arXiv subjects

Rupert Klein

Publications and source records attributed to Rupert Klein.

At least 37 records · Page 2Linked to original sources

arXiv2022

Global well-posedness for the thermodynamically refined passively transported nonlinear moisture dynamics with phase changes

In this work we study the global solvability of moisture dynamics with phase changes for warm clouds. We thereby in comparison to previous studies [Hittmeir-Klein-Li-Titi (2017)] take into account the different gas constants for dry air and water vapor as well as the different heat capacities for dry air, water vapor and liquid water, which leads to a much stronger coupling of the moisture balances and the thermodynamic equation. This refined thermodynamic setting has been demonstrated to be essential e.g. in the case of deep convective cloud columns in [Hittmeir-Klein (2017)]. The more complicated structure requires careful derivations of sufficient a priori estimates for proving global existence and uniqueness of solutions.

math.AP↗

arXiv2022

Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains

We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Frenkel-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach which directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in case of homogeneous systems the tensor-train ranks of state vectors only marginally depend on the chain length which results in a linear growth of the storage consumption. However, the CPU time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wavepacket width and the corresponding stabilization energy on the exciton-phonon coupling strength, though only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the restrictions of the Frenkel-Holstein type Hamiltonians.

physics.comp-ph↗

arXiv2021

The dynamic state index with moisture and phase changes

The dynamic state index (DSI) is a scalar field that combines variational information on the total energy and enstrophy of a flow field with the second law of thermodynamics. Its magnitude is a combined local measure for non-stationarity, diabaticity, and dissipation in the flow, and it has been shown to provide good qualitative indications for the onset and presence of precipitation and the organization of storms. The index has been derived thus far for ideal fluid models only, however, so that one may expect more detailed insights from a revised definition of the quantity that includes more complex aerothermodynamics. The present paper suggests definitions of DSI-like indicators for flows of moist air with phase changes and precipitation. In this way, the DSI is generalized to signal deviations from a variety of different types of balanced states. A comparison of these indices evaluated with respect to one and the same flow field enables the user to test whether the flow internally balances any combination of the physical processes encoded in the generalized DSI-indices.

physics.ao-ph↗

arXiv2021

Geometry and organization of coherent structures in stably stratified atmospheric boundary layers

Global intermittency is observed in the stably stratified Atmospheric Boundary Layer (ABL) and corresponds to having large nonturbulent flow regions to develop in an otherwise turbulent flow. In this paper, the differences between continuous and intermittent turbulence are quantified with the help of coherent structures. Eight classes of coherent structures are identified from literature, most of which are indicated by scalar criteria derived from velocity fields. A method is developed to geometrically classify structures into three categories: blob-like, tube-like or sheet-like. An alternate definition of the intermittency factor $γ$ based on coherent structures is introduced to separate turbulent and nonturbulent parts of a flow. Applying this conditioning technique and the geometrical characterization on direct numerical simulations (DNS) of an Ekman flow, we find the following: (i) structures with similar geometries (either tube-like or sheet-like) are found regardless of the strength of stratification; (ii) global intermittency affects all regions of the ABL - viscous sublayer, buffer layer, inner, and outer layer; (iii) for the highly stratified case, sweep/ejection pairs form well-separated clusters within the viscous sublayer which can possibly explain the abundance of hairpin-like vortices with a particular orientation; (iv) nonturbulent regions are occupied with streamwise velocity fluctuations and there is a switch between high- and low-speed streaks at a particular height for all stratified cases.

physics.flu-dyn↗

arXiv2021

Definition, detection, and tracking of persistent structures in atmospheric flows

Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence.

physics.ao-ph↗

arXiv2021

On the relation between pressure and coupling potential in adaptive resolution simulations of open systems in contact with a reservoir

In a previous paper [Gholami et al. Adv.Th.Sim.4, 2000303 (2021)], we have identified a precise relation between the chemical potential of a fully atomistic simulation and the simulation of an open system in the adaptive resolution method (AdResS). The starting point was the equivalence derived from the statistical partition functions between the grand potentials, $Ω$, of the open system and of the equivalent subregion in the fully atomistic simulation of reference. In this work, instead, we treat the identity for the grand potential based on the thermodynamic relation $Ω=-pV$ and investigate the behaviour of the pressure in the coupling region of the adaptive resolution method (AdResS). We confirm the physical consistency of the method for determining the chemical potential described by the previous work and strengthen it further by identifying a clear numerical relation between the potential that couples the open system to the reservoir on the one hand and the local pressure of the reference fully atomistic system on the other hand. Such a relation is of crucial importance in the perspective of coupling the AdResS method for open system to the continuum hydrodynamic regime.

cond-mat.stat-mech↗

arXiv2021

A one-step blended soundproof-compressible model with balanced data assimilation: theory and idealised tests

A challenge arising from the local Bayesian assimilation of data in an atmospheric flow simulation is the imbalances it may introduce. Acoustic fast-mode imbalances of the order of the slower dynamics can be negated by employing a blended numerical model with seamless access to the compressible and the soundproof pseudo-incompressible dynamics. Here, the blended modelling strategy by Benacchio et al., MWR, vol. 142 (2014) is upgraded in an advanced numerical framework and extended with a Bayesian local ensemble data assimilation method. Upon assimilation of data, the model configuration is switched to the pseudo-incompressible regime for one time-step. After that, the model configuration is switched back to the compressible model for the duration of the assimilation window. The switching between model regimes is repeated for each subsequent assimilation window. An improved blending strategy for the numerical model ensures that a single time-step in the pseudo-incompressible regime is sufficient to suppress imbalances coming from the initialisation and data assimilation. This improvement is based on three innovations: (i) the association of pressure fields computed at different stages of the numerical integration with actual time levels; (ii) a conversion of pressure-related variables between the model regimes derived from low Mach number asymptotics; and (iii) a judicious selection of the pressure variables used in converting numerical model states when a switch of models occurs. Idealised two-dimensional travelling vortex and buoyancy-driven bubble convection experiments show that acoustic imbalances arising from data assimilation can be eliminated by using this blended model, thereby achieving balanced analysis fields.

math.NA↗

arXiv2021

QG-DL: Dynamics of a diabatic layer in the quasi-geostrophic framework

Quasi-geostrophic (QG) theory describes the dynamics of synoptic scale flows in the trophosphere that are balanced with respect to both acoustic and internal gravity waves. Within this framework, effects of (turbulent) friction near the ground are usually represented by Ekman Layer theory. The troposphere covers roughly the lowest ten kilometers of the atmosphere while Ekman layer heights are typically just a few hundred meters. However, this two-layer asymptotic theory does not explicitly account for substantial changes of the potential temperature stratification due to diabatic heating associated with cloud formation or with radiative and turbulent heat fluxes, which, in the middle latitudes, can be particularly important in about the lowest three kilometers. To address this deficiency, this paper extends the classical QG-Ekman layer model by introducing an intermediate, dynamically and thermodynamically active layer, called the "diabatic layer" (DL) from here on. The flow in this layer is also in acoustic, hydrostatic, and geostrophic balance but, in contrast to QG flow, variations of potential temperature are not restricted to small deviations from a stable and time independent background stratification. Instead, within the diabatic layer, diabatic processes are allowed to affect the leading-order stratification. As a consequence, the diabatic layer modifies the pressure field at the top of the Ekman layer, and with it the intensity of Ekman pumping seen by the quasi-geostrophic bulk flow. The result is the proposed extended quasi-geostrophic three-layer QG-DL-Ekman model for mid-latitude (dry and moist) dynamics.

physics.ao-ph↗

arXiv2021

Balanced data assimilation for highly-oscillatory mechanical systems

Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, the ensemble Kalman filter also has limitations due to its inherent Gaussian and linearity assumptions. These limitations can manifest themselves in dynamically inconsistent state estimates. We investigate this issue in this paper for highly oscillatory Hamiltonian systems with a dynamical behavior which satisfies certain balance relations. We first demonstrate that the standard ensemble Kalman filter can lead to estimates which do not satisfy those balance relations, ultimately leading to filter divergence. We also propose two remedies for this phenomenon in terms of blended time-stepping schemes and ensemble-based penalty methods. The effect of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for two model scenarios. First, we consider balanced motion for highly oscillatory Hamiltonian systems and, second, we investigate thermally embedded highly oscillatory Hamiltonian systems. The first scenario is relevant for applications from meteorology while the second scenario is relevant for applications of data assimilation to molecular dynamics.

math.NA↗

arXiv2021

Nonequilibrium induced by reservoirs: Physico-mathematical models and numerical tests

In a recently proposed computational model of open molecular systems out of equilibrium [Ebrahimi Viand et al. J.Chem.Phys. 153, 101102 (2020)], the action of different reservoirs enters as a linear sum into the Liouville-type evolution equations for the open system's statistics. The linearity of the coupling is common to different mathematical models of open systems and essentially relies on neglecting the feedback of the system onto the reservoir due to their interaction. In this paper, we test the range of applicability of the computational model with a linear coupling to two different reservoirs, which induces a nonequilibrium situation. To this end, we studied the density profiles of Lennard-Jones liquids in large thermal gradients using nonequilibrium molecular dynamics simulations with open boundaries. We put in perspective the formulation of an extension of the mathematical model that can account for nonlinear effects.

cond-mat.stat-mech↗

arXiv2020

Thermodynamic relations at the coupling boundary in adaptive resolution simulations for open systems

The adaptive resolution simulation (AdResS) technique couples regions with different molecular resolutions and allows the exchange of molecules between different regions in an adaptive fashion. The latest development of the technique allows to abruptly couple the atomistically resolved region with a region of non-interacting point-like particles. The abrupt set-up was derived having in mind the idea of the atomistically resolved region as an open system embedded in a large reservoir at a given macroscopic state. In this work, starting from the idea of open system, we derive thermodynamic relations for AdResS which justify conceptually and numerically the claim of AdResS as a technique for simulating open systems. In particular, we derive the relation between the chemical potential of the AdResS set-up and that of its reference fully atomistic simulation. The implication of this result is that the grand potential of AdResS can be explicitly written and thus, from a statistical mechanics point of view, the atomistically resolved region of AdResS can be identified with a well defined open system.

cond-mat.stat-mech↗

arXiv2020

Intensification of tilted atmospheric vortices by asymmetric diabatic heating

Päschke et al. (JFM, 701, 137--170 (2012)) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, \ia, that an azimuthal Fourier mode~1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of tilt and heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order unity in the limit. Formally, this restricts the applicability of the theory to rather weak vortices in the near equatorial region. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to low hurricane strengths. In addition, the paper presents an extended discussion of the asymptotics as regards their physical interpretation and their implications for the overall vortex dynamics. The paper's second contribution is a series of three-dimensional numerical simulations examining the effect of different orientations of dipolar heat release on idealized tropical cyclones. Comparisons with numerical solutions of the asymptotic equations yield evidence that supports the original predictions. In addition, the influence of asymmetric diabatic heat release on the time evolution of centerline tilt is analysed further, and a steering mechanism based on the orientation of the heating dipole is revealed.

physics.flu-dyn↗

arXiv2020

Liouville-type equations for the n-particle distribution functions of an open system

In this work we derive a mathematical model for an open system that exchanges particles and momentum with a reservoir from their joint Hamiltonian dynamics. The complexity of this many-particle problem is addressed by introducing a countable set of n-particle phase space distribution functions just for the open subsystem, while accounting for the reservoir only in terms of statistical expectations. From the Liouville equation for the full system we derive a set of coupled Liouville-type equations for the n-particle distributions by marginalization with respect to reservoir states. The resulting equation hierarchy describes the external momentum forcing of the open system by the reservoir across its boundaries, and it covers the effects of particle exchanges, which induce probability transfers between the n- and (n+1)-particle distributions. Similarities and differences with the Bergmann-Lebowitz model of open systems (P.G.Bergmann, J.L. Lebowitz, Phys.Rev., 99:578--587 (1955)) are discussed in the context of the implementation of these guiding principles in a computational scheme for molecular simulations.

math-ph↗

arXiv2020

Asymptotics for moist deep convection I: Refined scalings and self-sustaining updrafts

