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Dynamics of a chain of interacting magnetic particles in a one-dimensional periodic energy landscape
No full textWe explore the dynamics of a one-dimensional chain of paramagnetic colloidal particles in a periodic potential. The model accounts for a constant external force, along with magnetic dipolar attraction and hard-core repulsive interactions between particles. Numerical simulations reveal the emergence of a traveling kink – a chain defect propagating along the chain. We show that the kink emerges beyond a critical force threshold and identify parameter regimes corresponding to distinct dynamic modes such as a pinned kink, a running kink, a cluster kink, and chain drift
Impact of the external knee flexion moment on patello-femoral loading derived from in vivo loads and kinematics
No full textIntroduction: Anterior knee pain and other patello-femoral (PF) complications frequently limit the success of total knee arthroplasty as the final treatment of end stage osteoarthritis. However, knowledge about the in-vivo loading conditions at the PF joint remains limited, as no direct measurements are available. We hypothesised that the external knee flexion moment (EFM) is highly predictive of the PF contact forces during activities with substantial flexion of the loaded knee.
Materials and methods: Six patients (65–80 years, 67–101 kg) with total knee arthroplasty (TKA) performed two activities of daily living: sit-stand-sit and squat. Tibio-femoral (TF) contact forces were measured in vivo using instrumented tibial components, while synchronously internal TF and PF kinematics were captured with mobile fluoroscopy. The measurements were used to compute PF contact forces using patient specific musculoskeletal models. The relationship between the EFM and the PF contact force was quantified using linear regression.
Results: Mean peak TF contact forces of 1.97–3.24 times body weight (BW) were found while peak PF forces reached 1.75 to 3.29 times body weight (BW). The peak EFM ranged from 3.2 to 5.9 %BW times body height, and was a good predictor of the PF contact force (R2 = 0.95 and 0.88 for sit-stand-sit and squat, respectively).
Discussion: The novel combination of in vivo TF contact forces and internal patellar kinematics enabled a reliable assessment of PF contact forces. The results of the regression analysis suggest that PF forces can be estimated based solely on the EFM from quantitative gait analysis. Our study also demonstrates the relevance of PF contact forces, which reach magnitudes similar to TF forces during activities of daily living
Characterizing inertial and diabatic energy transfers in tropical cyclones: Data
No full textThe multiscale organization of tropical cyclones (TCs) is investigated by means of three-dimensional data produced by the atmospheric model CM1. We provide a sample dataset in NetCDF format covering the TC evolution from incipient to mature under the influence of externally imposed wind shear. This dataset serves as a testbed for applying energy-tranfer analyses based on the Duchon-Robert index as well as diabatic transfer based on an asymptotic theory on TCs
Mathematical Optimization for Machine Learning
No full textMathematical optimization and machine learning are closely related. This proceedings volume of the Thematic Einstein Semester 2023 of the Berlin Mathematics Research Center MATH+ collects recent progress on their interplay in topics such as discrete optimization, nonlinear programming, optimal control, first-order methods, multilevel optimization, machine learning in optimization, physics-informed learning, and fairness in machine learning
A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming
No full textThe current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set
Warm-starting modeling to generate alternatives for energy transition paths in the Berlin-Brandenburg area
No full textEnergy system optimization models are key to investigate energy transition paths towards a decarbonized future. Since this approach comes with intrinsic uncertainties, it is insufficient to compute a single optimal solution assuming perfect foresight to provide a profound basis for decision makers. The paradigm of modeling to generate alternatives enables to explore the near-optimal solution space to a certain extent. However, large-scale energy models require a non-negligible computation time to be solved. We propose to use warm start methods to accelerate the process of finding close-to-optimal alternatives. In an extensive case study for the energy transition of the Berlin-Brandenburg area, we make use of the sector-coupled linear programming oemof-B3 model to analyze a scenario for the year 2050 with a resolution of one
hour and 100% reduction of greenhouse gas emissions. We demonstrate that we can actually achieve a significant computational speedup
Detection of dynamic communities in temporal networks with sparse data
No full textTemporal networks are a powerful tool for studying the dynamic nature of a wide range of real-world complex systems, including social, biological and physical systems. In particular, detection of dynamic communities within these networks can help identify important cohesive structures and fundamental mechanisms driving systems behaviour. However, when working with real-world systems, available data is often limited and sparse, due to missing data on systems entities, their evolution and interactions, as well as uncertainty regarding temporal resolution. This can hinder accurate representation of the system over time and result in incomplete or biased community dynamics. In this paper, we compare established methods for community detection and, using synthetic data experiments and real-world case studies, we evaluate the impact of data sparsity on the quality of identified dynamic communities. Our results give valuable insights on the evolution of systems with sparse data, which are less studied in existing literature, but are frequently encountered in real-world applications
Fluid flow inside slit-shaped nanopores: the role of surface morphology at the molecular scale
No full textNon-equilibrium molecular dynamics (NEMD) simulations of fluid flow have highlighted the peculiarities of nanoscale flows compared to classical fluid mechanics; in particular, boundary conditions can deviate from the no-slip behavior at macroscopic scales. For fluid flow in slit-shaped nanopores, we demonstrate that surface morphology provides an efficient control on the slip length, which approaches zero when matching the molecular structures of the pore wall and the fluid. Using boundary-driven, energy-conserving NEMD simulations with a pump-like driving mechanism, we examine two types of pore walls—mimicking a crystalline and an amorphous material—that exhibit markedly different surface resistances to flow. The resulting flow velocity profiles are consistent with Poiseuille theory for incompressible, Newtonian fluids when adjusted for surface slip. For the two pores, we observe partial slip and no-slip behavior, respectively. The hydrodynamic permeability corroborates that the simulated flows are in the Darcy regime. However, the confinement of the fluid gives rise to an effective viscosity below its bulk value; wide pores exhibit a crossover between boundary and bulk-like flows. In addition, the thermal isolation of the flow causes a linear increase in fluid temperature along the flow, which we relate to strong viscous dissipation and heat convection, utilizing conservation laws of fluid mechanics. Noting that the investigated fluid model does not form droplets, our findings challenge the universality of previously reported correlations between slippage, solvophobicity, and a depletion zone. Furthermore, they underscore the need for molecular-scale modeling to accurately capture the fluid dynamics near boundaries and in nanoporous materials, where macroscopic models may not be applicable
Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales
No full textReaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual particle/agent level, and in realistic applications, they often display interaction with their environment through energy or material exchange with a reservoir. This requires intricate mathematical considerations, especially in the case of material exchange since the varying number of particles/agents results in ``on-the-fly'' modification of the system dimension. In this work, we first overview the probabilistic description of reaction-diffusion processes at the particle level, which readily handles varying number of particles. We then extend this model to consistently incorporate interactions with macroscopic material reservoirs. Based on the resulting expressions, we bridge the probabilistic description with macroscopic concentration-based descriptions for linear and nonlinear reaction-diffusion systems, as well as for an archetypal open reaction-diffusion system. Using these mathematical bridges across scales, we finally develop numerical schemes for open reaction-diffusion systems, which we implement in two illustrative examples. This work establishes a methodological workflow to bridge particle-based probabilistic descriptions with macroscopic concentration-based descriptions of reaction-diffusion in open settings, laying the foundations for a multiscale theoretical framework upon which to construct theory and simulation schemes that are consistent across scales