arXiv subjects

Tristram J. Alexander

Publications and source records attributed to Tristram J. Alexander.

At least 19 recordsLinked to original sources

arXiv2025

Meso-scale structures in signed networks

Meso-scale structures in signed networks have been studied under the limiting assumption of the validity of social balance theory, which predicts positive connections within groups and negative connections between groups. Here, we propose and apply a methodology that overcomes this limitation and is able to find and characterize also the different possible unbalanced structures in signed networks. Applying our methodology to 24 empirical networks, from social-political, financial, and biological domains, we find that unbalanced meso-scale structures are prevalent in real-world networks, including cases with substantial balance at the micro-scale of triangles. In particular, we find that assortativity often prevails regardless of the interaction sign and that core-periphery structures are typical in online social networks. Our findings highlight the complexity of meso-scale relational structures, the importance of using computational methods that are a priori agnostic to specific patterns, and the importance of independently evaluating micro- and meso-scale predictions of social balance theory.

cs.SI↗

arXiv2024

Human-interpretable clustering of short-text using large language models

Clustering short text is a difficult problem, due to the low word co-occurrence between short text documents. This work shows that large language models (LLMs) can overcome the limitations of traditional clustering approaches by generating embeddings that capture the semantic nuances of short text. In this study clusters are found in the embedding space using Gaussian Mixture Modelling (GMM). The resulting clusters are found to be more distinctive and more human-interpretable than clusters produced using the popular methods of doc2vec and Latent Dirichlet Allocation (LDA). The success of the clustering approach is quantified using human reviewers and through the use of a generative LLM. The generative LLM shows good agreement with the human reviewers, and is suggested as a means to bridge the `validation gap' which often exists between cluster production and cluster interpretation. The comparison between LLM-coding and human-coding reveals intrinsic biases in each, challenging the conventional reliance on human coding as the definitive standard for cluster validation.

cs.CL↗

arXiv2024

Observation of fractional evolution in nonlinear optics

The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally in systems with nonlocal temporal or spatial interactions. However, systematic experiments have been rare due to challenges associated with the physical implementation. Here we report the observation and full characterization of a family of temporal optical solitons that are governed by a nonlinear wave equation with a fractional Laplacian. This equation has solutions with unique properties such as non-exponential tails and a very small time-bandwidth product.

physics.optics↗

arXiv2024

A generative model for community types in directed networks

Large complex networks are often organized into groups or communities. In this paper, we introduce and investigate a generative model of network evolution that reproduces all four pairwise community types that exist in directed networks: assortative, core-periphery, disassortative, and the newly introduced source-basin type. We fix the number of nodes and the community membership of each node, allowing node connectivity to change through rewiring mechanisms that depend on the community membership of the involved nodes. We determine the dependence of the community relationship on the model parameters using a mean-field solution. It reveals that a difference in the swap probabilities of the two communities is a necessary condition to obtain a core-periphery relationship and that a difference in the average in-degree of the communities is a necessary condition for a source-basin relationship. More generally, our analysis reveals multiple possible scenarios for the transition between the different structure types, and sheds light on the mechanisms underlying the observation of the different types of communities in network data.

cs.SI↗

arXiv2022

Solitons in media with mixed, high-order dispersion and cubic nonlinearity

Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present analytic expressions for families of bright soliton solutions at arbitrary dispersion orders and practical methods to obtain the associated dispersion relations. These results provide a framework for considering higher order dispersion solitons and show the potential for further investigation of solitons in higher order dispersion systems.

nlin.PS↗

arXiv2021

Dark solitons under higher order dispersion

We show theoretically that dark solitons can exist in the presence of pure quartic dispersion, and also in the presence of both quadratic and quartic dispersive effects, displaying a much greater variety of possible solutions and dynamics than for pure quadratic dispersion. The interplay of the two dispersion orders may lead to oscillatory non-vanishing tails, which enables the possibility of bound, potentially stable, multi-soliton states. Dark soliton-like states which connect to low amplitude oscillations are also shown to be possible. Dynamical evolution results corroborate the stability picture obtained, and possible avenues for dark soliton generation are explored.

nlin.PS↗

arXiv2021

Self-stabilization of light sails by damped internal degrees of freedom

We consider the motion of a light sail that is accelerated by a powerful laser beam. We derive the equations of motion for two proof-of-concept sail designs with damped internal degrees of freedom. Using linear stability analysis we show that perturbations of the sail movement in all lateral degrees of freedom can be damped passively. This analysis also shows complicated behaviour akin to that associated with exceptional points in PT-symmetric systems in optics and quantum mechanics. The excess heat that is produced by the damping mechanism is likely to be substantially smaller than the expected heating due to the partial absorption of the incident laser beam by the sail.

physics.class-ph↗

arXiv2020

The interaction of Kerr nonlinearity with even-orders of dispersion: an infinite hierarchy of solitons

Temporal solitons are optical pulses that arise from the balance of negative group-velocity dispersion and self-phase modulation. For decades only quadratic dispersion was considered, with higher order dispersion thought of as a nuisance. Following the recent reporting of pure-quartic solitons, we here provide experimental and numerical evidence for an infinite hierarchy of solitons that balance self-phase modulation and arbitrary negative pure, even-order dispersion. Specifically, we experimentally demonstrate the existence of solitons with pure-sextic ($β_6$), -octic ($β_8$) and -decic ($β_{10}$) dispersion, limited only by the performance of our components, and show numerical evidence for the existence of solitons involving pure $16^{\rm th}$ order dispersion. Phase-resolved temporal and spectral characterization reveals that these pulses, exhibit increasing spectral flatness with dispersion order. The measured energy-width scaling laws suggest dramatic advantages for ultrashort pulses. These results broaden the fundamental understanding of solitons and present new avenues to engineer ultrafast pulses in nonlinear optics and its applications.

