Found 2183 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

A percolation model for the emergence of the Bitcoin Lightning Network

The emergence of a connected component is studied numerically and analytically as a function of the parameters, and the

**phase****transition**separating regions in the phase space where the Lightning Network is sustainable or not is elucidated. Expand abstract. The Lightning Network is a so-called second-layer technology built on top of the Bitcoin blockchain to provide "off-chain" fast payment channels between users, which means that not all transactions are settled and stored on the main blockchain. In this paper, we model the emergence of the Lightning Network as a (bond) percolation process and we explore how the distributional properties of the volume and size of transactions per user may impact its feasibility. The agents are all able to reciprocally transfer Bitcoins using the main blockchain and also - if economically convenient - to open a channel on the Lightning Network and transact "off chain". We base our approach on fitness-dependent network models: as in real life, a Lightning channel is opened with a probability that depends on the "fitness" of the concurring nodes, which in turn depends on wealth and volume of transactions. The emergence of a connected component is studied numerically and analytically as a function of the parameters, and the

**phase****transition**separating regions in the**phase**space where the Lightning Network is sustainable or not is elucidated. We characterize the**phase**diagram determining the minimal volume of transactions that would make the Lightning Network sustainable for a given level of fees or, alternatively, the maximal cost the Lightning ecosystem may impose for a given average volume of transactions. The model includes parameters that could be in principle estimated from publicly available data once the evolution of the Lighting Network will have reached a stationary operable state, and is fairly robust against different choices of the distributions of parameters and fitness kernels.41 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Dynamical **phase** coexistence in the Fredrickson-Andersen model

We analyse a first-order dynamical

**phase****transition**that takes place in the Fredrickson--Andersen (FA) model. Expand abstract. We analyse a first-order dynamical

**phase****transition**that takes place in the Fredrickson--Andersen (FA) model. We construct a two-dimensional spin system whose thermodynamic properties reproduce the dynamical large deviations of the FA model and we analyse this system numerically, comparing our results with finite-size scaling theory. This allows us to rationalise recent results for the FA model, including the exponential divergence of its susceptibility at**phase**coexistence. We also discuss a simple interfacial model that reproduces quantitatively the behaviour of the FA model at coexistence.43 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in 2D XY arrays is addressed. Expand abstract.

The problem of magnetic

**transitions**between the low-temperature (macrospin ordered)**phases**in 2D XY arrays is addressed. The system is modeled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole-dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking $T_b$ temperature is lower than that ($T_\text{af}$) of the AF**transition**. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean field approximation. With the technique of a generalized Ott-Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the antiferromagnetic order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first order**phase****transitions**from AF to ferromagnetic state; the**phase**diagrams displaying stable and metastable regions of the system are presented.43 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Building continuous time crystals from rare events

Symmetry-breaking dynamical

**phase****transitions**(DPTs) abound in the fluctuations of nonequilibrium systems. Expand abstract. Symmetry-breaking dynamical

**phase****transitions**(DPTs) abound in the fluctuations of nonequilibrium systems. Here we show that the spectral features of a particular class of DPTs exhibit the fingerprints of the recently discovered time-crystal**phase**of matter. Using Doob's transform as a tool, we provide a mechanism to build time-crystal generators from the rare event statistics of some driven diffusive systems. An analysis of the Doob's smart field in terms of the order parameter of the**transition**then leads to the time-crystal exclusion process (tcEP), a stochastic lattice gas subject to an external packing field which presents a clear-cut steady-state**phase****transition**to a time-crystalline**phase**which breaks continuous time-translation symmetry and displays rigidity and long-range spatio-temporal order. A hydrodynamic analysis of the tcEP**transition**uncovers striking similarities, but also key differences, with the Kuramoto synchronization**transition**. Possible experimental realizations of the tcEP are also discussed.43 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

Synchronization and spatial patterns in forced swarmalators

However, the correlation between phase and spatial location decreases with the intensity of the force, going to zero in what appears to be a second order

**phase****transition**. Expand abstract. Swarlamators are particles capable of synchronize and swarm. Here we study the effects produced by an external periodic stimulus over a system of swarmalators that move in two dimensions. When the particles are fixed and interact with equal strength (Kuramoto oscillators) their

**phases**tend to synchronize and lock to the external stimulus if its intensity is sufficiently large. Here we show that in a system of swarmalators the force also shifts the**phases**and angular velocities leading to synchronization with the external frequency. However, the correlation between**phase**and spatial location decreases with the intensity of the force, going to zero in what appears to be a second order**phase****transition**. In the regime of zero correlation the particles form a static symmetric circular distribution, following a simple model of aggregation. Interestingly, for intermediate values of the force intensity, a different pattern emerges, with the particles splitting in two clusters centered at opposite sides of the stimulus' location, breaking the radial symmetry. The two-cluster pattern is stable and active, with the clusters slowly rotating around the source while exchanging particles.43 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

Sonic horizons and causality in the **phase** **transition** dynamics

A system gradually driven through a symmetry-breaking phase transition is subject to the Kibble-Zurek mechanism (KZM). Expand abstract.

