Linear Response Function Research Articles

Quantum algorithms for estimating physical quantities using block encodings

We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique for the manipulation of arbitrary non-unitary matrices on a quantum computer. We describe how to 'sketch' these quantities via the kernel polynomial method which is a standard strategy in numerical condensed matter physics. These algorithms use amplitude estimation to obtain a quadratic speedup in the accuracy over previous results, can capture any observables and Hamiltonians presented as linear combinations of Pauli matrices, and are modular enough to leverage future advances in Hamiltonian simulation and state preparation.

HPLC MS/MS method development for the quantitative determination of verapamil hydrochloride from Caco-2 cell monolayers

Aim. An understanding of the role that transporters, in particular P-glycoprotein (P-gp), can play in the absorption, distribution, metabolism and excretion (ADME) of candidate drugs, and an assessment of how these processes might impact on toxicity and the potential for drug-drug interactions in the clinic, is required to support drug development and registration. It is therefore necessary to validate preclinical assays for the in vitro evaluation of candidate drugs as substrates or inhibitors of human P-gp. 2. A simple, rapid HPLC MS/MS method was developed for determination of verapamil hydrochloride from confluent Caco-2 monolayers and from aqueous solution. Materials and methods. Chromatography was achieved on Discovery C18, 50 × 2.1 mm, 5 μm column. Samples were chromatographed in a gradient mode (eluent A (acetonitrile – water – formic acid, 5 : 95 : 0.1 v/v), eluent B (acetonitrile – formic acid, 100 : 0.1 v/v)). The initial content of the eluent B is 0%, which increases linearly by 1.0 min to 100% and to 1.01 min returns to the initial 0%. The mobile phase was delivered at a flow rate of 0.4 mL/min into the mass spectrometer ESI chamber. The sample volume was 5 μl. Results. Under these conditions, verapamil hydrochloride was eluted at 1.08 min. A linear response function was established at 1 – 100 ng/mL. The regression equation for the analysis was Y = 0.0162x + 0.00391 with coefficient of correction (R2) = 0.9992. According to the Caco-2 test results, verapamil showed low permeability. It should be noted that the recovery value for verapamil hydrochloride is 102.69%. The within-run coefficients of variation ranged between 0.336% and 0.617% for verapamil. The within-run percentages of nominal concentrations ranged between 98.82% and 100.62% for verapamil. The between-run coefficients of variation ranged between 0.334% and 0.612% for verapamil. The between-run percentages of nominal concentrations ranged between 98.97% and 101.76% for verapamil. The assay values on both the occasions (intra- and inter-day) were found to be within the accepted limits. Conclusion. From results of analysis, it can be concluded that developed method is simple and rapid for determination of verapamil hydrochloride from confluent Caco-2 monolayers and from aqueous solution. Acquired results demonstrate that proposed strategy can be effortlessly and advantageously applied for examination of verapamil hydrochloride from Caco-2 cell monolayers.

Bioanalytical method development and validation for the determination of metoprolol and meldonium in human plasma

Aim.The main purpose of this study was to develop a simple, precise, rapid and accurate method for the quantification of metoprolol and meldonium in human plasma. Materials and methods. The resolution of peaks of metoprolol was best achieved with Discovery C18, 50 × 2.1 mm, 5 μm column and meldonium - ZORBAX HILIC Plus, 50 × 2.1 mm, 3.5 μm column. Samples of metoprolol were chromatographed in a gradient mode (eluent A (acetonitrile – water – formic acid, 5 : 95 : 0.1 v/v), eluent B (acetonitrile – formic acid, 100 : 0.1 v/v)). The initial content of the eluent B is 0%, which increases linearly by 1.0 min to 100% and to 1.11 min returns to the initial 0%. The mobile phase was delivered at a flow rate of 0.400 mL/min into the mass spectrometer ESI chamber. The injection volume was 5μl. Samples of meldonium were chromatographed in a isocratic using mobile phase water – acetonitrile – ammonium formate buffer 200 мМ, 20 : 75 : 5 v/v). Results.The total chromatographic run time was 2.0 minutes and the elution of metoprolol, meldonium and IS occurred at ~1.39 and 1.18 minutes, respectively.A linear response function was established at 2 - 200 ng/mL for metoprolol and 50 -5000 ng/mL for meldonium in human plasma. The% mean recovery for metoprolol in LQC, MQC and HQC was 99.0%, 107.5% and 96.8%, for meldonium in LQC, MQC and HQC was 94.1%, 100.2% and 93.1% respectively. The lowest concentration with the RSD <20% was taken as LLOQ and was found to be 2.31 ng/mL for metoprolol, 47.70 ng/mL for meldonium. The % accuracy of LLOQ samples prepared with the different biological matrix lots were found 115.4% for metoprolol and 95.5% for meldonium, which were found within the range of 80.00–120.00% for the seven different plasma lots. % CV for LLOQ samples was observed as 12.8% and 7.7% respectively, which are within 20.00% of the acceptance criteria. Conclusion.A rapid method was developed for simultaneous determination of metoprolol and meldonium in human plasma. The method was strictly validated according to the ICH guidelines. Acquired results demonstrate that proposed strategy can be effortlessly and advantageously applied for routine examination of metoprolol and meldonium in human plasma.

