Perturbation Of State Research Articles

Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). I. Revisiting the NEVPT2 construction.

Over the last decade, the second-order N-electron valence state perturbation theory (NEVPT2) has developed into a widely used multireference perturbation method. To apply NEVPT2 to systems with large active spaces, the computational bottleneck is the construction of the fourth-order reduced density matrix. Both its generation and storage become quickly problematic beyond the usual maximum active space of about 15 active orbitals. To reduce the computational cost of handling fourth-order density matrices, the cumulant approximation (CU) has been proposed in several studies. A more conventional strategy to address the higher-order density matrices is the pre-screening approximation (PS), which is the default one in the ORCA program package since 2010. In the present work, the performance of the CU, PS, and extended PS (EPS) approximations for the fourth-order density matrices is compared. Following a pedagogical introduction to NEVPT2, contraction schemes, as well as the approximations to density matrices, and the intruder state problem are discussed. The CU approximation, while potentially leading to large computational savings, virtually always leads to intruder states. With the PS approximation, the computational savings are more modest. However, in conjunction with conservative cutoffs, it produces stable results. The EPS approximation to the fourth-order density matrices can reproduce very accurate NEVPT2 results without any intruder states. However, its computational cost is not much lower than that of the canonical algorithm. Moreover, we found that a good indicator of intrude states problems in any approximation to high order density matrices is the eigenspectra of the Koopmans matrices.

Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). II. The full rank NEVPT2 (FR-NEVPT2) formulation.

In Paper I, the performances of pre-screening (PS), extended PS (EPS), and cumulant (CU) approximations to the fourth-order density matrix were examined in the context of second-order N-electron valence state perturbation theory (NEVPT2). It has been found that the CU, PS, and even EPS approximations with loose thresholds may introduce intruder states. In the present work, the origin of these "false intruder" states introduced by approximated density matrices is discussed. Canonical NEVPT2 implementations employ a rank reduction trick. By analyzing its residual error, we find that the omission of the rank reduction leads to a more stable multireference perturbation theory for incomplete active space reference wave functions. Such a full rank (FR)-NEVPT2 formulation is equivalent to the conventional NEVPT2 method for the complete active space self-consistent field/complete active space configuration interaction reference wave function. A major drawback of the FR-NEVPT2 formulation is the necessity of the fifth-order density matrix. To avoid the construction of the high-order density matrices, the combination of the FR-NEVPT2 with the CU approximation is studied. However, we find that the CU approximation remains problematic as it still introduces intruder states. The question of how to robustly and efficiently perform internally contracted multireference perturbation theories with approximate densities remains a challenging field of investigation.

Numerical optimization of microfluidic vortex shedding for genome editing T cells with Cas9

Microfluidic vortex shedding (µVS) can rapidly deliver mRNA to T cells with high yield and minimal perturbation of the cell state. The mechanistic underpinning of µVS intracellular delivery remains undefined and µVS-Cas9 genome editing requires further studies. Herein, we evaluated a series of µVS devices containing splitter plates to attenuate vortex shedding and understand the contribution of computed force and frequency on efficiency and viability. We then selected a µVS design to knockout the expression of the endogenous T cell receptor in primary human T cells via delivery of Cas9 ribonucleoprotein (RNP) with and without brief exposure to an electric field (eµVS). µVS alone resulted in an equivalent yield of genome-edited T cells relative to electroporation with improved cell quality. A 1.8-fold increase in editing efficiency was demonstrated with eµVS with negligible impact on cell viability. Herein, we demonstrate efficient processing of 5 × 106 cells suspend in 100 µl of cGMP OptiMEM in under 5 s, with the capacity of a single device to process between 106 to 108 in 1 to 30 s. Cumulatively, these results demonstrate the rapid and robust utility of µVS and eµVS for genome editing human primary T cells with Cas9 RNPs.

Low-Thrust Maneuverability Using Bilinear Tangent Guidance near Small Bodies

This paper examines the ability of a bilinear tangent guidance law to perform continuous-thrust, single-burn orbital maneuvers in the small-body orbital environment (solar radiation pressure, etc.) and the capability of a Newton–Raphson predictor–corrector algorithm to perform free-time, state-to-state spacecraft guidance on initial state perturbations. This paper shows that low-thrust bilinear tangent is able to perform a wide variety of maneuvers with a wide variety of thrust levels around asteroid Bennu. Additionally, this paper shows that even with a high control authority, the size of initial state perturbations that can be corrected depends on the size of the target state’s complex backward-reachable subspace and the location of the initial state of the maneuver in that subspace. For example, a 5 mN thruster on a 1000 kg spacecraft performed an aggressive shape and plane change maneuver for less than 3.5 g of fuel. The derived guidance algorithm then corrected 100% of initial state perturbations drawn from and distributions. Ultimately, this paper shows that Newton–Raphson predictor–corrector bilinear tangent guidance is a capable guidance scheme when used on perturbations that lie within the reachable subspace of the target state.

