arXiv subjects

Alex Hansen

Publications and source records attributed to Alex Hansen.

At least 19 recordsLinked to original sources

arXiv2026

On the Smallness of the Large Language Models Scaling Exponents

We discuss reasons why the scaling exponents of current Large Language Models (LLMs) applications are indicating an unsustainable regime in terms of energy resources. We further show that attributing the smallness of such exponents to a numerical bias due to the neglect of a non-zero value of the loss function in the limit of infinite data (``pedestal effect") does not remove the unsustainability issue. Finally, the effects of the smoothness (roughness) of the data on the scaling exponents is commented upon based on an analogy with phenomenological models of fluid turbulence.

cs.AI↗

arXiv2026

Coordination-number dependent universality in Mixed Wet Percolation

Mixed-wet percolation was introduced recently in the context of two-phase flow in porous media. In this model, the sites of the primal lattice are occupied with a certain probability $p$, and bonds are placed on the dual lattice between two adjacent occupied and unoccupied sites of the primal lattice. The occupied bonds on the dual lattice form perimeter clusters. In this paper, we investigate the scaling properties of the geometric quantities associated with the perimeter clusters of mixed-wet percolation on the dual triangular and dual honeycomb lattices. Although mixed-wet percolation on the dual triangular lattice with a higher coordination number ($z=6$) exhibits ordinary site percolation, the model on the dual honeycomb lattice with a lower coordination number ($z=3$) exhibits the properties of the hull of ordinary site percolation clusters. Such a $z$ dependent breakdown of universality in mixed-wet percolation is rare in the percolation literature. The perimeter clusters in the triangular lattice represent the boundary of the site clusters in the primal lattice, whereas the perimeters in the honeycomb lattice represent their hulls. Because of the low $z$ of the honeycomb lattice, the external and internal perimeters remain isolated. However, the combined external and internal perimeters form cluster boundaries of the site clusters that belong to the site percolation universality class.

cond-mat.stat-mech↗

arXiv2026

Flow of yield stress fluid in a percolating network

We study the flow of a Bingham yield-stress fluid in a pore network model where the throats have radii drawn from a uniform distribution. We consider the case in which a fraction of the largest radii is blocked. The fluid can flow only through the percolating cluster that exists when the fraction is above the percolation threshold. Two distinct flow regimes are identified: above the percolation threshold the flow curve can be characterized by deterministic values of the critical pressure drop, permeability, and other observables, with subleading fluctuations that we quantify. At the percolation threshold these quantities become non-self-averaging, and their scaling is governed exclusively by the critical percolation backbone, independent of the specific realization of the radii.

physics.flu-dyn↗

arXiv2026

Immiscible two-phase flow in porous media: a statistical mechanics approach

The central problem in the physics of immiscible two-phase flow in porous media is to find a proper description of the flow at scales large enough so that the medium may be regarded as a continuum: the scale-up problem. So far, the only workable approach to the multiphase flow scale-up problem has been a set of phenomenological equations that have obvious weaknesses. Attempts at going beyond this relative permeability theory have so far not led to practical applications due to exploding complexity. Edwin T. Jaynes proposed in the fifties a generalization of statistical mechanics to non-thermal systems based on the information theoretical entropy of Shannon. This approach is used to construct a description of immiscible two-phase flow in porous media at the continuum scales, which is directly related to the physics at the pore scale, and at a level of complexity that is manageable. The approach leads to a thermodynamics-like formalism at the continuum scale with all the relations between variables that "normal" thermodynamics has to offer. New emergent variables appear. Among these, the co-moving velocity stands out as a key variable with implications for ordinary thermodynamics. We present here a short review of this approach.

physics.flu-dyn↗

arXiv2026

Glassy phase transition in immiscible steady-state two-phase flow in porous media

Two-phase flow in porous media is a ubiquitous phenomenon that has been studied for well over a century. However, we still lack a successful theory that predicts flow on a macroscopic length scale (the so-called Darcy scale) on the basis of a "microscopic" model. Here we show that the characteristic features of two-phase flow on the Darcy scale can be predicted by mapping the distribution of droplets in 2-phase flow onto the distribution of spins in a spin-glass model. The success of this approach is surprising, as two-phase flow is a non-equilibrium phenomenon, whereas the properties of the spin glass are obtained using equilibrium statistical mechanics. To obtain this mapping, we follow the approach of Meshulam and Bialek (Rev. Mod. Phys. 97, 045002 (2025)) and use the Jaynes maximum entropy principle to derive the spin-glass Hamiltonian using machine learning trained on many realizations of the two-phase flow pattern in a dynamic pore network model. With this mapping, we can construct a "phase diagram" for the 2-phase flow system. We find that the critical line separating the paramagnetic phase from a spin glass phase coincides with the transition where the dependence of the rate of two-phase flow on the imposed pressure gradient changes from linear to non-linear. The glassy phase of the spin model coincides with a flow regime characterized by hysteresis and strong fluctuations over a wide range of time scales. It is tempting to identify this flow regime as a dynamic glass state.

