Methods for suspensions of passive and active filaments

Flexible filaments and fibres are essential components of important complex fluids that appear in many biological and industrial settings. Direct simulations of these systems that capture the motion and deformation of many immersed filaments in suspension remain a formidable computational challenge due to the complex, coupled fluid--structure interactions of all filaments, the numerical stiffness associated with filament bending, and the various constraints that must be maintained as the filaments deform. In this paper, we address these challenges by describing filament kinematics using quaternions to resolve both bending and twisting, applying implicit time-integration to alleviate numerical stiffness, and using quasi-Newton methods to obtain solutions to the resulting system of nonlinear equations. In particular, we employ geometric time integration to ensure that the quaternions remain unit as the filaments move. We also show that our framework can be used with a variety of models and methods, including matrix-free fast methods, that resolve low Reynolds number hydrodynamic interactions. We provide a series of tests and example simulations to demonstrate the performance and possible applications of our method. Finally, we provide a link to a MATLAB/Octave implementation of our framework that can be used to learn more about our approach and as a tool for filament simulation

First measurement of the magnetic field on FK Com and its relation to the contemporaneous starspot locations

In this study we present simultaneous low-resolution longitudinal magnetic field measurements and high-resolution spectroscopic observations of the cool single giant FK Com. The variation of the magnetic field over the rotational period of 2.4 days is compared with the starspot location obtained using Doppler imaging techniques, V-band photometry and V-I colours. The chromospheric activity is studied simultaneously with the photospheric activity using high resolution observations of the Halpha, Hbeta and Hgamma line profiles. Both the maximum (272 +/- 24 G) and minimum (60 +/- 17 G) in the mean longitudinal magnetic field, , are detected close to the phases where cool spots appear on the stellar surface. A possible explanation for such a behaviour is that the active regions at the two longitudes separated by 0.2 in phase have opposite polarities.Comment: 10 Pages, 11 figures (quality of Figures 7,8 and 10 reduced), accepted for publication in MNRA

Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

The boundary charge that accumulates at the edge of a one-dimensional single-channel insulator is known to possess the universal property that its change under a lattice shift towards the edge by one site is given by the sum of the average bulk electronic density and a topologically invariant contribution, restricted to the values 0 and −1 [Pletyukhov et al., Phys. Rev. B 101, 165304 (2020)]. This quantized contribution is associated with particle-hole duality, ensures charge conservation, and fixes the mod(1) ambiguity appearing in the modern theory of polarization. In the present paper we generalize the above-mentioned single-channel results to the multichannel case by employing the technique of boundary Green's functions. We show that the topological invariant associated with the change in boundary charge under a lattice shift in multichannel models can be expressed as a winding number of a certain combination of components of bulk Green's functions as a function of the complex frequency, as it encircles the section of the energy axis that corresponds to the occupied part of the spectrum. We observe that this winding number is restricted to values ranging from −Nc to zero, where Nc is the number of channels (orbitals) per site. Furthermore, we consider translationally invariant one-dimensional multichannel models with an impurity and introduce topological indices which correspond to the quantized charge that accumulates around said impurity. These invariants are again given in terms of winding numbers of combinations of components of bulk Green's functions. Through this construction we provide a rigorous mathematical proof of the so-called nearsightedness principle formulated by Kohn [Kohn, Phys. Rev. Lett. 76, 3168 (1996)] for noninteracting multichannel lattice models

Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids

We compare two fermionic renormalization group methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor man's method setup to resum ``leading-log'' divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional renormalization group method and leads to a set of differential equations which can only for certain setups and in limiting cases be solved analytically, while in general it must be integrated numerically. Both methods are claimed to be applicable for inhomogeneities of arbitrary strength and to capture effects of the two-particle interaction, such as interaction dependent exponents, up to leading order. We critically review this for the simplest case of a single impurity. While on first glance the poor man's approach seems to describe the crossover from the ``perfect'' to the ``open chain fixed point'' we collect evidence that difficulties may arise close to the ``perfect chain fixed point''. Due to a subtle relation between the scaling dimensions of the two fixed points this becomes apparent only in a detailed analysis. In the functional renormalization group method the coupling of the different scattering channels is kept which leads to a better description of the underlying physics.Comment: 25 pages, accepted for publication in NJP, remarks added on the poor man's RG treatment of the Y-junction and the Breit-Wigner line shape

Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

We generalize our recent results for the hard-wall boundary and interface charges in one-dimensional single-channel continuum [S. Miles et al., Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [N. Müller et al., Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance xφ∈[0,L] (where L is a potential periodicity) is given by a perfectly linear function of xφ plus an integer-valued topological invariant I, the so-called boundary invariant. We provide two equivalent representations for I(xφ): the winding-number representation and the bound-state representation. The winding-number representation allows one to write I as a winding index of a particular functional of bulk Green's function. The corresponding integration contour is chosen in the complex frequency plane to encircle the occupied part of the spectrum residing on the real axis. In turn, in the bound-state representation, I is expressed through the sum of the winding number of the boundary Green's function and the number of bound states supported by the cavity of size xφ below the chemical potential. We observe that during a single cycle in the variation of xφ, the boundary invariant exhibits exactly ν downward jumps, each by a unit of electron charge, whenever ν energy bands are completely filled leading to the value I(L)=−ν. Additionally, for translationally invariant models interrupted by a localized impurity we derive the winding-number expression for the excess charge accumulated on the said impurity. We observe that the charge accumulated on a single repulsive impurity is restricted to the values −Nc,⋯,0, where Nc is the number of channels (spin or orbital components) in the system. For systems with weak potential amplitudes, we additionally develop Green's-function-based low-energy theory, allowing one to analytically access the physics of multichannel continuum systems in the low-energy approximation

Interference and interaction effects in multi-level quantum dots

Using renormalization group techniques, we study spectral and transport properties of a spinless interacting quantum dot consisting of two levels coupled to metallic reservoirs. For strong Coulomb repulsion $U$ and an applied Aharonov-Bohm phase $\phi$, we find a large direct tunnel splitting $|\Delta|\sim (\Gamma/\pi)|\cos(\phi/2)|\ln(U/\omega_c)$ between the levels of the order of the level broadening $\Gamma$. As a consequence we discover a many-body resonance in the spectral density that can be measured via the absorption power. Furthermore, for $\phi=\pi$, we show that the system can be tuned into an effective Anderson model with spin-dependent tunneling.Comment: 5 pages, 4 figures included, typos correcte

Cotunneling at resonance for the single-electron transistor

We study electron transport through a small metallic island in the perturbative regime. Using a recently developed diagrammatic technique, we calculate the occupation of the island as well as the conductance through the transistor in forth order in the tunneling matrix elements, a process referred to as cotunneling. Our formulation does not require the introduction of a cut-off. At resonance we find significant modifications of previous theories and good agreement with recent experiments.Comment: 5 pages, Revtex, 5 eps-figure

Interaction-driven spin precession in quantum-dot spin valves

We analyze spin-dependent transport through spin valves composed of an interacting quantum dot coupled to two ferromagnetic leads. The spin on the quantum dot and the linear conductance as a function of the relative angle $\theta$ of the leads' magnetization directions is derived to lowest order in the dot-lead coupling strength. Due to the applied bias voltage spin accumulates on the quantum dot, which for finite charging energy experiences a torque, resulting in spin precession. The latter leads to a non-trivial, interaction-dependent, $\theta$-dependence of the conductance. In particular, we find that the spin-valve effect is reduced for all $\theta \neq \pi$.Comment: 5 pages, 3 figures, version to be published in Phys. Rev. Let

Tailoring Fibre Structure Enabled by X-ray Analytics for Targeted Biomedical Applications

The rising interest in designing fibres via spinning techniques combining the properties of various polymeric materials into advanced functionalised materials is directed towards targeted biomedical applications such as drug delivery, wearable sensors or tissue engineering. Understanding how these functional polymers exhibit multiscale structures ranging from the molecular level to nano-, micro-and millimetre scale is a key prerequisite for their challenging applications that can be addressed by a non-destructive X-ray based analytical approach. X-ray multimodalities combining X-ray imaging, scattering and diffraction allow the study of morphology, molecular structure, and the analysis of nano-domain size and shape, crystallinity and preferential orientation in 3D arrangements. The incorporation of X-ray analytics in the design process of polymeric fibers via their nanostructure under non-ambient conditions (i.e. temperature, mechanical load, humidity…) allows for efficient optimization of the fabrication process as well as quality control along the product lifetime under operating environmental conditions. Here, we demonstrate the successful collaboration between the laboratory of Biomimetic Textiles and Membranes and the Center of X-ray Analytics at Empa for the design, characterisation and optimisation of advanced functionalised polymeric fibrous material systems

Microscopic theory of single-electron tunneling through molecular-assembled metallic nanoparticles

We present a microscopic theory of single-electron tunneling through metallic nanoparticles connected to the electrodes through molecular bridges. It combines the theory of electron transport through molecular junctions with the description of the charging dynamics on the nanoparticles. We apply the theory to study single-electron tunneling through a gold nanoparticle connected to the gold electrodes through two representative benzene-based molecules. We calculate the background charge on the nanoparticle induced by the charge transfer between the nanoparticle and linker molecules, the capacitance and resistance of molecular junction using a first-principles based Non-Equilibrium Green's Function theory. We demonstrate the variety of transport characteristics that can be achieved through ``engineering'' of the metal-molecule interaction.Comment: To appear in Phys. Rev.