physics.optics↗

arXiv2020

Polychromatic soliton molecules

Soliton molecules, bound states composed of interacting fundamental solitons, exhibit remarkable resemblance with chemical compounds and phenomena in quantum mechanics. Whereas optical molecules composed of two or more temporally locked solitons have been observed in a variety of platforms, soliton molecules formed by bound solitons at different frequencies have only recently been theoretically proposed. Here, we report the observation of polychromatic soliton molecules within a mode-locked laser cavity, achieving the desired dispersion by implementing a spectral pulse-shaper. This system supports two or more coincident solitons with different frequencies, but common group velocities. Our results open new directions of exploration in nonlinear dynamics within systems with complex dispersion and offer a convenient platform for optical analogies to mutual trapping and spectral tunneling in quantum mechanics.

physics.optics↗

arXiv2020

Scaling laws and dynamics of hashtags on Twitter

In this paper we quantify the statistical properties and dynamics of the frequency of hashtag use on Twitter. Hashtags are special words used in social media to attract attention and to organize content. Looking at the collection of all hashtags used in a period of time, we identify the scaling laws underpinning the hashtag frequency distribution (Zipf's law), the number of unique hashtags as a function of sample size (Heaps' law), and the fluctuations around expected values (Taylor's law). While these scaling laws appear to be universal, in the sense that similar exponents are observed irrespective of when the sample is gathered, the volume and nature of the hashtags depends strongly on time, with the appearance of bursts at the minute scale, fat-tailed noise, and long-range correlations. We quantify this dynamics by computing the Jensen-Shannon divergence between hashtag distributions obtained $τ$ times apart and we find that the speed of change decays roughly as $1/τ$. Our findings are based on the analysis of 3.5 billion hashtags used between 2015 and 2016.

physics.soc-ph↗

arXiv2009

Truncated-Bloch-wave solitons in optical lattices

We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized states which differ by the number of intensity peaks. These families do not bifurcate from the band edge, and their power curves exhibit double branches. Linear stability analysis demonstrates that in deep lattice potentials the states corresponding to the lower branches are stable, whereas those corresponding to the upper branches are unstable, independently of the number of peaks.

physics.atom-ph↗

arXiv2009

Excited spin states and phase separation in spinor Bose-Einstein condensates

We analyze the structure of spin-1 Bose-Einstein condensates in the presence of a homogenous magnetic field. We classify the homogenous stationary states and study their existence, bifurcations, and energy spectra. We reveal that the phase separation can occur in the ground state of polar condensates, while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogenous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a $^{23}$Na condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.

cond-mat.quant-gas↗

arXiv2008

Stable higher-charge discrete vortices in hexagonal optical lattices

We show that double-charge discrete optical vortices may be completely stable in hexagonal photonic lattices where single-charge vortices always exhibit dynamical instabilities. Even when unstable the double-charge vortices typically have a much weaker instability than the single-charge vortices, and thus their breakup occurs at longer propagation distances.

physics.optics↗

arXiv2008

Spin-Domain Formation in Antiferromagnetic Condensates

Antiferromagnetic condensates are generally believed not to display modulational instability and subsequent spin-domain formation. Here we demonstrate that in he presence of a homogeneous magnetic field antiferromagnetic spin-1 Bose-Einstein condensates can undergo spatial modulational instability followed by the subsequent generation of spin domains. Employing numerical simulations for realistic conditions, we show how this novel effect can be observed in sodium condensates confined in an optical trap. Finally, we link this instability and spin-domain formation with stationary modes of the condensate.

cond-mat.other↗

arXiv2008

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realises a flashing ratchet for matter-wave solitons. The average velocity of a soliton and the directed soliton current induced by the ratchet depend on the number of atoms in the soliton. We employ this feature to study collisions between ratchet-driven solitons and find that soliton transport can be induced through their interactions. In the regime when matter-wave solitons are narrow compared to the lattice period the ratchet dynamics is well described by the effective Hamiltonian theory.

cond-mat.other↗

arXiv2006

Multi-component gap solitons in spinor Bose-Einstein condensates

We model the nonlinear behaviour of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or anti-ferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multi-component structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA), frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetisation, i.e. intrinsic precession of the local spin. Finally, we demonstrate that non-stationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.

cond-mat.other↗

arXiv2006

Melting of Discrete Vortices via Quantum Fluctuations

We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, {\em quantum discrete vortices} (or {\em q-vortices}), and study their "melting" under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on q-vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.

cond-mat.other↗

arXiv2005

Three-dimensional matter-wave vortices in optical lattices

We predict the existence of spatially localized nontrivial vortex states of a Bose-Einstein condensate with repulsive atomic interaction confined by a three-dimensional optical lattice. Such vortex-like structures include planar vortices, their co- and counter-rotating bound states, and distinctly three-dimensional non-planar vortex states. We demonstrate numerically that many of these vortex structures are remarkably robust, and therefore can be generated and observed in experiment.

cond-mat.other↗