HPLC-MS/MS method development for the quantitative determination of nifedipine for Caco-2 permeability assay

Aim. Poorly water-soluble drugs such as nifedipineoffer challenging problems in drug formulation as poor solubility is generally associated with poor dissolution characteristics and thus with poor oral bioavailability (BCS class II drugs). Methods of quantitative determination of nifedipine by methods of spectrophotometry and chromatography are described in the scientific literature. However, methods are not developedfor examination of nifedipine from Caco-2 cell monolayers. Caco-2 cell monolayers have been extensively used for years as a tool to test permeability, assess the oral absorption potential and study the absorption mechanism of compounds. Therefore, the aim of this study was to develop and validate an efficient HPLC MS/MS method for determination of nifedipine from Caco-2 cell monolayers. Materials and methods. Chromatography was achieved on DiscoveryC18, 50 × 2.1 mm, 5 μm column. Samples were chromatographed in a gradient mode (eluent A (acetonitrile – water – formic acid, 5 : 95 : 0.1 v/v), eluent B (acetonitrile – formic acid, 100 : 0.1 v/v)). The initial content of the eluent B is 0%, which increases linearly by 1.0 min to 100% and to 1.01 min returns to the initial 0%. The mobile phase was delivered at a flow rate of 0.4 mL/min into the mass spectrometer ESI chamber. The sample volume was 5 μl. Results. Under these conditions, nifedipine was eluted at 1.83 min. A linear response function was established at 1 – 100 ng/mL. The regression equation for the analysis was Y = 0.0323x-0.00121 with coefficient of correction (R2) = 0.9987. According to the Caco-2 test results, nifedipine showed high permeability. The within-run coefficients of variation ranged between 0.331% and 0.619% for nifedipine. The within-run percentages of nominal concentrations ranged between 98.80% and 100.63% for nifedipine. The between-run coefficients of variation ranged between 0.332% and 0.615% for nifedipine. The between-run percentages of nominal concentrations ranged between 98.98% and 101.71% for nifedipine. The assay values on both the occasions (intra- and inter-day) were found to be within the accepted limits. Conclusion. From results of analysis, it can be concluded that developed method is simple and rapid for determination of nifedipine from confluent Caco-2 monolayers and from aqueous solution. Acquired results demonstrate that proposed strategy can be effortlessly and advantageously applied for examination of nifedipine from Caco-2 cell monolayers.

Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

We propose a scheme for the construction of charge and spin linear-response functions of an interacting electronic system via quantum phase estimation and statistical sampling on a quantum computer. By using the unitary decomposition of electronic operators for avoiding the difficulty due to their non-unitarity, we provide the circuits equipped with ancillae for probabilistic preparation of qubit states on which the necessary non-unitary operators have acted. We perform simulations of such construction of the response functions for C2 and N2 molecules by comparing with the accurate ones based on the full configuration interaction calculations. It is found that the accurate detection of subtle structures coming from the weak poles in the response functions requires a large number of measurements.

A Review Of The Linear Response Function In Condensed Matter Physics And Their Application In Some Elementary Processes

Linear response theory in quantum theory with its linear response function and its quantization process has been formulated. The relation between the linear response function with its generalized susceptibility, its symmetry properties, and its analyticity has been studied. These properties produce the dispersion relation or Kramers-Kronig relation. The explicit form of the quantum response function and generalized susceptibility also been reviewed. Applications of linear response functions have been described for three elementary processes. The process discussed is the magnetic field disturbance in the magnetic system that generates magnetic susceptibility, and the electric field disturbance in the electrical system that generates electrical conductivity tensor and the ferromagnet Heisenberg that generates its generalized susceptibility.

