. Given the fundamental linear response assumption of Marcus theory, one possible explanation for this apparent failure is that the underlying free energy surfaces governing the reactions are not harmonic; i.e., hydrated electron structural fluctuations exhibit non-Gaussian behavior. In this work, we test this hypothesis by using simulations to calculate the hydrated electron vertical detachment energy distribution. We consider both cavity and noncavity models for the hydrated electron, between which the actual hydrated electron behavior is expected to lie. Our results identify a possible origin for non-Gaussian behavior of the hydrated electron but show that it is not of sufficient magnitude to explain the failure of Marcus theory to describe its reactions. Thus, other explanations must be sought.

Confirming the role of nuclear tunneling in aqueous ferrous–ferric electron transfer

We revisit the well-known aqueous ferrous-ferric electron transfer reaction in order to address recent suggestions that nuclear tunneling can lead to significant deviation from the linear response assumption inherent in the Marcus picture of electron transfer. A recent study of this reaction by Richardson and co-workers [Phys. Chem. Chem. Phys. 22, 10687 (2020)] has found a large difference between their new path-integral method, golden-rule quantum transition state theory (GR-QTST), and the saddle point approximation of Wolynes (Wolynes theory). They suggested that this difference could be attributed to the existence of multiple tunneling pathways, leading Wolynes theory to significantly overestimate the rate. This was used to argue that the linear response assumptions of Marcus theory may break down for liquid systems when tunneling is important. If true, this would imply that the commonly used method for studying such systems, where the problem is mapped onto a spin-boson model, is invalid. However, we have recently shown that size inconsistency in GR-QTST can lead to poor predictions of the rate in systems with many degrees of freedom. We have also suggested an improved method, the path-integral linear golden-rule (LGR) approximation, which fixes this problem. Here, we demonstrate that the GR-QTST results for ferrous-ferric electron transfer are indeed dominated by its size consistency error. Furthermore, by comparing the LGR and Wolynes theory results, we confirm the established picture of nuclear tunneling in this system. Finally, by comparing our path-integral results to those obtained by mapping onto the spin-boson model, we reassess the importance of anharmonic effects and the accuracy of this commonly used mapping approach.

Improved intact peptide and protein quantitation by LC-MS: Battling the deleterious effects of analyte adsorption.

Peptide and protein quantitation by liquid chromatography-mass spectrometry relies on the assumption of linear signal response with concentration. At low concentrations, analyte adsorption to pipette tips, sample vials and equipment can have significant deleterious effects on signal response. Meanwhile at high concentrations, linearity breaks down due to competitive ionization, signal suppression, and the formation of peptide or protein multimers. These effects result in calibration curves that are more sigmoidal than linear. Linearity at low protein levels for identification and quantitation is of paramount importance in the discovery and validation of biomarker molecules. Herein, we demonstrate the benefits of using commercial low-bind microcentrifuge tubes and LC vials on the response of a 27-mer peptide, Vn96, and the intact proteins apomyoglobin and carbonic anhydrase. Linear curves were acquired for Vn96 while apomyoglobin required the addition of intact carbonic anhydrase as an adsorption competitor to achieve linearity. A linear calibration curve for carbonic anhydrase was also acquired by using the polypeptide ubiquitin as an adsorption competitor and internal standard. Linear response was recorded for approximately two orders of magnitude for apomyoglobin and carbonic anhydrase and three orders of magnitude for Vn96 with detection limits ranging from 0.33 to 19 fmol/µL. Finally, we used low-bind vials for the online enzymatic digestion of apomyoglobin where a high concentration of apomyoglobin acted as an adsorption blocker for the low level trypsin enzyme. Fortunately, the liberated tryptic peptides showed no affinity for the walls of the low-bind vials. In this study, we take a comprehensive approach to combat analyte adsorption by showing the significance of utilizing low-bind vials and adsorption competitors to greatly improve upon signal sensitivity at low concentrations of target molecules. The use of these methodologies should improve the low-level detection of molecules by mass spectrometry.

