arXiv subjects

Henk Mulder

Publications and source records attributed to Henk Mulder.

6 recordsLinked to original sources

arXiv2026

Analytic patch trees: branch interface inheritance and fractal dimension fields

The extension of the analytic fractal curve trees of (2601.17490} to analytic surface patch trees reveals a new geometric structure: branch points are replaced by interface curves that transmit the full analytical state of parent patches to their children. These interfaces prove to be central in determining the topology of the surface patch trees, including for the conditions for self-similarity of the interfaces, the patches and thus the trees. We establish the analytic conditions for the integrability and well-posedness of the surface patch trees and introduce further restrictions for conformality. We demonstrate that patch trees have a natural foliation that slices the trees into one dimensional curve trees, each of which has their own Hausdorff dimension, jointly creating a smooth dimension field. We extend the two dimensional surface model to arbitrary dimensions $n$ where $n-1$ interface manifolds transport the $n$ field state of the parent patches to their child branches. We note that the balance or discrepancy between patch field dimension and the dimensions in which the branches may evolve, determine the analytical regime from essentially geometrical to essentially operational.

cs.CG↗

arXiv2026

Smooth Fractal Trees: Analytic Generators and Discrete Equivalence

We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this setting, geometric curves are obtained as projections of generator trajectories, and branching is implemented as a primitive operation through exact inheritance of generator state. At every finite depth, the resulting structure is a finite union of analytic curve segments that is smooth across branch events. Two structural results relate this generator-driven construction to classical discrete models of tree-based fractals. First, a combinatorial universality theorem shows that any discrete tree specification, including those arising from iterated function systems and L-systems, can be compiled into an analytic generator tree whose induced discrete scaffold is isomorphic at every finite depth. Second, under standard contractive assumptions, a canopy set equivalence theorem establishes that the accumulation set of analytic branch endpoints coincides with the attractor of the corresponding discrete construction. These results separate local geometric regularity from global fractal complexity, showing that fractality is determined by recursive branching and scaling rather than by local non-smoothness. The framework provides a smooth representation of tree-based fractals that preserves both their finite combinatorial structure and their asymptotic limit geometry.

math.DS↗

arXiv2022

The Apertif Radio Transient System (ARTS): Design, Commissioning, Data Release, and Detection of the first 5 Fast Radio Bursts

Fast Radio Bursts must be powered by uniquely energetic emission mechanisms. This requirement has eliminated a number of possible source types, but several remain. Identifying the physical nature of Fast Radio Burst (FRB) emitters arguably requires good localisation of more detections, and broadband studies enabled by real-time alerting. We here present the Apertif Radio Transient System (ARTS), a supercomputing radio-telescope instrument that performs real-time FRB detection and localisation on the Westerbork Synthesis Radio Telescope (WSRT) interferometer. It reaches coherent-addition sensitivity over the entire field of the view of the primary dish beam. After commissioning results verified the system performed as planned, we initiated the Apertif FRB survey (ALERT). Over the first 5 weeks we observed at design sensitivity in 2019, we detected 5 new FRBs, and interferometrically localised each of these to 0.4--10 sq. arcmin. All detections are broad band and very narrow, of order 1 ms duration, and unscattered. Dispersion measures are generally high. Only through the very high time and frequency resolution of ARTS are these hard-to-find FRBs detected, producing an unbiased view of the intrinsic population properties. Most localisation regions are small enough to rule out the presence of associated persistent radio sources. Three FRBs cut through the halos of M31 and M33. We demonstrate that Apertif can localise one-off FRBs with an accuracy that maps magneto-ionic material along well-defined lines of sight. The rate of 1 every ~7 days next ensures a considerable number of new sources are detected for such study. The combination of detection rate and localisation accuracy exemplified by the 5 first ARTS FRBs thus marks a new phase in which a growing number of bursts can be used to probe our Universe.

astro-ph.HE↗

arXiv2020

Chromatic periodic activity down to 120 MHz in a Fast Radio Burst

Fast radio bursts (FRBs) are extragalactic astrophysical transients whose brightness requires emitters that are highly energetic, yet compact enough to produce the short, millisecond-duration bursts. FRBs have thus far been detected between 300 MHz and 8 GHz, but lower-frequency emission has remained elusive. A subset of FRBs is known to repeat, and one of those sources, FRB 20180916B, does so with a 16.3 day activity period. Using simultaneous Apertif and LOFAR data, we show that FRB 20180916B emits down to 120 MHz, and that its activity window is both narrower and earlier at higher frequencies. Binary wind interaction models predict a narrower periodic activity window at lower frequencies, which is the opposite of our observations. Our detections establish that low-frequency FRB emission can escape the local medium. For bursts of the same fluence, FRB 20180916B is more active below 200 MHz than at 1.4 GHz. Combining our results with previous upper-limits on the all-sky FRB rate at 150 MHz, we find that there are 3-450 FRBs/sky/day above 50 Jy ms at 90% confidence. We are able to rule out the scenario in which companion winds cause FRB periodicity. We also demonstrate that some FRBs live in clean environments that do not absorb or scatter low-frequency radiation.

astro-ph.HE↗

arXiv2017

Definition of geometric space around analytic fractal trees using derivative coordinate funtions

The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space around these fractal trees. We present the canonical and degenerate form of this fractal space and extend the fractal geometrical space to R3 specifically and Rn by a recurrence relation. We also discuss the usage of such fractal geometry.

cs.CG↗

arXiv2015

Derivative coordinates for analytic tree fractals and fractal engineering

We introduce an alternative coordinate system based on derivative polar and spherical coordinate functions and construct a root-to-canopy analytic formulation for tree fractals. We develop smooth tree fractals and demonstrate the equivalence of their canopies with iterative straight lined tree fractals. We then consider implementation and application of the analytic formulation from a computational perspective. Finally we formulate the basis for concatenation and composition of fractal trees as a basis for fractal engineering of which we provide some examples.

cs.CG↗