arXiv subjects

Brian Chan

Publications and source records attributed to Brian Chan.

4 recordsLinked to original sources

arXiv2023

Event Shape Selection Method in Search of the Chiral Magnetic Effect in Heavy-ion Collisions

The search for the chiral magnetic effect (CME) in heavy-ion collisions has been impeded by the significant background arising from the anisotropic particle emission pattern, particularly elliptic flow. To alleviate this background, the event shape selection (ESS) technique categorizes collision events according to their shapes and projects the CME observables to a class of events with minimal flow. In this study, we explore two event shape variables to classify events and two elliptic flow variables to regulate the background. Each type of variable can be calculated from either single particles or particle pairs, resulting in four combinations of event shape and elliptic flow variables. By employing a toy model and the realistic event generator, event-by-event anomalous-viscous fluid dynamics (EBE-AVFD), we discover that the elliptic flow of resonances exhibits correlations with both the background and the potential CME signal, making the resonance flow unsuitable for background control. Through the EBE-AVFD simulations of Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV with various input scenarios, we ascertain that the optimal ESS strategy for background control entails utilizing the single-particle elliptic flow in conjunction with the event shape variable based on particle pairs.

nucl-th↗

arXiv2021

A preliminary result for generalized intersecting families

Intersecting families and blocking sets feature prominently in extremal combinatorics. We examine the following generalization of an intersecting family investigated by Hajnal, Rothschild, and others. If $s \geq 1$, $k \geq 2$, and $u \geq 1$ are integers, then say that an $s$-uniform family $\mathcal{F}$ is $(k,u)$-intersecting if for all $A_1, A_2, \cdots, A_k \in \mathcal{F}$, $|A_i \cap A_j| \geq u$ for some $1 \leq i < j \leq k$. In this note, we investigate the following parameter. If $s$, $k$, $u$, $\ell$ are integers satisfying $s \geq 1$, $k \geq 2$, $1 \leq u \leq s$, and $2 \leq \ell < k$, then let $N^{(u)}_{k,\ell}(s)$ denote the smallest integer $r$, if it exists, such that any $(k,u)$-intersecting $s$-uniform family is the union of at most $r$ families that are $(\ell,u)$-intersecting. Using a Sunflower Lemma type argument, we prove that $N^{(u)}_{k,\ell}(s)$ always exists and that the following inequality always holds: $$N^{(u)}_{k,\ell}(s) \; \leq \; \bigg{\lceil} \dfrac{ k - 1 }{\ell - 1} \cdot {s \choose u} \bigg{\rceil}$$

math.CO↗

arXiv2019

A generalization of balanced tableaux and marriage problems with unique solutions

We consider families of finite sets that we call shellable and that have been characterized by Chang and by Hirst and Hughes as being the families of sets that admit unique solutions to Hall's marriage problem. In this paper, we introduce a natural generalization of Edelman and Greene's balanced tableaux that involves families of sets that satisfy Hall's marriage Condition and certain words in $[n]^m$, then prove that shellable families can be characterized by a strong existence condition relating to this generalization. As a consequence of this characterization, we show that the average number of such generalized tableaux is given by a generalization of the hook-length formula.

math.CO↗

arXiv2015

A Free-Form Prediction for the Reappearance of Supernova Refsdal in the Hubble Frontier Fields Cluster MACSJ1149.5+2223

The massive cluster MACSJ1149.5+2223(z=0.544) displays five very large lensed images of a well resolved spiral galaxy at $z_{\rm spect}=1.491$. It is within one of these images that the first example of a multiply-lensed supernova has been detected recently as part of the Grism Lens-Amplified Survey from Space. The depth of this data also reveals many HII regions within the lensed spiral galaxy which we identify between the five counter-images. Here we expand the capability of our free-form method to incorporate these HII regions locally, with other reliable lensed galaxies added for a global solution. This improved accuracy allows us to estimate when the Refsdal supernova will appear within the other lensed images of the spiral galaxy to an accuracy of $\sim$ 7\%. We predict this supernova will reappear in one of the counter-images (RA=11:49:36.025, DEC=+22:23:48.11, J2000) and on November 1$^{st}$ 2015 (with an estimated error of $\pm$ 25 days) it will be at the same phase as it was when it was originally discovered, offering a unique opportunity to study the early phases of this supernova and to examine the consistency of the mass model and the cosmological model that have an impact on the time delay prediction.

astro-ph.CO↗