physics.flu-dyn↗

arXiv2025

A new kind of science

We discuss whether science is in the process of being transformed from a quest for causality to a quest for correlation in light of the recent development in artificial intelligence. We observe that while a blind trust in the most seductive promises of AI is surely to be avoided, a judicious combination of computer simulation based on physical insight and the machine learning ability to explore ultra-dimensional spaces, holds potential for transformative progress in the way science is going to be pursued in the years to come.

physics.soc-ph↗

arXiv2025

Isaac Lab: A GPU-Accelerated Simulation Framework for Multi-Modal Robot Learning

We present Isaac Lab, the natural successor to Isaac Gym, which extends the paradigm of GPU-native robotics simulation into the era of large-scale multi-modal learning. Isaac Lab combines high-fidelity GPU parallel physics, photorealistic rendering, and a modular, composable architecture for designing environments and training robot policies. Beyond physics and rendering, the framework integrates actuator models, multi-frequency sensor simulation, data collection pipelines, and domain randomization tools, unifying best practices for reinforcement and imitation learning at scale within a single extensible platform. We highlight its application to a diverse set of challenges, including whole-body control, cross-embodiment mobility, contact-rich and dexterous manipulation, and the integration of human demonstrations for skill acquisition. Finally, we discuss upcoming integration with the differentiable, GPU-accelerated Newton physics engine, which promises new opportunities for scalable, data-efficient, and gradient-based approaches to robot learning. We believe Isaac Lab's combination of advanced simulation capabilities, rich sensing, and data-center scale execution will help unlock the next generation of breakthroughs in robotics research.

cs.RO↗

arXiv2025

From Interface Dynamics to Darcy Scale Description of Multiphase Flow in Porous Media

An outstanding characteristic of porous media, desired in many applications, is the large surface area, which facilitates solid-fluid interactions, making porous media an extreme case in colloid and interface science. In two-fluid systems, wetting and the balance of capillary and viscous forces control fluid displacement processes, leading to a wide range of complex flow regimes with rich spatio-temporal dynamics. Macroscopic two-phase flow is historically described through the phenomenological extensions of Darcy's law. Besides many other shortcomings and inconsistencies, it covers only connected pathway flow in the capillary-dominated flow regime in a rigorous manner while other flow regimes with moving interfaces and associated topological changes are entirely implicit. Given the lack of adequate descriptions, upscaling multiphase flow from pore to Darcy scale represents a long-standing challenge paving into the fields of thermodynamics, statistical mechanics and integral geometry. In this review, we compare novel concepts which have been largely motivated by experimental insights, enabled by significant advances in pore-scale imaging and modeling over the last decade.

physics.flu-dyn↗

arXiv2025

Pressure drop-flow rate nonlinearity in bubble trains through a capillary bundle

We investigate the effective rheology of a train of elongated bubbles of negligible viscosity flowing in capillary tubes. Building upon the classical Bretherton theory for a single bubble, we extend the analysis to a train of bubbles in a single capillary tube and finally to an array of parallel, noninteracting capillary tubes, i.e., a capillary bundle. Our goal is to characterize the nonlinear pressure drop-flow rate relation of this simplified two-phase system by incorporating the thin-film hydrodynamics at small capillary numbers. We model the structural heterogeneity of the bundle by assuming that the tube radii follow a truncated power-law distribution and examine deviations of the system from the Darcy law in terms of both its statistical properties and the parameters characterizing the bubble train (i.e., the tube slenderness ratio, the volume fraction, and the number of bubbles). The main result is that two-phase flow alters the effective rheology, leading to deviations from Darcy-type behavior across the entire parameter space investigated. Specifically, for a limited number of bubbles, the flow exhibits a smooth transition from the Bretherton regime, where the pressure drop scales with the flow rate to the power of 2/3, to weaker sublinear regimes with exponents between 2/3 and unity. Interestingly, increasing the number of bubbles or narrowing the pore-size distribution leads to only minor deviations from the Bretherton regime. The resulting pressure drop-flow rate exponents are qualitatively similar to those reported in the literature for immiscible two-phase flow in porous media, despite the inherent simplicity of the capillary bundle model.