Charge and pairing dynamics in the attractive Hubbard model: Mode coupling and the validity of linear-response theory

Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to non-equilibrium situations. Here we examine the validity of such an approach within the attractive Hubbard model for which the dynamics of pairing and charge-density wave orders is computed using the time-dependent Hartree-Fock approximation (TDHF). Our calculations reveal that the `linear-response assumption' is justified for small to moderate non-equilibrium situations (i.e., pump pulses) when the symmetry of the pump-induced state differs from that of the external field. This is the case, when we consider the pairing response in a charge-ordered state or the charge-order response in a superconducting state. The situation is very different when the non-equilibrium state and the external probe field have the same symmetry. In this case, we observe significant changes of the response in magnitude but also due to mode coupling when moving away from an equilibrium state, indicating the failure of the linear-response assumption.

Controlling deformations of electro-active truss structures with nonlinear history-dependent response

This study presents simulations of shape changing in active truss structures that undergo non-linear and time dependent response. The truss structure comprises of slender members with electro-active (piezoelectric) components joined by pins, allowing for large deformations due to rotations at the pins. A nonlinear time-dependent electro-mechanical constitutive model is considered for the piezoelectric components in the truss systems. In order to find the actuation inputs to achieve a desired shape, the required shape is defined with respect to reference configuration for a equivalent 3 dimensional continuum. The mapping between reference and current configuration is used to calculate the macroscopic strains in the continuum. The corresponding strains along the longitudinal axes of the truss members whose ends coincide with certain material points in the continuum are then calculated. The strains corresponding to the predefined shapes are achieved by applying electric field through the piezoelectric materials, and as a result the truss system undergoes the desired shape changes. The shape changing behaviors in electro-active truss systems are analyzed using a finite element (FE) method, incorporating nonlinear material and geometry. Numerical implementation of the active truss structures is also presented. Two types of truss configurations are considered which are planar and beam configurations. The planar configuration is formed by arrangement of cubical truss elements while the beam configuration consists of several tetrahedral truss elements. Several shape configurations of the planar and beam truss structures are shown as examples. While considerable amount of work has been done with piezo-actuated truss systems under the assumption of linear piezoelectric response, we study the influence of the nonlinear hysteretic electro-mechanical behavior and highlight the differences in the deformations of the truss structures when the nonlinear and time-dependent electro-mechanical and linear electro-mechanical models are considered for the piezoelectric components.

Vertical ground motion and its effects on liquefaction resistance of fully saturated sand deposits.

Soil liquefaction has been extensively investigated over the years with the aim to understand its fundamental mechanism and successfully remediate it. Despite the multi-directional nature of earthquakes, the vertical seismic component is largely neglected, as it is traditionally considered to be of much lower amplitude than the components in the horizontal plane. The 2010–2011 Canterbury earthquake sequence in New Zealand is a prime example that vertical accelerations can be of significant magnitude, with peak amplitudes well exceeding their horizontal counterparts. As research on this topic is very limited, there is an emerging need for a more thorough investigation of the vertical motion and its effect on soil liquefaction. As such, throughout this study, uni- and bidirectional finite-element analyses are carried out focusing on the influence of the input vertical motion on sand liquefaction. The effects of the frequency content of the input motion, of the depth of the deposit and of the hydraulic regime, using variable permeability, are investigated and exhaustively discussed. The results indicate that the usual assumption of linear elastic response when compressional waves propagate in a fully saturated sand deposit does not always hold true. Most importantly post-liquefaction settlements appear to be increased when the vertical component is included in the analysis.

On spurious detection of linear response and misuse of the fluctuation–dissipation theorem in finite time series

Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model of the observations, based on results for central limit theorems for deterministic dynamical systems, and used to detect linear response breakdown. We apply the method to discrete maps which do not obey linear response and show that the successful detection of breakdown depends on the length of the time series, the magnitude of the perturbation and on the choice of the observable.We find that in order to reliably reject the assumption of linear response for typical observables sufficiently large data sets are needed. Even for simple systems such as the logistic map, one needs of the order of 106 observations to reliably detect the breakdown with a confidence level of 95%; if less observations are available one may be falsely led to conclude that linear response theory is valid. The amount of data required is larger the smaller the applied perturbation. For judiciously chosen observables the necessary amount of data can be drastically reduced, but requires detailed a priori knowledge about the invariant measure which is typically not available for complex dynamical systems.Furthermore we explore the use of the fluctuation–dissipation theorem (FDT) in cases with limited data length or coarse-graining of observations. The FDT, if applied naively to a system without linear response, is shown to be very sensitive to the details of the sampling method, resulting in erroneous predictions of the response.