Adaptive robust state stabilisation of uncertain non linear time-varying systems with delayed perturbation

The problem of robust stabilisation for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown and an improved adaptation law with modification is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds, we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes in the presence of multiple delayed state perturbations is globally uniformly practically exponentially stable. Finally, a numerical example is given to demonstrate the validity of the results.

Connecting steady emission and very high energy flaring states in blazars: the case of Mrk 421

ABSTRACT Various attempts have been made in the literature at describing the origin and the physical mechanisms behind flaring events in blazars with radiative emission models, but detailed properties of multiwavelength (MWL) light curves still remain difficult to reproduce. We have developed a versatile radiative code, based on a time-dependent treatment of particle acceleration, escape, and radiative cooling, allowing us to test different scenarios to connect the continuous low-state emission self-consistently with that during flaring states. We consider flares as weak perturbations of the quiescent state and apply this description to the 2010 February MWL flare of Mrk 421, the brightest very high energy (VHE) flare ever detected from this archetypal blazar, focusing on interpretations with a minimum number of free parameters. A general criterion is obtained, which disfavours a one-zone model connecting low and high state under our assumptions. A two-zone model combining physically connected acceleration and emission regions yields a satisfactory interpretation of the available time-dependent MWL light curves and spectra of Mrk 421, although certain details remain difficult to reproduce. The two-zone scenario finally proposed for the complex quiescent and flaring VHE emitting region involves both Fermi-I and Fermi-II acceleration mechanisms, respectively, at the origin of the quiescent and flaring emission.

Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram

We derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4)$\times$U(4) symmetry, and we find that the exact ground states at integer filling $-4\le \nu\le 4$ relative to charge neutrality are Chern insulators of Chern numbers $\nu_C=4-|\nu|,2-|\nu|,\cdots,|\nu|-4$, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $\nu=0,\pm2$ has exact ground states of Chern number $0$, while $\nu=\pm1,\pm3$ has perturbative ground states of Chern number $\nu_C=\pm1$, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $\nu_C=0$ ($0<|\nu_C|<4-|\nu|$) at integer fillings $\nu$ are fully (partially) intervalley coherent, while the insulator states with Chern number $|\nu_C|=4-|\nu|$ are valley polarized. However, for $0<|\nu_C|\le4-|\nu|$, the fully intervalley coherent states are highly competitive (0.005meV/electron higher). At nonzero magnetic field $|B|>0$, a first-order phase transition for $\nu=\pm1,\pm2$ from Chern number $\nu_C=\text{sgn}(\nu B)(2-|\nu|)$ to $\nu_C=\text{sgn}(\nu B)(4-|\nu|)$ is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.

Error suppression in adiabatic quantum computing with qubit ensembles

Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size Nc where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than Nc, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.

Auxiliary Atomic Relay Center Facilitates Enhanced Magnetic Couplings in Blatter's Radical.

The recent accomplishments in obtaining strong ferromagnetic exchange interactions in organic diradicals have made the field quite fascinating and even more promising toward its technological applications. In this context, herein, we report a unique combination of remarkably strong ferromagnetic exchange interactions coupled with molecular rigidity, utilizing superstable Blatter's radical as a spin source. The planar analogues of the parent Blatter's radical obtained by annulation with a chalcogen coupled to nitronyl nitroxide (NN) are investigated using density functional theory along with the wave function-based multiconfigurational self-consistent field methods, for example, complete active space self-consistent field (CASSCF)-N-electron valence state perturbation theory (NEVPT2). The calculations reveal phenomenal modulation in exchange couplings upon annulation such that remarkably strong ferromagnetic interactions are realized especially for a certain class of the Blatter-NN diradicals. The modulation of spin-spin interactions is rationalized by variation in spin density distribution and molecular torsional angles. We demonstrate that annulation in OMMs opens an additional coupling pathway via auxiliary X-atom acting as the atomic relay center which strongly manipulates the magnitude of exchange couplings.

Excited states in the adiabatic connection fluctuation-dissipation theory: Recovering missing correlation energy from the negative part of the density response spectrum.

The adiabatic connection (AC) theory offers an alternative to the perturbation theory methods for computing correlation energy in the multireference wavefunction framework. We show that the AC correlation energy formula can be expressed in terms of the density linear response function as a sum of components related to positive and negative parts of the transition energy spectrum. Consequently, generalization of the adiabatic connection fluctuation-dissipation theory to electronically excited states is obtained. The component of the linear response function related to the negative-transition energy enters the correlation energy expression with an opposite sign to that of the positive-transition part and is non-negligible in the description of excited states. To illustrate this, we analyze the approximate AC model in which the linear response function is obtained in the extended random phase approximation (ERPA). We demonstrate that AC can be successfully combined with the ERPA for excited states, provided that the negative-excitation component of the response function is rigorously accounted for. The resulting AC0D model, an extension of the AC0 scheme introduced in our earlier works, is applied to a benchmark set of singlet excitation energies of organic molecules. AC0D constitutes a significant improvement over AC0 by bringing the excitation energies of the lowest excited states to a satisfactory agreement with theoretical best estimates, which parallels or even exceeds the accuracy of the n-electron valence state perturbation theory method. For higher excitations, AC0D is less reliable due to the gradual deterioration of the underlying ERPA linear response.