physics.flu-dyn↗

arXiv2025

Heat and super-diffusive melting fronts in unsaturated porous media

When water is present in a medium with pore sizes in a range around 10nm the corresponding freezing point depression will cause long range broadening of a melting front. Describing the freezing-point depression by the Gibbs-Thomson equation and the pore size distribution by a power law, we derive a non-linear diffusion equation for the fraction of melted water. This equation yields super-diffusive spreading of the melting front with a diffusion exponent which is given by the spatial dimension and the exponent describing the pore size distribution. We derive this solution analytically from energy conservation in the limit where all the energy is consumed by the melting and explore the validity of this approximation numerically. Finally, we explore a geological application of the theory to the case of one-dimensional sub-surface melting fronts in granular or soil systems. These fronts, which are produced by heating of the surface, spread at a super-diffusive rate and affect the subsurface to significantly larger depths than would a system without the effects of freezing point depression.

cond-mat.soft↗

arXiv2025

A new thermodynamic function for binary mixtures: the co-molar volume

We have developed a new theory relating partial molar volumes of binary mixtures to the specific (Voronoi) volumes. A simple relation gives new insight into the physical meaning of partial molar volumes in terms of the actual volumes occupied by the molecules. Partial molar quantities are defined through the use of the Euler theorem for homogeneous functions. These properties have been in use for a long time, despite the fact that they do not give an intuitive picture of the properties they are to represent. For instance, the partial molar volume of a given component in a mixture is the change in the total volume with a change in composition, hence it represents the derivative of a volume. The molar volume is a measurable property in the laboratory, and as such a body of thermodynamics, but the derived partial molar volume is not a direct measure of the physical volume occupied by the added component. On the other hand, the physical volume can be computed using e.g. molecular dynamics simulations by Voronoi tesselation. We shall call this volume the specific volume. To bridge the partial molar volume and the specific volume, we define a single new thermodynamic variable - the co-molar volume - thus bringing the latter into thermodynamics. We demonstrate this bridge through molecular dynamics simulations. The co-molar volume is closely related to the co-moving velocity defined in immiscible two-phase flow in porous media.

physics.chem-ph↗

arXiv2025

Mixed-wet percolation on a dual square lattice

We present a percolation model that is inspired by recent works on immiscible two-phase flow in a mixed-wet porous medium made of a mixture of grains with two different wettability properties. The percolation model is constructed on a dual lattice where the sites on the primal lattice represent the grains of the porous medium, and the bonds on the dual lattice represent the pores in between the grains. The bonds on the dual lattice are occupied based on the two adjacent sites on the primal lattice, which represent the pores where the capillary forces average to zero. The spanning cluster of the bonds, therefore, represents the flow network through which the two immiscible fluids can flow without facing any capillary barrier. It turns out to be a percolation transition of the perimeters of a site percolation problem. We study the geometrical properties at the criticality of the perimeter system numerically. A scaling theory is developed for these properties, and their scaling relations with the respective density parameters are studied. We also verified their finite-size scaling relations. Though the site clusters and their perimeters look very different compared to ordinary percolation, the singular behaviour of the associated geometrical properties remains unchanged. The critical exponents are found to be those of the ordinary percolation.

cond-mat.stat-mech↗

arXiv2025

Geometric structure of parameter space in immiscible two-phase flow in porous media

In a recent paper, a continuum theory of immiscible and incompressible two-phase flow in porous media based on generalized thermodynamic principles was formulated (Transport in Porous Media, 125, 565 (2018)). In this theory, two immiscible and incompressible fluids flowing in a porous medium are treated as an effective fluid, substituting the two interacting subsystems for a single system with an effective viscosity and pressure gradient. In assuming Euler homogeneity of the total volumetric flow rate and comparing the resulting first order partial differential equation to the total volumetric flow rate in the porous medium, one can introduce of a novel velocity that relates the two pairs of velocities. This velocity, the co-moving velocity, describes the mutual co-carrying of fluids due to immiscibility effects and interactions between the fluid clusters and the porous medium itself. The theory is based upon general principles of thermodynamics, and allows for many relations and analogies to draw upon for a two-phase flow systems. The goal of this work is to provide relations between geometric concepts and the variables appearing in the thermodynamics-like theory of two-phase flow. We encounter two interpretations of the velocities of the fluids: as tangent vectors (derivations) acting on functions, or as coordinates on an affine line. The two views are closely related, with the former viewpoint being more useful in relation to the underlying geometrical structure of equilibrium thermodynamics, and the latter being more useful in concrete computations and finding examples of constitutive relations. We apply these straightforward geometric contexts to interpret the relations between the velocities, and from this obtain a general form for the co-moving velocity.