Moist processes are among the most important drivers of atmospheric dynamics,and scale analysis and asymptotics are cornerstones of theoretical meteorology. Accounting for moist processes in systematic scale analyses therefore seems of considerable importance for the field. Klein & Majda (TCFD, 20, 525--552, (2006)) proposed a scaling regime for the incorporation of moist bulk microphysics closures in multiscale asymptotic analyses of tropical deep convection. This regime is refined here to allow for mixtures of ideal gases and to establish consistency with a more general multiple scales modelling framework for atmospheric flows. Deep narrow updrafts, so-called "hot towers", constitute principal building blocks of larger scale storm systems. They are analysed here in a sample application of the new scaling regime. A single quasi-onedimensional columnar cloud is considered on the vertical advective (or tower life cycle) time scale. The refined asymptotic scaling regime is essential for this example as it reveals a new mechanism for the self-sustainance of such updrafts. Even for strongly positive convectively available potential energy (CAPE), a vertical balance of buoyancy forces is found in the presence of precipitation. This balance induces a diagnostic equation for the vertical velocity and it is responsible for the generation of self-sustained balanced updrafts. The time dependent updraft structure is encoded in a Hamilton-Jacobi equation for the precipitation mixing ratio. Numerical solutions of this equation suggest that the self-sustained updrafts may strongly enhance hot tower life cycles.

physics.flu-dyn↗

arXiv2020

Open Systems out of Equilibrium: Theory and Simulation

We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution molecular dynamics technique (AdResS). We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with results obtained from the simulation of a larger, locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.

cond-mat.stat-mech↗

arXiv2020

Global Well-posedness for the Primitive Equations Coupled to Nonlinear Moisture Dynamics with Phase Changes

In this work we study the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. This moisture model contains closures for the phase changes condensation and evaporation, as well as the processes of autoconversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. It has been used by Klein and Majda in \cite{KM} and corresponds to a basic form of the bulk microphysics closure in the spirit of Kessler \cite{Ke} and Grabowski and Smolarkiewicz \cite{GS}. The moisture balances are strongly coupled to the thermodynamic equation via the latent heat associated to the phase changes. In \cite{HKLT} we assumed the velocity field to be given and proved rigorously the global existence and uniqueness of uniformly bounded solutions of the moisture balances coupled to the thermodynamic equation. In this paper we present the solvability of a full moist atmospheric flow model, where the moisture model is coupled to the primitive equations of atmospherical dynamics governing the velocity field. For the derivation of a priori estimates for the velocity field we thereby use the ideas of Cao and Titi \cite{CT}, who succeeded in proving the global solvability of the primitive equations.

math.AP↗

arXiv2019

Dynamic Evolution of a Transient Supersonic Trailing Jet Induced by a Strong Incident Shock Wave

The dynamic evolution of a highly underexpanded transient supersonic jet at the exit of a pulse detonation engine is investigated via high-resolution time-resolved schlieren and numerical simulations. Experimental evidence is provided for the presence of a second triple shock configuration along with a shocklet between the reflected shock and the slipstream, which has no analogue in a steady-state underexpanded jet. A pseudo-steady model is developed, which allows for the determination of the post-shock flow condition for a transient propagating oblique shock. This model is applied to the numerical simulations to reveal the mechanism leading to the formation of the second triple point. Accordingly, the formation of the triple point is initiated by the transient motion of the reflected shock, which is induced by the convection of the vortex ring. While the vortex ring embedded shock move essentially as a translating strong oblique shock, the reflected shock is rotating towards its steady state position. This results in a pressure discontinuity that must be resolved by the formation of a shocklet.

physics.flu-dyn↗

arXiv2019

WavePacket: A Matlab package for numerical quantum dynamics. III: Quantum-classical simulations and surface hopping trajectories

WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I [Comp. Phys. Comm. 213, 223-234 (2017)] and Part II [Comp. Phys. Comm. 228, 229-244 (2018)] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagations to WavePacket. In those simulations classical phase-space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces trajectories may switch between surfaces. To model these transitions, two classes of stochastic algorithms have been implemented: (1) J. C. Tully's fewest switches surface hopping and (2) Landau-Zener based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring non-adiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.0.2 which is essentially an object-oriented rewrite of previous versions, allowing to perform fully classical, quantum-classical and quantum-mechanical simulations on an equal footing, i.e., for the same physical system described by the same WavePacket input. The software package is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics are available.

physics.comp-ph↗