Structural, magnetic and Mössbauer studies of Nd 0.6Sr0.4FexMn1-xO3 perovskites

The effect of iron doping on the structural and magnetic properties of the manganite perovskites Nd0.6Sr0.4FexMn1-xO3 (0.1 ≤ x ≤ 1.0) was studied. Auto-combustion sol-gel method was used to prepare the compounds. X-ray diffraction refinement indicated that all the compounds crystallized in orthorhombic single-phase with Pnma space group. Scanning electron microscopy micrographs revealed a group of packed grains of about 0.2–1.0 μm whereas the average particle size was found to be in the range of about 40–80 nm via transmission electron microscopy. The zero-field cooled and field cooled magnetization curves, under an applied magnetic field of 0.02 T, revealed that the samples with 0.1 ≤ x ≤ 0.4 exhibit a paramagnetic to ferromagnetic transition with decreasing temperature while the samples with (0.5 ≤ x ≤ 1.0) do not demonstrate such phase transition. At room temperature the dependence of magnetization on the x iron concentration, as revealed by the corresponding M − H curves, can be interpreted as the cumulative result of changes in superparamagnetic, paramagnetic and antiferromagnetic contributions. 57Fe transmission Mӧssbauer spectra were recorded at room-temperature (295 K) and liquid nitrogen temperature (78 K) for all the samples. Iron ions were found to be present in these compounds exclusively in a paramagnetic high-spin Fe3+ state for 0.1 ≤ x ≤ 0.5 at 295 K and for 0.1 ≤ x ≤ 0.3 at 78 K. At higher iron concentrations an antiferromagnetic state of iron clusters is formed due to the Fe3+ – Fe3+ superexchange interaction. Room temperature 57Fe quadrupole splitting was found to increase near linearly with the x iron concentration up to x = 0.6. For x ≥ 0.6 the formation of paramagnetic Fe4+ is observed at 295 K, which at lower temperatures undergoes charge disproportionation leading to the appearance of Fe5+ species as observed at 78 K. Perturbations of the magnetic state of iron ions was found to lead to substantial broadening of the Mössbauer absorption peaks of magnetic components, which is interpreted as the effect of nearest neighbor Fe5+ and Mn ions at 78 K, and as that of electron-hopping related Fe3+ - Fe4+ valence fluctuations at 295 K.

Global solutions to the ideal MHD system with a strong magnetic background

We consider the Cauchy problem of the ideal MHD system with a constant non-zero background magnetic field e. We provide a new proof of global existence for small perturbations of an initial stable state (0,e). The proof is based on the null structure of the system and some new weighted energy estimates established along the characteristics.

IMCC: A Novel Quantitative Approach Revealing Variation of Global Modular Map and Local Inter-Module Coordination Among Differential Drug's Targeted Cerebral Ischemic Networks.

Stroke is a common disease characterized by multiple genetic dysfunctions. In this complex disease, detecting the strength of inter-module coordination (genetic community interaction) and subsequent modular rewiring is essential to characterize the reactive biosystematic variation (biosystematic perturbation) brought by multiple-target drugs, whose effects are achieved by hitting on a series of targets (target profile) jointly. Here, a quantitative approach for inter-module coordination and its transition, named as IMCC, was developed. Applying IMCC to mouse cerebral ischemia–related gene microarray, we investigated a holistic view of modular map and its rewiring from ischemic stroke to drugs (baicalin, BA; ursodeoxycholic acid, UA; and jasminoidin, JA) perturbation states and locally identified the cooperative pathological module pair and its dissection. Our result suggested the global modular map in cerebral ischemia exhibited a characteristic “core–periphery” architecture, and this architecture was rewired by the effective drugs heterogeneously: BA and UA converged modules into an intensively connected integrity, whereas JA diverged partial modules and widened the remaining inter-module paths. Locally, the PMP dissociation brought by drugs contributed to the reversion of the pathological condition: the focus of the cellular function shift from survival after nervous system injury into development and repair, including neurotrophin regulation, hormone releasing, and chemokine signaling activation. The core targets and mechanisms were validated by in vivo experiments. Overall, our result highlights the holistic inter-module coordination rearrangement rather than a target or a single module that brings phenotype alteration. This strategy may lead to systematically explore detailed variation of inter-module pharmacological action mode of multiple-target drugs, which is the principal problem of module pharmacology for network-based drug discovery.