LC-MS/MS Method Development and Validation for the Determination of Nifedipine in Human Plasma

The main purpose of this study was to develop a simple, precise, rapid, green and accurate method for the simultaneous quantification of nifedipine in human plasma; The resolution of peaks was best achieved with Intersil ODS gum C18 (4.6 × 50 mm, 3.5 μm) column. Samples were chromatographed in a gradient mode (acetonitrile – water – formic acid). The mobile phase was delivered at a flow rate of 0.500 mL/min into the mass spectrometer ESI chamber; The total chromatographic run time was 4 minutes. Nifedipine eluted at ~3.24 min. A linear response function was established at 1 - 130 ng/mL in human plasma. The % mean recovery in LQC, MQC and HQC was 104.1 %, 105.0 % and 108.7 %. The lowest concentration with the RSD <20% was taken as LLOQ and was found to be 1.01 ng/mL. The % accuracy of LLOQ samples prepared with the different biological matrix lots was found 100.5 % for nifedipine, which was found within the range of 80.00-120.00 % for the seven different plasma lots. A rapid method was developed for the determination of nifedipine in human plasma. The method was strictly validated according to the ICH guidelines. Acquired results demonstrate that proposed strategy can be effortlessly and advantageously applied for routine examination of nifedipine in human plasma.

Growth kinetics and aging phenomena in a frustrated system

We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links $a$ can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in a radical way. Small $a$ does not prevent the system from a complete ordering, but this occurs in an extremely (logarithmically) slow manner. However, larger values of this parameter destroy complete ordering, due to frustration, and the evolution is comparatively faster (algebraic). Our study shows a precise correspondence between the kind of developing order, ferromagnetic versus frustrated, and the speed of evolution. The aging properties of the system are studied by focusing on the scaling properties of two-time quantities, the autocorrelation and linear response functions. We find that the contribution of equilibrium and an aging part to these functions occurs differently in the various regions of the phase diagram of the model. When quenching inside the ferromagnetic phase, the two-time quantities are obtained by the addition of these parts. Instead, in the paramagnetic phase, these two contributions enter multiplicatively. Both of the scaling forms are shown with excellent accuracy, and the corresponding scaling functions and exponents have been determined and discussed.

Measuring the frequency response of the honeybee thorax

Insects with asynchronous flight muscles are believed to flap at the effective fundamental frequency of their thorax–wing system. Flapping in this manner leverages the natural elasticity of the thorax to reduce the energetic requirements of flight. However, to the best of our knowledge, the fundamental frequency of the insect wing–muscle–thorax system has not been measured. Here, we measure the linear frequency response function (FRF) of honeybee Apis mellifera thoraxes about their equilibrium state in order to determine their fundamental frequencies. FRFs relate the input force to output acceleration at the insect tergum and are acquired via a mechanical vibration shaker assembly. When compressed 50 μm, the thorax fundamental frequency averaged across all subjects was about 50% higher than reported wingbeat frequencies. We suspect that the measured fundamental frequencies are higher in the experiment than during flight due to boundary conditions and posthumous muscle stiffening. Next, we compress the thorax between 100–300 μm in 50 μm intervals to assess the sensitivity of the fundamental frequency to geometric modifications. For all specimens considered, the thorax fundamental frequency increased nearly monotonically with respect to level of compression. This implies that the thorax behaves as a nonlinear hardening spring when subject to large displacements, which we confirmed via static force–displacement testing. While there is little evidence that insects utilize this non-linearity during flight, the hardening characteristic may be emulated by small resonant-type flapping wing micro air vehicles to increase flapping frequency bandwidth. Overall, methods established through this work provide a foundation for further dynamical studies on insect thoraxes moving forward.

