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1. Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling

   https://doi.org/https://doi.org/10.1016/j.jaerosci.2021.105746  

   Suresh, Vikram; Gopalakrishnan, Ranganathan (February 2021, Journal of aerosol science)

   null (Ed.)

   The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Potential applications and caveats to the usage of LD are included as a summary. 

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2. Dynamics of Inertial Particles in Flows with Stochasticity

   https://doi.org/10.1175/JPO-D-24-0117.1  

   Rogers, Mason; Rypina, Irina I (July 2025, Journal of Physical Oceanography)

   Abstract Because of their buoyancy, rigidity, and finite size, inertial particles do not obey the same dynamics as fluid parcels. The motion of small spherical particles in a fluid flow is described by the Maxey–Riley equations and depends nonlinearly on the velocity of the fluid in which the particles are immersed. Fluid velocities in the ocean often have a strong small-scale turbulent component which is difficult to observe or model, presenting a challenge to predicting the evolution of distributions of inertial particles in the ocean. To overcome this challenge, we assume that the turbulent velocity imposes a random force on particles and consider a stochastic analog of the Maxey–Riley equations. By performing a perturbation analysis of the stochastic Maxey–Riley equations, we obtain a simple and accurate partial differential equation for the spatial distribution of particles. The equation is of the advection–diffusion type and handles the uncertainty introduced by unresolved turbulent flow features. In several numerical test cases, distributions of particles obtained by solving the newly derived equation compare favorably with distributions obtained from Monte Carlo simulations of individual particle trajectories and with theoretical predictions. The advection–diffusion form of our newly derived equation is amenable to inclusion within many existing ocean circulation models. Significance StatementWe introduce a new model for describing spatial distributions of small rigid objects, such as plastic debris, in the ocean. The model takes into account the effects of finite particle size and particle buoyancy, which cause particle trajectories to differ from fluid parcel trajectories. Our model also represents small-scale turbulence stochastically. 

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3. Source Region and Propagation of Dayside Large‐Scale Traveling Ionospheric Disturbances

   https://doi.org/10.1029/2020GL089451  

   Nishimura, Y.; Zhang, S. R.; Lyons, L. R.; Deng, Y.; Coster, A. J.; Moen, J. I.; Clausen, L. B.; Bristow, W. A.; Nishitani, N. (September 2020, Geophysical Research Letters)

   Abstract We examined the source region of dayside large‐scale traveling ionospheric disturbances (LSTIDs) and their relation to cusp energy input. Aurora and total electron content (TEC) observations show that LSTIDs propagate equatorward away from the cusp and demonstrate the cusp region as the source region. Enhanced energy input to the cusp initiated by interplanetary magnetic field (IMF) southward turning triggers the LSTIDs, and each LSTID oscillation is correlated with a TEC enhancement in the dayside oval with tens of minutes periodicity. Equatorward‐propagating LSTIDs are likely gravity waves caused by repetitive heating in the cusp. The cusp source can explain the high LSTID occurrence on the dayside during geomagnetically active times. Poleward‐propagating ΔTEC patterns in the polar cap propagate nearly at the convection speed. While they have similar ΔTEC signatures to gravity wave‐driven LSTIDs, they are suggested to be weak polar cap patches quasiperiodically drifting from the cusp into the polar cap via dayside reconnection. 

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4. Enhanced avionic sensing based on Wigner’s cusp anomalies

   https://doi.org/10.1126/sciadv.abg8118  

   Kononchuk, Rodion; Feinberg, Joshua; Knee, Joseph; Kottos, Tsampikos (June 2021, Science Advances)

   null (Ed.)

   Typical sensors detect small perturbations by measuring their effects on a physical observable, using a linear response principle (LRP). It turns out that once LRP is abandoned, new opportunities emerge. A prominent example is resonant systems operating near N th-order exceptional point degeneracies (EPDs) where a small perturbation ε ≪ 1 activates an inherent sublinear response ∼ ε N ≫ ε in resonant splitting. Here, we propose an alternative sublinear optomechanical sensing scheme that is rooted in Wigner’s cusp anomalies (WCAs), first discussed in the framework of nuclear reactions: a frequency-dependent square-root singularity of the differential scattering cross section around the energy threshold of a newly opened channel, which we use to amplify small perturbations. WCA hypersensitivity can be applied in a variety of sensing applications, besides optomechanical accelerometry discussed in this paper. Our WCA platforms are compact, do not require a judicious arrangement of active elements (unlike EPD platforms), and, if chosen, can be cavity free. 

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5. Complex harmonic capacitors

   https://doi.org/10.1007/s00526-025-02956-0  

   Iwaniec, Tadeusz; Onninen, Jani; Radice, Teresa (April 2025, Calculus of Variations and Partial Differential Equations)

   Abstract The concept of complex harmonic potential in a doubly connected condenser (capacitor) is introduced as an analogue of the real-valued potential of an electrostatic vector field. In this analogy the full differential of a complex potential plays the role of the gradient of the scalar potential in the theory of electrostatics. The main objective in the non-static fields is to rule out having the full differential vanish at some points. Nevertheless, there can be critical points where the Jacobian determinant of the differential turns into zero. The latter is in marked contrast to the case of real-valued potentials. Furthermore, the complex electric capacitor also admits an interpretation of the stored energy intensively studied in the theory of hyperelastic deformations. Engineers interested in electrical systems, such as energy storage devises, might also wish to envision complex capacitors aselectromagnetic condenserswhich, generally, store more energy that the electric capacitors. 

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