Manifestations of projection-induced memory: General theory and the tilted single file.

Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous phenomenological approaches emerged, which can more or less successfully reproduce or account for experimental observations in condensed matter, biological and/or single-particle systems. However, as far as their predictions are concerned these approaches are not unique, often build on conceptually orthogonal ideas, and are typically employed on an ad hoc basis. It therefore seems timely and desirable to establish a systematic, mathematically unifying and clean approach starting from more fine-grained principles. Here we analyze projection-induced ergodic non-Markovian dynamics, both reversible as well as irreversible, using spectral theory. We investigate dynamical correlations between histories of projected and latent observables that give rise to memory in projected dynamics, and rigorously establish conditions under which projected dynamics is Markovian or renewal. A systematic metric is proposed for quantifying the degree of non-Markovianity. As a simple, illustrative but non-trivial example we study single file diffusion in a tilted box, which, for the first time, we solve exactly using the coordinate Bethe ansatz. Our results provide a solid foundation for a deeper and more systematic analysis of projection-induced non-Markovian dynamics and anomalous diffusion

Thermal susceptibility of the Planck-LFI receivers

This paper is part of the Prelaunch status LFI papers published on JINST: http://www.iop.org/EJ/journal/-page=extra.proc5/jinst . This paper describes the impact of the Planck Low Frequency Instrument front end physical temperature fluctuations on the output signal. The origin of thermal instabilities in the instrument are discussed, and an analytical model of their propagation and impact on the receivers signal is described. The experimental test setup dedicated to evaluate these effects during the instrument ground calibration is reported together with data analysis methods. Finally, main results obtained are discussed and compared to the requirements.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Journal of Instrumentation. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at 10.1088/1748-0221/4/12/T1201

Faster uphill relaxation in thermodynamically equidistant temperature quenches

We uncover an unforeseen asymmetry in relaxation: for a pair of thermodynamically equidistant temperature quenches, one from a lower and the other from a higher temperature, the relaxation at the ambient temperature is faster in the case of the former. We demonstrate this finding on hand of two exactly solvable many-body systems relevant in the context of single-molecule and tracer-particle dynamics. We prove that near stable minima and for all quadratic energy landscapes it is a general phenomenon that also exists in a class of non-Markovian observables probed in single-molecule and particle-tracking experiments. The asymmetry is a general feature of reversible overdamped diffusive systems with smooth single-well potentials and occurs in multiwell landscapes when quenches disturb predominantly intrawell equilibria. Our findings may be relevant for the optimization of stochastic heat engines

Toolbox for quantifying memory in dynamics along reaction coordinates

Memory effects in time series of experimental observables are ubiquitous, have important consequences for the interpretation of kinetic data, and may even affect the function of biomolecular nanomachines such as enzymes. Here we propose a set of complementary methods for quantifying conclusively the magnitude and duration of memory in a time series of a reaction coordinate. The toolbox is general, robust, easy to use, and does not rely on any underlying microscopic model. As a proof of concept we apply it to the analysis of memory in the dynamics of the end-to-end distance of the analytically solvable Rouse-polymer model, an experimental time series of extensions of a single DNA hairpin measured by optical tweezers, and the fraction of native contacts in a small protein probed by atomistic molecular dynamics simulations

BetheSF V2: 3-point propagator and additional external potentials

In a recent paper (Comput. Phys. Commun. 258 (2021) 107569) we obtained exactly the tagged-particle propagator in a single-file with N particels diffusing in a generic confining potential via the coordinate Bethe-Ansatz. A naïve implementation of this solution requires a non-polynomial algorithm. To speed-up the computation we implemented a more efficient algorithm that exploits the particle exchange-symmetry. In this new version we expand the code-base to allow for the computation of the three point Green's function. The latter is required e.g. in the analysis of the breaking of time-translational invariance. In addition we include the support for two canonical potentials of general interest: one presenting an energy barrier and one featuring an asymmetric potential landscape

BetheSF: Efficient computation of the exact tagged-particle propagator in single-file systems via the Bethe eigenspectrum

Single-file diffusion is a paradigm for strongly correlated classical stochastic many-body dynamics and has widespread applications in soft condensed matter and biophysics. However, exact results for single-file systems are sparse and limited to the simplest scenarios. We present an algorithm for computing the non-Markovian time-dependent conditional probability density function of a tagged-particle in a single-file of particles diffusing in a confining external potential. The algorithm implements an eigenexpansion of the full interacting many-body problem obtained by means of the coordinate Bethe ansatz. While formally exact, the Bethe eigenspectrum involves the generation and evaluation of permutations, which becomes unfeasible for single-files with an increasing number of particles . Here we exploit the underlying exchange symmetries between the particles to the left and to the right of the tagged-particle and show that it is possible to reduce the complexity of the algorithm from the worst case scenario down to . A C++ code to calculate the non-Markovian probability density function using this algorithm is provided. Solutions for simple model potentials are readily implemented including single-file diffusion in a flat and a ‘tilted’ box, as well as in a parabolic potential. Notably, the program allows for implementations of solutions in arbitrary external potentials under the condition that the user can supply solutions to the respective single-particle eigenspectra