Estimation of ramipril and telmisartan in human plasma by LC–MS/MS: Application in pharmacokinetic study

AbstractA highly sensitive and specific liquid chromatography–tandem mass spectrometry method has been developed for simultaneous estimation of Ramipril and Telmisartan in human plasma using Ramipril d5 and telmisartan d3 as internal standards. Liquid chromatography–tandem mass spectrometry was operated under the multiple reaction monitoring mode using the electrospray ionization technique. Simple liquid–liquid extraction process was used to extract Ramipril, Telmisartan, and internal standard from human plasma. The total run time was 2.5 min and the elution of ramipril and telmisartan were 0.97 and 1.17 min, respectively. This was achieved with a mobile phase consisting of 2 mM ammonium acetate in 0.1% formic acid as mobile phase A and 100% acetonitrile as mobile phase B in the ratio 20:80 with a flow rate of 0.7 mL/min on a betasil C18 column. The developed method was validated in human plasma with a lower limit of quantitation of 0.5 and 0.98 ng/mL for ramipril and telmisartan, respectively. A linear response function was established for the range of concentrations 0.5–50.0 ng/mL (r > 0.998) and 0.98–800.0 ng/mL (r > 0.998) for ramipril and telmisartan, respectively. The intra‐ and interday precision values for ramipril and telmisartan met the acceptance as per United States Food and Drug Administration guidelines. Ramipril and telmisartan were stable in a battery of stability studies viz., bench‐top, auto‐sampler, and freeze–thaw cycles, long‐term matrix stability. The developed method was applied to a pharmacokinetic study in humans.

Neutral modes of surface temperature and the optimal ocean thermal forcing for global cooling

Inquiry into the climate response to external forcing perturbations has been the central interest of climate dynamics. But the understanding of two important aspects of climate change response—nonlinearity and regionality—is still lacking. Here a Green’s function approach is developed to estimate the linear response functions (LRFs) for both the linear and quadratic nonlinear response to ocean thermal forcing in a climate model, whereby the most excitable temperature modes, aka the neutral modes, can be identified for the current Earth climate. The resultant leading mode of the nonlinear response is characterized by a polar-amplified global cooling pattern, unveiling an intrinsic inclination of the modern climate towards cooling. Moreover, optimal forcing patterns are identified to most efficiently excite the corresponding neutral mode patterns. The forcing-response framework developed herein can be utilized to determine the optimal forcing patterns to inform solar geoengineering experiments and to interpret regional climate response and feedback in general.

Toward the Reconstruction of Substorm‐Related Dynamical Pattern of the Radiowave Auroral Absorption

AbstractIn addition to existing empirical models describing the average distributions of energetic electron precipitation into the auroral ionosphere at different activity levels, we develop and test a semiempirical approach to construct dynamical models describing the recurrent features of spatiotemporal development of auroral absorption in the ionosphere during individual substorms. Its key ingredients are (a) usage of linear prediction filter technique to extract from riometer data the response function to the injection of unit magnitude and (b) characterization of injection parameters by midlatitude magnetic variations caused by the substorm current wedge. Using global riometer network we test the method performance for stations in the middle of auroral zone (at corrected geomagnetic latitudes of 65–67°) where generally the absorption amplitude is largest. In this paper we use the midlatitude positive bay index, recently developed by X. Chu and R. McPherron, to drive the model. We evaluate the model performance, discuss the dynamical properties of energetic electron precipitation as revealed by the linear prediction filter response function analyses, and finally, we discuss possible future improvements of this method intended for both science and applications.

Block-oriented system identification for nonlinear modeling of all-solid-state Li-ion battery technology

The high energy density characteristic of the all-solid-state battery technology makes it one of the promising competitors of current liquid electrolyte-based lithium-ion batteries. However, due to the low ionic conductivity of solid materials and existing issues in active material-solid electrolyte interfaces, all-solid-state batteries show strong nonlinear behavior when the amplitude of input current is relatively high. In this paper, we have developed a methodology based on block-oriented nonlinear systems that can detect, quantize, and model the battery behavior, accurately. For this purpose, two solid-state coin cells, which have different ionic conductivity at the cathode interface are manufactured and excited with multisine input current. The Best Linear Approximation (BLA) method has been used to separate linear frequency response function (FRF) from nonlinear distortion. Then, a Hammerstein-Wiener system has been developed and parametrized to model the nonlinear distortions caused by ionic conductivity variation of the solid electrolyte at the cathode layer. Furthermore, the developed model has been utilized to detect possible faults in the electrode-electrolyte interface based on the nonlinearity level of the measured voltage.