A system gradually driven through a symmetry-breaking

**phase****transition**is subject to the Kibble-Zurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes non-adiabatic near the critical point. In the simplest approximation, that stage can be regarded as "impulse" where the state of the system remains unchanged. It leads to the correct KZM scaling laws. However, such "freeze-out" might suggest that the coherence length of the nascent order parameter remains unchanged as the critical region is traversed. By contrast, the original causality-based discussion emphasized the role of the {\it sonic horizon}: domains of the broken symmetry**phase**can expand with a velocity limited by the speed of the relevant sound. This effect was demonstrated in the quantum Ising chain where the dynamical exponent $z=1$ and quasiparticles excited by the**transition**have a fixed speed of sound. To elucidate the role of the sonic horizon, in this paper we study two systems with $z>1$ where the speed of sound is no longer fixed, and the fastest excited quasiparticles set the size of the sonic horizon. Their effective speed decays with the increasing**transition**time. In the extreme case, the dynamical exponent $z$ can diverge such as in the Griffiths region of the random Ising chain where localization of excited quasiparticles freezes the growth of the correlation range when the critical region is traversed. Of particular interest is an example with $z43 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

**Phase** **Transition** of Degeneracy in Minor-Closed Families

Given an infinite family ${\mathcal G}$ of graphs and a monotone property ${\mathcal P}$, an (upper) threshold for ${\mathcal G}$ and ${\mathcal P}$ is a "fastest growing" function $p: \mathbb{N} \to [0,1]$ such that $\lim_{n \to \infty} \Pr(G_n(p(n)) \in {\mathcal P})= 1$ for any sequence $(G_n)_{n \in \mathbb{N}}$ over ${\mathcal G}$ with $\lim_{n... Expand abstract.

Given an infinite family ${\mathcal G}$ of graphs and a monotone property ${\mathcal P}$, an (upper) threshold for ${\mathcal G}$ and ${\mathcal P}$ is a "fastest growing" function $p: \mathbb{N} \to [0,1]$ such that $\lim_{n \to \infty} \Pr(G_n(p(n)) \in {\mathcal P})= 1$ for any sequence $(G_n)_{n \in \mathbb{N}}$ over ${\mathcal G}$ with $\lim_{n \to \infty}\lvert V(G_n) \rvert = \infty$, where $G_n(p(n))$ is the random subgraph of $G_n$ such that each edge remains independently with probability $p(n)$. In this paper we study the upper threshold for the family of $H$-minor free graphs and for the graph property of being $(r-1)$-degenerate, which is one fundamental graph property that has been shown widely applicable to various problems in graph theory. Even a constant factor approximation for the upper threshold for all pairs $(r,H)$ is expected to be very difficult by its close connection to a major open question in extremal graph theory. We determine asymptotically the thresholds (up to a constant factor) for being $(r-1)$-degenerate for a large class of pairs $(r,H)$, including all graphs $H$ of minimum degree at least $r$ and all graphs $H$ with no vertex-cover of size at most $r$, and provide lower bounds for the rest of the pairs of $(r,H)$. The results generalize to arbitrary proper minor-closed families and the properties of being $r$-colorable, being $r$-choosable, or containing an $r$-regular subgraph, respectively.

44 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

Attraction, Dynamics, and **Phase** **Transitions** in Fire Ant Tower-Building

Next, we explore the trade-offs between attraction and random motion to characterize the dynamics and

**phase****transition**of the tower building process. Expand abstract. Many insect species, and even some vertebrates, assemble their bodies to form multi-functional materials that combine sensing, computation, and actuation. The tower-building behavior of red imported fire ants, Solenopsis invicta, presents a key example of this phenomenon of collective construction. While biological studies of collective construction focus on behavioral assays to measure the dynamics of formation and studies of swarm robotics focus on developing hardware that can assemble and interact, algorithms for designing such collective aggregations have been mostly overlooked. We address this gap by formulating an agent-based model for collective tower-building with a set of behavioral rules that incorporate local sensing of neighboring agents. We find that an attractive force makes tower building possible. Next, we explore the trade-offs between attraction and random motion to characterize the dynamics and

**phase****transition**of the tower building process. Lastly, we provide an optimization tool that may be used to design towers of specific shapes, mechanical loads, and dynamical properties such as mechanical stability and mobility of the center of mass.45 days ago

8/10 relevant

bioRxiv

8/10 relevant

bioRxiv

Constraining strongly supercooled **phase** **transitions** by overproduction of
black holes

We study the formation of black holes from bubble collisions in cosmological first order

**phase****transitions**. Expand abstract. We study the formation of black holes from bubble collisions in cosmological first order

**phase****transitions**. We show that if false vacuum bubbles are formed in these collisions, new very strong constraints can be put on models due to overproduction of black holes.46 days ago

8/10 relevant

arXiv

8/10 relevant

arXiv

Fluid models with **phase** **transition** for kinetic equations in swarming

We analyze the profile of equilibria for general potentials identifying a family of potentials leading to

**phase****transitions**. Expand abstract. We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case, the equilibria depend on the density and the orientation of the mean velocity, whereas the mean speed is not anymore a free parameter and a

**phase****transition**occurs in the homogeneous kinetic equation. We analyze the profile of equilibria for general potentials identifying a family of potentials leading to**phase****transitions**. Finally, we derive the fluid equations when the interaction frequency becomes very large.48 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv