# Les 20 dernières publications du LPTMS

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## Velocity and diffusion constant of an active particle in a one-dimensional force field – Archive ouverte HAL

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}Gregory Schehr^{2}#### Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Velocity and diffusion constant of an active particle in a one-dimensional force field.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020, 130 (4), pp.40002. ⟨10.1209/0295-5075/130/40002⟩. ⟨hal-02881224⟩We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of period $L$. They involve the "active potential" which allows to define a global bias. Upon varying parameters, such as an external force $F$, the dynamics undergoes transitions from non-ergodic trapped states, to various moving states, some with non analyticities in the $V_L$ versus $F$ curve. A random landscape in the presence of a bias leads, for large $L$, to anomalous diffusion $x \sim t^\mu$, $\mu<1$, or to a phase with a finite velocity that we calculate.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle – Archive ouverte HAL

### Francesco Mori

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle.

*Physical Review Letters*, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal-02512214⟩We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Champs Aléatoires et Systèmes hors d'Équilibre

## Universal Scaling of the Velocity Field in Crack Front Propagation – Archive ouverte HAL

### Clément Le Priol

^{1}Pierre Le Doussal^{2}Laurent Ponson^{3}Alberto Rosso^{4}Julien Chopin^{5}#### Clément Le Priol, Pierre Le Doussal, Laurent Ponson, Alberto Rosso, Julien Chopin. Universal Scaling of the Velocity Field in Crack Front Propagation.

*Physical Review Letters*, American Physical Society, 2020, 124 (6), ⟨10.1103/PhysRevLett.124.065501⟩. ⟨hal-02512228⟩The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. Champs Aléatoires et Systèmes hors d'Équilibre
- 3. DALEMBERT - Institut Jean Le Rond d'Alembert
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. IF-UFB - Instituto de Fisica, Universidade Federal da Bahia

## Universal gap statistics for random walks for a class of jump densities – Archive ouverte HAL

### Matteo Battilana

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}#### Matteo Battilana, Satya N. Majumdar, Gregory Schehr. Universal gap statistics for random walks for a class of jump densities.

*Markov Processes And Related Fields*, Polymat Publishing Company, 2020. ⟨hal-02518812⟩We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,n}-M_{k+1,n}$ where $M_{k,n}$ is the $k$-th maximum of the RW between step 1 and step $n$. In the limit of large $n$, we show that the probability density function of the gaps $P_{k,n}(\Delta) = \Pr(d_{k,n} = \Delta)$ reaches a stationary density $P_{k,n}(\Delta) \to p_k(\Delta)$. For large $k$, we demonstrate that the typical fluctuations of the gap, for $d_{k,n}= O(1/\sqrt{k})$ (and $n \to \infty$), are described by a non-trivial scaling function that is independent of $k$ and of the jump probability density function $f_p(\eta)$, thus corroborating our conjecture about the universality of the regime of typical fluctuations (see G. Schehr, S. N. Majumdar, Phys. Rev. Lett. 108, 040601 (2012)). We also investigate the large fluctuations of the gap, for $d_{k,n} = O(1)$ (and $n \to \infty$), and show that these two regimes of typical and large fluctuations of the gaps match smoothly.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Topological effects and conformal invariance in long-range correlated random surfaces – Archive ouverte HAL

### Nina Javerzat

^{1}Sebastian Grijalva^{1}Alberto Rosso^{1}Raoul Santachiara^{1}#### Nina Javerzat, Sebastian Grijalva, Alberto Rosso, Raoul Santachiara. Topological effects and conformal invariance in long-range correlated random surfaces.

*SciPost Phys.*, 2020, 9 (4), pp.050. ⟨10.21468/SciPostPhys.9.4.050⟩. ⟨hal-02863162⟩We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter ($H$) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $H\leq-\frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $-\frac{3}{4}

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence – Archive ouverte HAL

### Giuseppe Petrillo

^{1}Eugenio Lippiello^{1}François Landes^{2}Alberto Rosso^{3}#### Giuseppe Petrillo, Eugenio Lippiello, François Landes, Alberto Rosso. The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence.

*Nature Communications*, Nature Publishing Group, 2020. ⟨hal-02908552⟩Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

- 1. Department of Mathematics and Physics [Caserta]
- 2. LRI - Laboratoire de Recherche en Informatique
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## The convex hull of the run-and-tumble particle in a plane – Archive ouverte HAL

### Alexander K HartmannSatya N Majumdar

^{1}Hendrik Schawe^{2}Gregory Schehr^{1}Alexander Hartmann^{2}Satya Majumdar^{1}#### Alexander K Hartmann, Satya N Majumdar, Hendrik Schawe, Gregory Schehr, Alexander Hartmann, et al.. The convex hull of the run-and-tumble particle in a plane.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2020, 2020 (5), pp.053401. ⟨10.1088/1742-5468/ab7c5f⟩. ⟨hal-02881103⟩We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its direction randomly. We consider two different statistical ensembles where we either fix (i) the total number of tumblings $n$ or (ii) the total duration $t$ of the time interval. In both cases, we derive exact expressions for the average perimeter of the convex hull and then compare to numerical estimates finding excellent agreement. Further, we numerically compute the full distribution of the perimeter using Markov chain Monte Carlo techniques, in both ensembles, probing the far tails of the distribution, up to a precision smaller than $10^{-100}$. This also allows us to characterize the rare events that contribute to the tails of these distributions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg

## Symmetries in $B \to D^* \ell \nu$ angular observables – Archive ouverte HAL

### Marcel AlgueróSébastien Descotes-Genon

^{1}Joaquim MatiasMartín Novoa-Brunet^{2}#### Marcel Algueró, Sébastien Descotes-Genon, Joaquim Matias, Martín Novoa-Brunet. Symmetries in $B \to D^* \ell \nu$ angular observables.

*JHEP*, 2020, 06, pp.156. ⟨10.1007/JHEP06(2020)156⟩. ⟨hal-02518081⟩We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D$^{∗}$ℓν for ℓ = e, μ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D$^{∗}$ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure $ {F}_L^{D\ast } $ in B → D$^{∗}$τν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of $ {F}_L^{D\ast } $ remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light right-handed neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.

- 1. IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Stochastic growth in time-dependent environments – Archive ouverte HAL

### Guillaume Barraquand

^{1}Pierre Le Doussal^{1}Alberto Rosso^{2}#### Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso. Stochastic growth in time-dependent environments.

*Physical Review E*, American Physical Society (APS), 2020, 101 (4), ⟨10.1103/PhysRevE.101.040101⟩. ⟨hal-02565202⟩We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{-\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution saturates at large times towards a non-universal limiting distribution. When $\alpha<1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ and the limiting statistics are similar to the case when $c(t)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the log-gamma polymer model (3) Numerical simulations.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Statistics of the number of records for random walks and Lévy flights on a 1D lattice – Archive ouverte HAL

### Philippe Mounaix

^{1}Satya Majumdar^{2}Grégory Schehr^{2}#### Philippe Mounaix, Satya Majumdar, Grégory Schehr. Statistics of the number of records for random walks and Lévy flights on a 1D lattice.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2020, 53 (41), pp.415003. ⟨10.1088/1751-8121/abac97⟩. ⟨hal-02958283⟩We study the statistics of the number of records R n for a symmetric, n-step, discrete jump process on a 1D lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability distribution. This process includes, as a special case, the standard nearest neighbor lattice random walk. We derive explicitly the generating function of the distribution P (R n) of the number of records, valid for arbitrary discrete jump distributions. As a byproduct, we provide a relatively simple proof of the generalized Sparre Andersen theorem for the survival probability of a random walk on a line, with discrete or continuous jump distributions. For the discrete jump process, we then derive the asymptotic large n behavior of P (R n) as well as of the average number of records E(R n). We show that unlike the case of random walks with symmetric and continuous jump distributions where the record statistics is strongly universal (i.e., independent of the jump distribution for all n), the record statistics for lattice walks depends on the jump distribution for any fixed n. However, in the large n limit, we show that the distribution of the scaled record number R n /E(R n) approaches a universal, half-Gaussian form for any discrete jump process. The dependence on the jump distribution enters only through the scale factor E(R n), which we also compute in the large n limit for arbitrary jump distributions. We present explicit results for a few examples and provide numerical checks of our analytical predictions.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## State transition graph of the Preisach model and the role of return-point memory – Archive ouverte HAL

### M. Mert Terzi

^{1}Muhittin Mungan#### M. Mert Terzi, Muhittin Mungan. State transition graph of the Preisach model and the role of return-point memory.

*Physical Review E*, 2020, 102 (1), ⟨10.1103/PhysRevE.102.012122⟩. ⟨hal-02908545⟩The Preisach model has been useful as a null-model for understanding memory formation in periodically driven disordered systems. In amorphous solids for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by one of us, the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft-spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return point memory in organizing the graph into a hierarchy of loops and sub-loops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the individual hysteretic behavior of the individual elements, but by a coarser parameter, a permutation $\rho$ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states $| \mathcal{R} |$ constituting the main hysteresis loop and its nested subloops. We find that $| \mathcal{R} |$ is equal to the number of increasing subsequences contained in the permutation $\rho$.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Scalable quantum computing with qudits on a graph – Archive ouverte HAL

### E. O. Kiktenko

^{1}A. S. NikolaevaPeng XuG. V. Shlyapnikov^{2}A. K. Fedorov^{3}#### E. O. Kiktenko, A. S. Nikolaeva, Peng Xu, G. V. Shlyapnikov, A. K. Fedorov. Scalable quantum computing with qudits on a graph.

*Physical Review A*, American Physical Society 2020, 101 (2), ⟨10.1103/PhysRevA.101.022304⟩. ⟨hal-02512218⟩We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multi-qudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.