CRYSTAL CHEMISTRY OF THREE-COMPONENT WHITE DWARFS AND NEUTRON STAR CRUSTS: PHASE STABILITY, PHASE STRATIFICATION, AND PHYSICAL PROPERTIES

ABSTRACT A systematic search for multicomponent crystal structures is carried out for five different ternary systems of nuclei in a polarizable background of electrons, representative of accreted neutron star crusts and some white dwarfs. Candidate structures are “bred” by a genetic algorithm and optimized at constant pressure under the assumption of linear response (Thomas–Fermi) charge screening. Subsequent phase equilibria calculations reveal eight distinct crystal structures in the T = 0 bulk phase diagrams, five of which are complicated multinary structures not previously predicted in the context of compact object astrophysics. Frequent instances of geometrically similar but compositionally distinct phases give insight into structural preferences of systems with pairwise Yukawa interactions, including and extending to the regime of low-density colloidal suspensions made in a laboratory. As an application of these main results, we self-consistently couple the phase stability problem to the equations for a self-gravitating, hydrostatically stable white dwarf, with fixed overall composition. To our knowledge, this is the first attempt to incorporate complex multinary phases into the equilibrium phase-layering diagram and mass–radius-composition dependence, both of which are reported for He–C–O and C–O–Ne white dwarfs. Finite thickness interfacial phases (“interphases”) show up at the boundaries between single-component body-centered cubic (bcc) crystalline regions, some of which have lower lattice symmetry than cubic. A second application—quasi-static settling of heavy nuclei in white dwarfs—builds on our equilibrium phase-layering method. Tests of this nonequilibrium method reveal extra phases that play the role of transient host phases for the settling species.

Incremental dynamical downscaling for probabilistic analysis based on multiple GCM projections.

A dynamical downscaling method for probabilistic regional‐scale climate change projections was developed to cover the inherent uncertainty associated with multiple general circulation model (GCM) climate simulations. The climatological increments estimated by GCM results were statistically analyzed using the singular vector decomposition. Both positive and negative perturbations from the ensemble mean with the magnitudes of their standard deviations were extracted and added to the ensemble mean of the climatological increments. The analyzed multiple modal increments were utilized to create multiple modal lateral boundary conditions for the future climate regional climate model (RCM) simulations by adding them to reanalysis data. The incremental handling of GCM simulations realized approximated probabilistic climate change projections with the smaller number of RCM simulations. For the probabilistic analysis, three values of a climatological variable simulated by RCMs for a mode were analyzed under an assumption of linear response to the multiple modal perturbations.

Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations

We introduce a general framework for analyzing the thermodynamics of small systems that are driven by both a periodic temperature variation and some external parameter modulating their energy. This set-up covers, in particular, periodic micro and nano-heat engines. In a first step, we show how to express total entropy production by properly identified time-independent affinities and currents without making a linear response assumption. In linear response, kinetic coefficients akin to Onsager coefficients can be identified. Specializing to a Fokker-Planck type dynamics, we show that these coefficients can be expressed as a sum of an adiabatic contribution and one reminiscent of a Green-Kubo expression that contains deviations from adiabaticity. Furthermore, we show that the generalized kinetic coefficients fulfill an Onsager-Casimir type symmetry tracing back to microscopic reversibility. This symmetry allows for non-identical off-diagonal coefficients if the driving protocols are not symmetric under time-reversal. We then derive a novel constraint on the kinetic coefficients that is sharper than the second law and provides an efficiency-dependent bound on power. As one consequence, we can prove that the power vanishes at least linearly when approaching Carnot efficiency. We illustrate our general framework by explicitly working out the paradigmatic case of a Brownian heat engine realized by a colloidal particle in a time-dependent harmonic trap subject to a periodic temperature profile. This case study reveals inter alia that our new general bound on power is asymptotically tight.

Induction of chromosomal aberrations at fluences of less than one HZE particle per cell nucleus.