Polarization singularity index determination by using a tilted lens.

The superposition of spin and orbital angular momentum states of light generates polarization singularities. By perturbing and disintegrating their component orbital angular momentum (OAM) states, the polarization singularity indices can be determined. The spatially varying polarization distribution of these beams possesses information about the helical wavefront structures of the component OAM states, although they have plane wavefronts. The polarization singular beam (PSB) is focused using a tilted lens, and the intensity distribution at a predicted position in the direction of propagation is used to determine the component OAM content in the beam. Astigmatism introduced by the tilt of the lens modulates the vortex beam to introduce intensity nulls in the propagated beam. We demonstrate by simulations and experiments the index determination of the V points and C points using a tilted lens. This method is effective in the index determination of V points and C points formed by the superposition of component scalar vortices having opposite-sign topological charges. The degeneracy of C points with the same Stokes indices can be lifted through this technique.

Phase transitions and assortativity in models of gene regulatory networks evolved under different selection processes.

We study a simplified model of gene regulatory network evolution in which links (regulatory interactions) are added via various selection rules that are based on the structural and dynamical features of the network nodes (genes). Similar to well-studied models of 'explosive' percolation, in our approach, links are selectively added so as to delay the transition to large-scale damage propagation, i.e. to make the network robust to small perturbations of gene states. We find that when selection depends only on structure, evolved networks are resistant to widespread damage propagation, even without knowledge of individual gene propensities for becoming 'damaged'. We also observe that networks evolved to avoid damage propagation tend towards disassortativity (i.e. directed links preferentially connect high degree 'source' genes to low degree 'target' genes and vice versa). We compare our simulations to reconstructed gene regulatory networks for several different species, with genes and links added over evolutionary time, and we find a similar bias towards disassortativity in the reconstructed networks.

Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators.

The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous or endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures.

Assessing uncertainties from physical parameters and modelling choices in an atmospheric large eddy simulation model.

In this study, we investigate uncertainties in a large eddy simulation of the atmosphere, employing modern uncertainty quantification methods that have hardly been used yet in this context. When analysing the uncertainty of model results, one can distinguish between uncertainty related to physical parameters whose values are not exactly known, and uncertainty related to modelling choices such as the selection of numerical discretization methods, of the spatial domain size and resolution, and the use of different model formulations. While the former kind is commonly studied e.g. with forward uncertainty propagation, we explore the use of such techniques to also assess the latter kind. From a climate modelling perspective, uncertainties in the convective response and cloud formation are of particular interest, since these affect the cloud-climate feedback, one of the dominant sources of uncertainty in current climate models. Therefore we analyse the DALES model in the RICO case, a well-studied convection benchmark. We use the VECMA toolkit for uncertainty propagation, assessing uncertainties stemming from physical parameters as well as from modelling choices. We find substantial uncertainties due to small random initial state perturbations, and that the choice of advection scheme is the most influential of the modelling choices we assessed.This article is part of the theme issue ‘Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico’.

Reliability and reproducibility in computational science: implementing validation, verification and uncertainty quantification in silico.

Reliability and reproducibility in computational science: implementing validation, verification and uncertainty quantification in silico.

On the modelling of large-scale atmospheric flow

We derive, from the general, governing equations for a viscous, compressible fluid, a generic system of equations that describe the dynamics of the steady atmosphere. This formulation uses suitable rotating coordinates based on an ellipsoidal model for the Earth's geoid and allows for thermodynamic forcing. We invoke only the thin-shell approximation and the geometrical approximation (nearly spherical), retaining all other parameters. Thus we present a general theory for atmospheric flows, based on well-defined approximation methods. This leads to a perturbation of the stationary background state which produces a somewhat familiar, general structure, but with a forcing that is generated by a suitable form of the perturbation temperature field. We show how the new system recovers the classical Ekman, geostrophic and thermal-wind models, expressed more generally in rotating, spheroidal geometry. The new system is also used to present solutions for the Hadley-Ferrel-polar cell structure, for the Walker circulation and to describe the flow in the middle atmosphere. In all these examples, our approach enables us to describe in detail the velocity field and to show how it is possible to identify the heat sources required to maintain the motion.

Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data

We evaluate a number of different finite-element approaches for fluid–structure (contact) interaction problems against data from physical experiments. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change in the fluid domain and the contact between the wall and the particle. In the finite-element simulations, we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare the results obtained with the well-established Arbitrary Lagrangian–Eulerian (ALE) approach and an unfitted moving domain method together with a simple and common approach for contact avoidance. For the full fluid–structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency, we use the geometrical symmetry of the experimental setup to reformulate the FSI system into two spatial dimensions. Finally, we show full three-dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries, and the results are made freely available to aid reproducibility.