- 1. IPE - Schmidt United Institute of Physics of the Earth [Moscow]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Russian Quantum Center

## Rigorous bounds on dynamical response functions and time-translation symmetry breaking – Archive ouverte HAL

### Marko Medenjak

^{1}Tomaz Prosen^{2}Lenart Zadnik^{3}#### Marko Medenjak, Tomaz Prosen, Lenart Zadnik. Rigorous bounds on dynamical response functions and time-translation symmetry breaking.

*SciPost Physics*, SciPost Foundation, 2020, 9 (1), ⟨10.21468/SciPostPhys.9.1.003⟩. ⟨hal-02935659⟩Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Flo-quet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

- 1. IPM - institut de Physique Théorique Philippe Meyer
- 2. FMF - Faculty of Mathematics and Physics [Ljubljana]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Reversal of contractility as a signature of self-organization in cytoskeletal bundles – Archive ouverte HAL

### Martin Lenz

^{1}#### Martin Lenz. Reversal of contractility as a signature of self-organization in cytoskeletal bundles.

*eLife*, eLife Sciences Publication, 2020, 9, ⟨10.7554/eLife.51751⟩. ⟨hal-02518848⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Optimizing Brownian escape rates by potential shaping – Archive ouverte HAL

### Marie Chupeau

^{1}Jannes GladrowAlexei Chepelianskii^{2}Ulrich F. KeyserEmmanuel Trizac^{1}Ulrich Keyser#### Marie Chupeau, Jannes Gladrow, Alexei Chepelianskii, Ulrich F. Keyser, Emmanuel Trizac, et al.. Optimizing Brownian escape rates by potential shaping.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2020, 117 (3), pp.1383-1388. ⟨10.1073/pnas.1910677116⟩. ⟨hal-02512216⟩Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPCT - Laboratoire de Physico-Chimie Théorique

## Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States – Archive ouverte HAL

### John MartinStefan WeigertOlivier Giraud

^{1}#### John Martin, Stefan Weigert, Olivier Giraud. Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States.

*Quantum*, Verein, 2020. ⟨hal-02881098⟩Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids – Archive ouverte HAL

### Alessandro Manacorda

^{1}Gregory Schehr^{2}Francesco Zamponi^{1}#### Alessandro Manacorda, Gregory Schehr, Francesco Zamponi. Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids.

*Journal of Chemical Physics*, American Institute of Physics, 2020, 152 (16), pp.164506. ⟨10.1063/5.0007036⟩. ⟨hal-02554137⟩- 1. Systèmes Désordonnés et Applications
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Multi-component colloidal gels: interplay between structure and mechanical properties – Archive ouverte HAL

### Claudia Ferreiro-CordovaMehdi Bouzid

^{1}Emanuela del GadoGiuseppe Foffi^{2}Claudia Ferreiro-Córdova#### Claudia Ferreiro-Cordova, Mehdi Bouzid, Emanuela del Gado, Giuseppe Foffi, Claudia Ferreiro-Córdova. Multi-component colloidal gels: interplay between structure and mechanical properties.

*Soft Matter*, Royal Society of Chemistry, 2020, 16 (18), pp.4414-4421. ⟨10.1039/C9SM02410G⟩. ⟨hal-02881157⟩We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solids

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes – Archive ouverte HAL

### Guillaume Lamour

^{1}Antoine Allard^{1, 2}Juan Pelta^{1}Sid Labdi^{1}Martin Lenz^{3}Clément Campillo^{1}#### Guillaume Lamour, Antoine Allard, Juan Pelta, Sid Labdi, Martin Lenz, et al.. Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes.

*Physical Review X*, American Physical Society, 2020, 10 (1), pp.011031. ⟨10.1103/PhysRevX.10.011031⟩. ⟨hal-02512272⟩Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the ill-understood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substrate-bound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tip-membrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of force-displacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membrane-protein interactions, including membrane remodeling in nanotube scission and vesicle formation.

- 1. LAMBE - UMR 8587 - Laboratoire Analyse, Modélisation et Matériaux pour la Biologie et l'Environnement
- 2. PCC - Physico-Chimie-Curie
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers – Archive ouverte HAL

### Stéphane Ouvry

^{1}Alexios Polychronakos#### Stéphane Ouvry, Alexios Polychronakos. Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers.

*Nucl.Phys.B*, 2020, 960, pp.115174. ⟨10.1016/j.nuclphysb.2020.115174⟩. ⟨hal-02886896⟩Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walks, and in particular for the triangular lattice chiral walks recently introduced by the authors. A key element in the enumeration is the derivation of some identities involving some remarkable trigonometric sums –which are also important building blocks of non trivial quantum models such as the Hofstadter model– and their explicit rewriting in terms of multiple binomial sums. An intriguing connection is also made with number theory and some classes of Apéry-like numbers, the cousins of the Apéry numbers which play a central role in irrationality considerations for ζ(2) and ζ(3) .

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques