arXiv subjects

Piotr Szymczak

Publications and source records attributed to Piotr Szymczak.

At least 19 recordsLinked to original sources

arXiv2026

Retreat to advance: self-blocking enables efficient mineral replacement

Mineral replacement reactions under advective flow often suffer from severe spatial inefficiency: dissolution causes the flow to self-focus into a few dominant wormholes that bypass the surrounding matrix, leaving most of the rock unreplaced. Here we show -- through two-dimensional pore-network simulations -- that replacement can be effective in two regimes. The first arises when the precipitation rate significantly exceeds the dissolution rate, leading to in situ replacement in which a uniform front of the secondary mineral advances through the matrix. The second, exploratory mode, occurs when the system repeatedly self-blocks and re-routes. In this regime, each channel lives only long enough to deliver reactant a short distance ahead of the front before its tip is cemented by the product phase; pressure re-routes through an adjacent corridor, and the cycle begins anew. Over time the replacement front advances as a mosaic of overlapping micro-fronts, distributing the secondary mineral almost uniformly. We derive design criteria for achieving exploratory-mode behaviour and discuss implications for both natural and engineered reactive-infiltration systems.

physics.flu-dyn↗

arXiv2026

A granular Büttiker-Landauer motor

Random walkers usually diffuse according to Fick's law. On average, they move down the gradient of their concentration and, in the absence of external force, tend to distribute themselves uniformly. In some experiments, however, this familiar notion is at odds with observation. Sand grains, for instance, gather along the nodal lines of a vibrated elastic plate to form a Chladni figure, thus accumulating where fluctuations are weak -- a fact that escapes the reach of Fick's law. On theoretical grounds, Büttiker [Zeitschrift für Physik B, 68, 1987] and Landauer [J Stat Phys, 53, 1988] proposed that particles submitted to a non-uniform temperature field would indeed gather where the temperature is low. They also predicted that, in the presence of a potential force, a non-uniform temperature could drive a steady current of particles, powered only by noise. Here, we present an experimental realization of these phenomena in a macroscopic system, which confirms the quantitative predictions of Büttiker.

cond-mat.stat-mech↗

arXiv2026

Thermodynamics of bouncing grains

When a horizontal plate vibrates strongly enough, it causes small particles such as sand grains to continually bounce on it and, over time, to diffuse across its surface. This phenomenon is the cause of the well-known Chladni figure, which is drawn by a higher density of grains gathering along the nodal lines of a resonating elastic plate. Using a heterogeneous, non-resonating plate, we investigate experimentally this type of diffusion. We find that, for the most part, is it comparable to classical molecular diffusion. We can define a temperature for the bouncing grains, and the system then obeys the fluctuation-dissipation theorem. We also recover Maxwell-Boltzmann statistics at equilibrium, when temperature is uniform. However, when temperature varies across the vibrating plate, the microscopic details of the grains' dynamics affect their macroscopic behavior: Fick's law, for instance, no longer applies. Instead, our experiments support a new transport relation that was recently proposed to represent diffusion in Chladni's experiment. Finally, we propose an expression for the heat flux associated to the non-equilibrium steady state predicted by this new relation, and test it against observations.

cond-mat.stat-mech↗

arXiv2026

Self-Organized Pattern Formation in Geological Soft Matter

Geological materials are often seen as the antithesis of soft; rocks are hard. However, during the formation of minerals and rocks, all the systems we shall discuss, indeed geological materials in general, pass through a stage where they are soft. This occurs either because they form at a high temperature - igneous or metamorphic rock - or because they form at a lower temperature but in the presence of water - sedimentary rock. For this reason it is useful to introduce soft-matter concepts into the geological domain. There is a universality in the diverse instances of geological patterns that may be appreciated by looking at the common aspect in their formation of having passed through a stage as soft matter.

physics.geo-ph↗

arXiv2026

Under pressure: poroelastic regulation of flow in espresso brewing

The sensory richness of coffee is widely recognised and arises from the complex chemistry and immersion in cultural practices of coffee preparation. In contrast, the physical complexity of espresso has received less attention. The multiphase reactive flow through a dissolving, elastic porous medium remains challenging to describe. Using a controlled experimental setup based on a café-grade espresso machine, we demonstrate that the interplay between elasticity and porosity governs the long-time flow rate during espresso extraction and, consequently, the concentration of solubles in the final beverage. We introduce a minimal model that captures the resulting non-linear pressure-flow relationship and propose a methodology capable of reproducing the time-dependent behaviour of the espresso brewing process. Finally, we show that dissolution dynamics play a central role in determining the temporal evolution of flow during extraction.

physics.flu-dyn↗

arXiv2026

Structural barriers to complete homogenization and wormholing in dissolving porous and fractured rocks

Dissolution in porous media and fractured rocks alters both the chemical composition of the fluid and the physical properties of the solid. Depending on system conditions, reactive flow may enlarge pores uniformly, widen pre-existing channels, or trigger instabilities that form wormholes. The resulting pattern reflects feedbacks among advection, diffusion, surface reaction, and the initial heterogeneity of the medium. Porous and fractured media can exhibit distinct characteristics -- for example, the presence of large fractures can significantly alter the network topology and overall connectivity of the system. We quantify these differences with three network models -- a regular pore network, a disordered pore network, and a discrete fracture network -- evaluated with a unified metric: the flow focusing profile. This metric effectively captures evolution of flow paths across all systems: it reveals a focusing front that propagates from the inlet in the wormholing regime, a system-wide decrease in focusing during uniform dissolution, and the progressive enlargement of pre-existing flow paths in the channeling regime. The metric shows that uniform dissolution cannot eliminate heterogeneity resulting from the network topology. This structural heterogeneity -- rather than just pore-diameter or fracture-aperture variance -- sets a fundamental limit on flow homogenization and must be accounted for when upscaling dissolution kinetics from pore or fracture scale to the reservoir level.

physics.geo-ph↗

arXiv2026

Self-assembled versus biological pattern formation in geology

Both abiotic self-organization and biological mechanisms have been put forward as the origin of a number of geological patterns. It is important to comprehend the formation mechanisms of such structures both to understand geological self-organization and in order to differentiate them from biological patterns -- fossils and bio-influenced structures -- seen in geological systems. Being able to distinguish the traces of biological activity from geological self-organization is fundamental both for understanding the origin of life on Earth and for the search for life beyond Earth.

nlin.PS↗

arXiv2024

Breakthrough-Induced Loop Formation in Evolving Transport Networks

Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However, the dynamics of their formation is usually not considered. Such structures often grow in response to the gradient of an external field. During evolution, extending branches compete for the available flux of the field, which leads to effective repulsion between them and screening of the shorter ones. Yet, in remarkably diverse processes, from unstable fluid flows to the canal system of jellyfish, loops suddenly form near the breakthrough when the longest branch reaches the boundary of the system. We provide a physical explanation for this universal behavior. Using a 1D model, we explain that the appearance of effective attractive forces results from the field drop inside the leading finger as it approaches the outlet. Furthermore, we numerically study the interactions between two fingers, including screening in the system and its disappearance near the breakthrough. Finally, we perform simulations of the temporal evolution of the fingers to show how revival and attraction to the longest finger leads to dynamic loop formation. We compare the simulations to the experiments and find that the dynamics of the shorter finger are well reproduced. Our results demonstrate that reconnection is a prevalent phenomenon in systems driven by diffusive fluxes, occurring both when the ratio of the mobility inside the growing structure to the mobility outside is low and near the breakthrough.

physics.flu-dyn↗

arXiv2024

Dislike of general opinion makes for tight elections

In modern democracies, the outcome of elections and referendums is often remarkably tight. The repetition of these divisive events are the hallmark of a split society; to the physicist, however, it is an astonishing feat for such large collections of diverse individuals. Many sociophysics models reproduce the emergence of collective human behavior with interacting agents, which respond to their environment according to simple rules, modulated by random fluctuations. A paragon of this class is the Ising model which, when interactions are strong, predicts that order can emerge from a chaotic initial state. In contrast with many elections, however, this model favors a strong majority. Here, we introduce a new element to this classical theory, which accounts for the influence of opinion polls on the electorate. This brings about a new phase in which two groups divide the opinion equally. These political camps are spatially segregated, and the sharp boundary that separates them makes the system size-dependent, even in the limit of a large electorate. Election data show that, over the last 30 years, countries with more than about a million voters often found themselves in this state, whereas elections in smaller countries yielded more consensual results. We suggest that this transition hinges on the electorate's awareness of the general opinion.

cond-mat.stat-mech↗

arXiv2023

Goldilocks fluctuations: dynamic constraints on loop formation in scale-free transport networks

Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a complete stability analysis of the dynamical behaviour of any loop formed by fluctuating flows. We find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing mapped to constant and fluctuating components. Loops require fluctuation in the relative size of the flux between nodes, not just a temporal variation in the flux at a given node. Hence, there is both a minimum and a maximum amount of fluctuation relative to the constant-flux component where loops are supported.

cond-mat.dis-nn↗

arXiv2023

A Stochastic Model of Translocation of Knotted Proteins

Knotted proteins, when forced through the pores, can get stuck if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, making translocation possible. We construct a simple energy landscape model of this process with a time-periodic potential that mimics the action of a molecular motor. We calculate the translocation time as a function of the period of the pulling force, discuss the asymptotic limits and biological relevance of the results.

cond-mat.stat-mech↗

arXiv2021

Stability of sedimenting flexible loops

We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the Euler-Bernoulli elastic forces for an inextensible fibre. Starting from an inclined circle, we simulate the dynamics using truncated Fourier modes to observe three distinct regimes of motion: absolute stability, two-, and three-dimensional dynamics, depending on therelative importance of elastic and gravitational forces. We identify the governing parameter and develop a simple semi-analytic stability criterion, which we verify numerically. In all cases, sedimenting loops converge to stable, planar shape equilibria with one free parameter related to the initial conditions and material properties of the fibre.

physics.flu-dyn↗

arXiv2020

Chirality for crooked curves

Chiral objects rotate when placed in a collimated flow or wind. We exploit this hydrodynamic intuition to construct a tensorial chirality measure for rigid filaments and curves. This tensor is trace-free, so if a curve has a right-handed twist about some axis, there is a perpendicular axis about which the twist is left-handed. Our measure places minimal requirements on the smoothness of the curve, hence it can be readily used to quantify chirality for biomolecules and polymers, polygonal and rectifiable curves, and other discrete geometrical structures.

cond-mat.soft↗

arXiv2019

Critical dynamics and tree-like spatiotemporal patterns in exciton-polaritoncondensates

We study nonresonantly pumped exciton-polariton system in the vicinity of the dynamical instability threshold. We find that the system exhibits unique and rich dynamics, which leads to spatiotemporal pattern formation. The patterns have a tree-like structure and are reminiscent of structures that appear in a variety of soft matter systems. Within the approximation of slow and fast time scales, we show that the polariton model exhibits self-replication point in analogy to reaction-diffusion systems.

cond-mat.quant-gas↗

arXiv2018

Periodic motion of sedimenting flexible knots

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic time scales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops.

cond-mat.soft↗

arXiv2016

Stabilizing effect of tip splitting on the interface motion

Pattern-forming processes, such as electrodeposition, dielectric breakdown or viscous fingering are often driven by instabilities. Accordingly, the resulting growth patterns are usually highly branched, fractal structures. However, in some of the unstable growth processes the envelope of the structure grows in a highly regular manner, with the perturbations smoothed out over the course of time. In this paper, we show that the regularity of the envelope growth can be connected to small-scale instabilities leading to the tip splitting of the fingers at the advancing front of the structure. Whenever the growth velocity becomes too large, the finger splits into two branches. In this way it can absorb an increased flux and thus damp the instability. Hence, somewhat counterintuitively, the instability at a small scale results in a stability at a larger scale. The quantitative analysis of these effects is provided by means of the Loewner equation, which one can use to reduce the problem of the interface motion to that of the evolution of the conformal mapping onto the complex plane. This allows an effective analysis of the multifingered growth in a variety of different geometries. We show how the geometry impacts the shape of the envelope of the growing pattern and compare the results with those observed in natural systems.

nlin.PS↗

arXiv2015

Steadily translating parabolic dissolution fingers

Dissolution fingers (or wormholes) are formed during the dissolution of a porous rock as a result of nonlinear feedbacks between the flow, transport and chemical reactions at pore surfaces. We analyze the shapes and growth velocities of such fingers within the thin-front approximation, in which the reaction is assumed to take place instantaneously with the reactants fully consumed at the dissolution front. We concentrate on the case when the main flow is driven by the constant pressure gradient far from the finger, and the permeability contrast between the inside and the outside of the finger is finite. Using Ivantsov ansatz and conformal transformations we find the family of steadily translating fingers characterized by a parabolic shape. We derive the reactant concentration field and the pressure field inside and outside of the fingers and show that the flow within them is uniform. The advancement velocity of the finger is shown to be inversely proportional to its radius of curvature in the small Péclet number limit and constant for large Péclet numbers.

nlin.PS↗

arXiv2014

Where do rivers grow? Path selection and growth in a harmonic field

River networks exhibit a complex ramified structure that has inspired decades of studies. Yet, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that a stream will follow local symmetry in order to maximize the water flux and that its trajectory is defined by the local field in its vicinity. We also study the growth of a real network. We use this principle to construct the history of a network and to find a growth law associated with it. The results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.

physics.geo-ph↗