Projecting Antarctica's contribution to future sea level rise from basal ice shelf melt using linear response functions of 16 ice sheet models (LARMIP-2)

Abstract. The sea level contribution of the Antarctic ice sheet constitutes a large uncertainty in future sea level projections. Here we apply a linear response theory approach to 16 state-of-the-art ice sheet models to estimate the Antarctic ice sheet contribution from basal ice shelf melting within the 21st century. The purpose of this computation is to estimate the uncertainty of Antarctica's future contribution to global sea level rise that arises from large uncertainty in the oceanic forcing and the associated ice shelf melting. Ice shelf melting is considered to be a major if not the largest perturbation of the ice sheet's flow into the ocean. However, by computing only the sea level contribution in response to ice shelf melting, our study is neglecting a number of processes such as surface-mass-balance-related contributions. In assuming linear response theory, we are able to capture complex temporal responses of the ice sheets, but we neglect any self-dampening or self-amplifying processes. This is particularly relevant in situations in which an instability is dominating the ice loss. The results obtained here are thus relevant, in particular wherever the ice loss is dominated by the forcing as opposed to an internal instability, for example in strong ocean warming scenarios. In order to allow for comparison the methodology was chosen to be exactly the same as in an earlier study (Levermann et al., 2014) but with 16 instead of 5 ice sheet models. We include uncertainty in the atmospheric warming response to carbon emissions (full range of CMIP5 climate model sensitivities), uncertainty in the oceanic transport to the Southern Ocean (obtained from the time-delayed and scaled oceanic subsurface warming in CMIP5 models in relation to the global mean surface warming), and the observed range of responses of basal ice shelf melting to oceanic warming outside the ice shelf cavity. This uncertainty in basal ice shelf melting is then convoluted with the linear response functions of each of the 16 ice sheet models to obtain the ice flow response to the individual global warming path. The model median for the observational period from 1992 to 2017 of the ice loss due to basal ice shelf melting is 10.2 mm, with a likely range between 5.2 and 21.3 mm. For the same period the Antarctic ice sheet lost mass equivalent to 7.4 mm of global sea level rise, with a standard deviation of 3.7 mm (Shepherd et al., 2018) including all processes, especially surface-mass-balance changes. For the unabated warming path, Representative Concentration Pathway 8.5 (RCP8.5), we obtain a median contribution of the Antarctic ice sheet to global mean sea level rise from basal ice shelf melting within the 21st century of 17 cm, with a likely range (66th percentile around the mean) between 9 and 36 cm and a very likely range (90th percentile around the mean) between 6 and 58 cm. For the RCP2.6 warming path, which will keep the global mean temperature below 2 ∘C of global warming and is thus consistent with the Paris Climate Agreement, the procedure yields a median of 13 cm of global mean sea level contribution. The likely range for the RCP2.6 scenario is between 7 and 24 cm, and the very likely range is between 4 and 37 cm. The structural uncertainties in the method do not allow for an interpretation of any higher uncertainty percentiles. We provide projections for the five Antarctic regions and for each model and each scenario separately. The rate of sea level contribution is highest under the RCP8.5 scenario. The maximum within the 21st century of the median value is 4 cm per decade, with a likely range between 2 and 9 cm per decade and a very likely range between 1 and 14 cm per decade.

Long-time structural relaxation of glass-forming liquids: Simple or stretched exponential?

This paper presents data for the physical aging of the density of squalane upon both non-linear and nearly linear temperature jumps from states of thermal equilibrium. Invoking the single-parameter-aging scenario [Hecksher et al., J. Chem. Phys. 142, 241103 (2015); Proc. Natl. Acad. Sci. U. S. A. 116, 16736-16741 (2019)], the linear-response aging relaxation function is extracted from the data. Based on this, it is shown that the relaxation toward equilibrium follows a simple exponential function at long times; a stretched-exponential function provides a poor fit. This demonstrates the existence of a terminal relaxation rate for the physical aging of squalane, corresponding to an effective long-time cutoff in the spectrum of structural relaxation times.