Respuesta del cultivo de maíz a la fertilización nitrogenada en la pampa ondulada, campañas 1980-81 - 1983-84 : I- análisis de los resultados

p.45-64Se presentan los resultados correspondientes a los experimentos de campo realizados a lo largo de las cuatro últimas campañas agrícolas dentro del marco del Programa de Investigación Experimental sobre Fertilización en el cultivo de maíz. La dosis de nutrientes estudiadas fueron de 0,60 y 120 kg N-ha (Campaña 1980-81) y 0,40 y 80 kg N-ha (restantes campañas), mientras que predominaron los materiales genéticos Dekalb, Cargill y Morgan. La red de ensayos, ubicada en la Pampa Ondulada, cubrió 31 situaciones sometidas a diversas combinaciones de factores culturales, edáficos y climáticos los que sufrieron una marcada variación a lo largo de los distintos años. Variaciones concomitantes fueron registradas tanto en el promedio de los rendimientos del tratamiento testigo (70, 61, 59 y 54 qq-ha, en cada uno de los respectivos años), como en la eficiencia de la primera dosis (7,8; 15,1; 10,9 y 15,3;respectivamente). Se determinó, a través del análisis de regresión del rendimiento en función de la dosis de N que el modelo parabólico presentó, en relación a otros modelos, el mejor ajuste a los datos individuales. Sin embargo, al efectuar un análisis de la población total de ensayos no fue posible obtener un buen ajuste a través de los modelos estudiados. Se demuestra finalmente la necesidad de elaborar modelos multivariados para explicar el hecho de que al pasar de la población de ensayos con respuesta significativa a los restantes, tanto los promedios de la eficiencia como del rendimiento del testigo presentan una marcada discontinuidad (de más de 20 a menos de 6 y de 51 a 69 qq-ha, respectivamente)

Dynamic validation of the Planck/LFI thermal model

The Low Frequency Instrument (LFI) is an array of cryogenically cooled radiometers on board the Planck satellite, designed to measure the temperature and polarization anisotropies of the cosmic microwave backgrond (CMB) at 30, 44 and 70 GHz. The thermal requirements of the LFI, and in particular the stringent limits to acceptable thermal fluctuations in the 20 K focal plane, are a critical element to achieve the instrument scientific performance. Thermal tests were carried out as part of the on-ground calibration campaign at various stages of instrument integration. In this paper we describe the results and analysis of the tests on the LFI flight model (FM) performed at Thales Laboratories in Milan (Italy) during 2006, with the purpose of experimentally sampling the thermal transfer functions and consequently validating the numerical thermal model describing the dynamic response of the LFI focal plane. This model has been used extensively to assess the ability of LFI to achieve its scientific goals: its validation is therefore extremely important in the context of the Planck mission. Our analysis shows that the measured thermal properties of the instrument show a thermal damping level better than predicted, therefore further reducing the expected systematic effect induced in the LFI maps. We then propose an explanation of the increased damping in terms of non-ideal thermal contacts.Comment: Planck LFI technical papers published by JINST: http://www.iop.org/EJ/journal/-page=extra.proc5/1748-022

Planck pre-launch status: calibration of the Low Frequency Instrument flight model radiometers

The Low Frequency Instrument (LFI) on-board the ESA Planck satellite carries eleven radiometer subsystems, called Radiometer Chain Assemblies (RCAs), each composed of a pair of pseudo-correlation receivers. We describe the on-ground calibration campaign performed to qualify the flight model RCAs and to measure their pre-launch performances. Each RCA was calibrated in a dedicated flight-like cryogenic environment with the radiometer front-end cooled to 20K and the back-end at 300K, and with an external input load cooled to 4K. A matched load simulating a blackbody at different temperatures was placed in front of the sky horn to derive basic radiometer properties such as noise temperature, gain, and noise performance, e.g. 1/f noise. The spectral response of each detector was measured as was their susceptibility to thermal variation. All eleven LFI RCAs were calibrated. Instrumental parameters measured in these tests, such as noise temperature, bandwidth, radiometer isolation, and linearity, provide essential inputs to the Planck-LFI data analysis.Comment: 15 pages, 18 figures. Accepted for publication in Astronomy and Astrophysic