physics.flu-dyn↗

arXiv2025

Thermodynamics-Like Formalism for Immiscible and Incompressible Two-Phase Flow in Porous Media

It is possible to formulate immiscible and incompressible two-phase flow in porous media in a mathematical framework resembling thermodynamics based on the Jaynes generalization of statistical mechanics. We review this approach and discuss the meaning of the emergent variables that appear, agiture, flow derivative and flow pressure, which are conjugate to the configurational entropy, the saturation and the porosity respectively. We conjecture that the agiture, the temperature-like variable, is directly related to the pressure gradient. This has as a consequence that the configurational entropy, a measure of how the fluids are distributed within the porous media and the accompanying velocity field, and the differential mobility of the fluids are related. We also develop elements of another version of the thermodynamics-like formalism where fractional flow rather than saturation is the control variable, since this is typically the natural control variable in experiments.

physics.flu-dyn↗

arXiv2024

Linearity of the co-moving velocity

The co-moving velocity is a new variable in the description of immiscible two-phase flow in porous media. It is the saturation-weighted average over the derivatives of the seepage velocities of the two immiscible fluids with respect to saturation. Based on analysis of relative permeability data and computational modeling, it has been proposed that the co-moving velocity is linear when plotted against the derivative of the average seepage velocity with respect to the saturation, the flow derivative. I show here that it is enough to demand that the co-moving velocity is characterized by an additive parameter in addition to the flow derivative to be linear. This has profound consequences for relative permeability theory as it leads to a differential equation relating the two relative permeabilities describing the flow. I present this equation together with two solutions.

physics.flu-dyn↗

arXiv2024

A geometrical interpretation of critical exponents

We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function might be sensitive to this change in dimensionality. We discuss how this phenomenon is observable in growth processes and near critical points for systems in equilibrium. In particular, we determine the fractal dimension $d_f$ for the Ising model and validate it via computer simulations for two dimensions.

cond-mat.stat-mech↗

arXiv2023

Influence of the imposed flow rate boundary condition on the flow of Bingham fluid in porous media

The flow of yield stress fluids in porous media presents interesting complexity due to the interplay between the non-linear rheology and the heterogeneity of the medium. A remarkable consequence is that the number of flow paths increases with the applied pressure difference and is responsible for a non-linear Darcy law. Previous studies have focused on the protocol where the pressure difference is imposed. Here we consider instead the case of imposed flow rate, $Q$. In contrast to Newtonian fluids, the two types of boundary conditions have an important influence on the flow field. Using a two-dimensional pore network model we observe a boundary layer of merging flow paths of size $\ell(Q) \sim Q^{-\mu/\delta}$ where $\mu = 0.42 \pm 0.02$ and $\delta \simeq 0.63 \pm 0.05$. Beyond this layer the density of the flow paths is homogeneous and grows as $Q^\mu$. Using a mapping to the directed polymer model we identify $\delta$ with the roughness exponent of the polymer. We also characterize the statistics of non-flowing surfaces in terms of avalanches pulled at one end.

physics.flu-dyn↗

arXiv2023

Disorder-induced non-linear growth of viscously-unstable immiscible two-phase flow fingers in porous media

The immiscible displacement of a fluid by another one inside a porous medium produces different types of patterns depending on the capillary number Ca and viscosity ratio M. At high Ca, viscous fingers resulting from the viscous instability between fluid-fluid interfaces are believed to exhibit the same Laplacian growth behavior as viscously-unstable fingers observed in Hele-Shaw cells by Saffman and Taylor [1], or as diffusion limited aggregates (DLA) [2]. I.e., the interface velocity depends linearly on the local gradient of the physical field that drives the growth process (for two-phase flow, the pressure field). However, steady-state two-phase flow in porous media is known to exhibit a regime for which the flow rate depends as a non-linear power law on the global pressure drop, due to the disorder in the capillary barriers at pore throats. A similar nonlinear growth regime was also evidenced experimentally for viscously-unstable drainage in two-dimensional porous media 20 years ago [3]. Here we revisit this flow regime using dynamic pore-network modeling, and explore the non-linearity in the growth properties. We characterize the previously-unstudied dependencies of the statistical finger width and nonlinear growth law's exponent on Ca, and discuss quantitatively, based on theoretical arguments, how disorder in the capillary barriers controls the growth process' non-linearity, and why the flow regime crosses over to Laplacian growth at sufficiently high Ca. In addition, the statistical properties of the fingering patterns are compared to those of Saffman-Taylor fingers, DLA growth patterns, and the results from the aforementioned previous experimental study.

physics.flu-dyn↗