Development and Validation of UPLC-ESI-MS/MS Technique for the Determination of 2-Isopropyl-4-(chloromethyl)thiazole in Ritonavir

The objective of this work was to develop and validate a rapid, highly sensitive ultra performance liquid chromatography-tandem mass spectrometry (UPLC-ESI-MS/MS) method for the quantification of 2-isopropyl-4-(chloromethyl)thiazole in ritonavir. Chromatographic conditions of this impurity were achieved on an AQUITY UPLC column HSS (high strength silica) T3 column (100 mm long, 2.1 mm internal diameter, 1.8 μm diameter) using a gradient elution with 0.1% formic acid in water and methanol at a flow rate of 0.3 mL/min. LCMS/MS was operated under the multiple reaction mode (MRM) using electrospray ionization technique in positive ion mode and the transitions of m/z 176.1[M+H]+→140.1 for quantifier, 176.1[M+H]+→71.0 for qualifier were used to measure the impurity, respectively. The total chromatographic run time was 10 min. Full validation of the analytical method was carried out, including its system precision, selectivity, linearity, accuracy, recovery, ruggedness, stability and robustness. A linear response function was achieved in the concentration range of 0.12-1.86 μg/g with r > 0.99. The detection limit and quantitation limit of this impurity were 0.06 and 0.12 μg/g, respectively. Consistent recoveries were obtained during intra- and inter-day precision experiments in validation ranged from 80-120%. The developed method could be helpful not only for quality control and also for risk management of potential genotoxicity of this impurity in ritonavir drug substance.

VeloxChem: A Python‐driven density‐functional theory program for spectroscopy simulations in high‐performance computing environments

AbstractAn open‐source program named VeloxChem has been developed for the calculation of electronic real and complex linear response functions at the levels of Hartree–Fock and Kohn–Sham density functional theories. With an object‐oriented program structure written in a Python/C++ layered fashion, VeloxChem enables time‐efficient prototyping of novel scientific approaches without sacrificing computational efficiency, so that molecular systems involving up to and beyond 500 second‐row atoms (or some 10,000 contracted and in part diffuse Gaussian basis functions) can be routinely addressed. In addition, VeloxChem is equipped with a polarizable embedding scheme for the treatment of the classical electrostatic interactions with an environment that in turn is modeled by atomic site charges and polarizabilities. The underlying hybrid message passing interface (MPI)/open multiprocessing (OpenMP) parallelization scheme makes VeloxChem suitable for execution in high‐performance computing cluster environments, showing even slightly beyond linear scaling for the Fock matrix construction with use of up to 16,384 central processing unit (CPU) cores. An efficient—with respect to convergence rate and overall computational cost—multifrequency/gradient complex linear response equation solver enables calculations not only of conventional spectra, such as visible/ultraviolet/X‐ray electronic absorption and circular dichroism spectra, but also time‐resolved linear response signals as due to ultra‐short weak laser pulses. VeloxChem distributed under the GNU Lesser General Public License version 2.1 (LGPLv2.1) license and made available for download from the homepage https://veloxchem.org.This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Density Functional Theory Theoretical and Physical Chemistry > Spectroscopy

Linear Response Theory and Green-Kubo Relations for Active Matter.

We address the question of how interacting active systems in a nonequilibrium steady state respond to an external perturbation. We establish an extended fluctuation-dissipation theorem for active Brownian particles (ABP), which highlights the role played by the local violation of detailed balance due to activity. By making use of a Markovian approximation we derive closed Green-Kubo expressions for the diffusivity and mobility of ABP and quantify the deviations from the Stokes-Einstein relation. We compute the linear response function to an external force using unperturbed simulations of ABP and compare the results with the analytical predictions of the transport coefficients. Our results show the importance of the interplay between activity and interactions in the departure from equilibrium linear response.

The linear response function of a mixed dislocation in ferroelectrics

Bending vibrations of a mixed dislocation in a uniaxial ferroelectric are considered, the dislocation line is located along the ferroelectric axis. Based on the complete system of equations describing the vibrations of a ferroelectric crystal with a dislocation, system of equations for the mixed dislocation dynamics in a linear approximation in the dislocation displacement is written. An expression for the Peach–Koehler force acting on the dislocation is obtained, and the linear response function of the mixed dislocation is found.

Generalized susceptibility of a screw dislocation in ferroelastics near structural phase transition

Small amplitude bending vibrations of a screw dislocation near structural phase transition is considered. Based on the full set of equations describing the vibrations of a crystal with a dislocation near the structural phase transition, written equations for the dynamics of screw dislocations in the linear approximation of the dislocation displacement. Fourier transform of the Peach-Koehler forces projection on the dislocation slip plane is obtained and a linear response function of a screw dislocation in ferroelastic crystal to an external force is found.