The assumption of a linear dose response used to describe the biological effects of high-LET radiation is fundamental in radiation protection methodologies. We investigated the dose response for chromosomal aberrations for exposures corresponding to less than one particle traversal per cell nucleus by high-energy charged (HZE) nuclei. Human fibroblast and lymphocyte cells were irradiated with several low doses of <0.1 Gy, and several higher doses of up to 1 Gy with oxygen (77 keV/μm), silicon (99 keV/μm) or Fe (175 keV/μm), Fe (195 keV/μm) or Fe (240 keV/μm) particles. Chromosomal aberrations at first mitosis were scored using fluorescence in situ hybridization (FISH) with chromosome specific paints for chromosomes 1, 2 and 4 and DAPI staining of background chromosomes. Nonlinear regression models were used to evaluate possible linear and nonlinear dose-response models based on these data. Dose responses for simple exchanges for human fibroblasts irradiated under confluent culture conditions were best fit by nonlinear models motivated by a nontargeted effect (NTE). The best fits for dose response data for human lymphocytes irradiated in blood tubes were a linear response model for all particles. Our results suggest that simple exchanges in normal human fibroblasts have an important NTE contribution at low-particle fluence. The current and prior experimental studies provide important evidence against the linear dose response assumption used in radiation protection for HZE particles and other high-LET radiation at the relevant range of low doses.

Spin-dependent thermoelectric effects in graphene-based spin valves

Using first-principles calculations combined with non-equilibrium Green's function (NEGF), we investigate spin-dependent thermoelectric effects in a spin valve which consists of zigzag graphene nanoribbon (ZGNR) electrodes with different magnetic configurations. We find that electron transport properties in the ZGNR-based spin valve are strongly dependent on the magnetic configurations. As a result, with a temperature bias, thermally-induced currents can be controlled by switching the magnetic configurations, indicating a thermal magnetoresistance (MR) effect. Moreover, based on the linear response assumption, our study shows that the remarkably different Seebeck coefficients in the various magnetic configurations lead to a very large and controllable magneto Seebeck ratio. In addition, we evaluate thermoelectric properties, such as the power factor, electron thermal conductance and figure of merit (ZT), of the ZGNR-based spin valve. Our results indicate that the power factor and the electron thermal conductance are strongly related to the transmission gap and electron-hole symmetry of the transmission spectrum. Moreover, the value of ZT can reach 0.15 at room temperature without considering phonon scattering. In addition, we investigate the thermally-controlled magnetic distributions in the ZGNR-based spin valve and find that the magnetic distribution, especially the local magnetic moment around the Ni atom, is strongly related to the thermal bias. The very large, multi-valued and controllable thermal magnetoresistance and Seebeck effects indicate the strong potential of ZGNR-based spin valves for extremely low-power consuming spin caloritronics applications. The thermally-controlled magnetic moment in the ZGNR-based spin valve indicates its possible applications for information storage.

QM/MM-Based Fitting of Atomic Polarizabilities for Use in Condensed-Phase Biomolecular Simulation.

Accounting for electronic polarization effects in biomolecular simulation (by using a polarizable force field) can increase the accuracy of simulation results. However, the use of gas-phase estimates of atomic polarizabilities αi usually leads to overpolarization in condensed-phase systems. In the current work, a combined QM/MM approach has been employed to obtain condensed-phase estimates of atomic polarizabilities for water and methanol (QM) solutes in the presence of (MM) solvents of different polarity. In a next step, the validity of the linear response and isotropy assumptions were evaluated based on the observed condensed-phase distributions of αi values. The observed anisotropy and low average values for the polarizability of methanol's carbon atom in polar solvents was explained in terms of strong solute-solvent interactions involving its adjacent hydroxyl group. Our QM/MM estimates for atomic polarizabilities were found to be close to values used in previously reported polarizable water and methanol models. Using our estimate for αO of methanol, a single set of polarizable force field parameters was obtained that is directly transferable between environments of different polarity.

The linear model and experimentally observed resonant field amplification in tokamaks and reversed field pinches

A review is given of the experimentally observed effects related to the resonant field amplification (RFA) and the Resistive Wall Mode (RWM) instability in tokamaks and reversed field pinches (RFPs). This includes the feedback rotation of RWM in RFX-mod RFP, dependence of the RWM growth rate on the plasma-wall separation observed in JT-60U, appearance of the slowly growing RWM precursors in JT-60U and similar phenomena in other devices. The experimental results are compared with theoretical predictions based on the model comprising the Maxwell equations, Ohm’s law for the conducting wall, the boundary conditions and assumption of linear plasma response to the external magnetic perturbations. The model describes the plasma reaction to the error field as essentially depending on two factors: the plasma proximity to the RWM stability threshold and the natural rotation frequency of the plasma mode. The linear response means that these characteristics are determined by the plasma equilibrium parameters only. It is shown that the mentioned effects in different devices under different conditions can be described on a common basis with only assumption that the plasma behaves as a linear system. To extend the range of the model validation, some predictions are derived with proposals for experimental studies of the RFA dynamics.

An Exact Calculation of the van der Waals Interaction between Two Spheres of Classical Dipolar Fluid

An exact treatment of the van der Waals interaction between two spherical dielectric bodies possessing purely classical degrees of freedom is presented. The spheres are described by multipole expansions of their fluctuating charge distributions, and the correlation between the fluctuations are taken into account using classical electrostatics and statistical mechanics. The presented approach avoids both the assumption of pairwise additivity of Hamaker theory and the implicit linear response assumption of Lifshitz theory. The resulting equations are solved numerically for D/a ≥ 0.01, where a is the radius of the spheres and D is their minimum separation, for a system with ε = 80, and the results are compared to the analytical Hamaker formula with a Hamaker constant calculated from Lifshitz theory.

Nonlinearity of Mechanochemical Motions in Motor Proteins

The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors — myosin V and kinesin KIF1A — and performed numerical investigations of their conformational relaxation properties within the coarse-grained elastic network approximation. We have found that the linearity assumption is deficient for ligand-induced conformational motions and can even be violated for characteristic thermal fluctuations. The deficiency is particularly pronounced in KIF1A where the normal mode description fails completely in describing functional mechanochemical motions. These results indicate that important assumptions of the theory of protein dynamics may need to be reconsidered. Neither a single normal mode nor a superposition of such modes yields an approximation of strongly nonlinear dynamics.

More on monotone instrumental variables

Econometric analyses of treatment response often use instrumental variable (IV) assumptions to identify treatment effects. The traditional IV assum ption holds that mean response is constant acros s the subpopulations of persons with different values of an observed covariate. Manski and Pepper (2000) introduced monotone instrumental variable (MIV) assumptions, which replace equalities with weak inequalities. This paper presents further ana lysis of the MIV idea. We use an e xplicit response m odel to en hance understanding of the content of MIV and traditional IV assumptions. We study the identifying power of MIV assumptions when combined with the homogeneous linear response assumption maintained in many studies of treatment response. We also consider estimation of MIV bounds, with particular attention to finite-sample bias. This paper was prepared for the tenth anniversary issue of the Econometric Journal. Our research on monotone in strumental variables (MIVs) was first circulated in 1998, th e y ear that the journal beg an publication. We are grateful for this opportunity to report further findings on MIVs and, in doing so, to mark the tenth anniversary of both the journal and the subject. We have benefitted from the comments of a referee. Manski’s research was supported in part by NSF Grant SES-0549544.

Cuaq+/Cuaq2+ Redox Reaction Exhibits Strong Nonlinear Solvent Response Due to Change in Coordination Number

We have carried out extensive Born-Oppenheimer molecular dynamics simulations to characterize the structure and energetics of the Cu(+)/Cu(2+) redox pair. Our simulations support recent experimental evidence suggesting that Cu(2+) adopts a 5-fold coordination in aqueous solution and not the traditionally assumed octahedral coordination. Cu(+) forms a linear dihydrate structure with a third water molecule occasionally binding in the equatorial plane. We show that the change in ligand coordination number from 2 for aqueous Cu(+) to 5 for aqueous Cu(2+) leads to marked deviations from the linear response assumption underlying Marcus theory of oxidation. The diabatic free energy curves deviate from parabolic behavior and the reorganization free energies for Cu(+) and Cu(2+) are asymmetric and differ by 1.0 eV. The calculated reorganization free energies can semiquantitatively explain the exceptionally small electron self-exchange rate between Cu(+) and Cu(2+) in aqueous solution.