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PICOSEC Micromegas (MM) is a precise timing gaseous detector based on a Cherenkov radiator coupled with a semi-transparent photocathode and an MM amplifying structure. The detector conceprt was successfully demonstrated through a single-channel prototype, achieving sub-25 ps time resolution with Minimum Ionizing Particles (MIPs). A series of studies followed, aimed at developing robust, large-area, and scalable detectors with high time resolution, complemented by specialized fast-response readout electronics. This work presents recent advancements towards large-area resistive PICOSEC MM, including 10 $\times$ 10 $\text{cm}^2$ area prototypes and a 20 $\times$ 20 $\text{cm}^2$ prototype, which features the jointing of four photocathodes. The time resolution of these detector prototypes was tested during the test beam, achieved a timing performance of around 25 ps for individual pads in MIPs. Meanwhile, customized electronics have been developed dedicated to the high-precision time measurement of the large-area PICOSEC MM. The performance of the entire system was evaluated during the test beam, demonstrating its capability for large-area integration. These advancements highlight the potential of PICOSEC MM to meet the stringent requirements of future particle physics experiments.

This note initiates the study of the Fatou\,--\,Julia sets of a complex harmonic mapping. Along with some fundamental properties of the Fatou and the Julia sets, we observe some contrasting behaviour of these sets as those with in case of a holomorphic function. The existence of harmonic mapping with a wandering domain is also shown.

In this paper, we extend a result of Schwick concerning normality and sharing values in one complex variable for families of holomorphic curves taking values in $\mathbb{P}^n$. We consider wandering moving hyperplanes (i.e., depending on the respective holomorphic curve in the family under consideration), and establish a sufficient condition of normality concerning shared hyperplanes.

A harmonic mapping $f=h+\overline{g}$ in $\mathbb{D}$ is $\varphi$-normal if $f^{\#}(z)=\mathcal{O}(|\varphi(z)|), \text{ as } |z|\to 1^-,$ where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish several sufficient conditions for harmonic mappings to be $\varphi$-normal. We also extend the five-point theorem of Lappan for $\varphi$-normal harmonic mappings., Comment: 10 pages

The dip-coating geometry, where a solid plate is withdrawn from or plunged into a liquid pool, offers a prototypical example of wetting flows involving contact-line motion. Such flows are commonly studied using the lubrication approximation approach which is intrinsically limited to small interface slopes and thus small contact angles. Flows for arbitrary contact angles, however, can be studied using a generalized lubrication theory that builds upon viscous corner flow solutions. Here we derive this generalized lubrication theory for viscoelastic liquids that exhibit normal stress effects and are modelled using the second-order fluid model. We apply our theory to advancing and receding contact lines in the dip-coating geometry, highlighting the influence of viscoelastic normal stresses for contact line motion at arbitrary contact angle., Comment: 27 pages, 9 figures

The complexity of interactions between the crystal-field and unusual non-collinear spin arrangement in non-trivial magnets demands novel tools to unravel the mystery underneath. In this work, we study such interaction dynamics of crystal-field-excitations (CFE) and low-energy magnetic excitations in orthochromite TmCrO3 with controls of temperature and magnetic field using high-resolution magneto-terahertz (THz) time-domain spectroscopy. The THz energy spectrum spanning 0.5-10 meV possesses a low-frequency spin-excitation (magnon) mode and a multitude of CFE modes at 10 K, all of which uniquely embody a range of phenomena. For the magnon mode, a temperature dependence of peak frequency is induced by magnetic interactions between Tm and Cr subsystems. While a change from blue- to red-shift of peak frequency of this mode marks the magnetization reversal transition, the spin reorientation temperature and change of magnetic anisotropy are depicted by different features of field- and temperature-dependent peak frequency dynamics. The modes corresponding to CFE are robust and laden with a multitude of sub-modes which are attributes of non-trivial interactions across different transitions. These modes are suppressed only upon substitution of Tb3+ at Tm3+ site, which suggests a dominant role of single-ion anisotropy in controlling entire THz excitations spectra. Overall, this remarkable range of phenomena seen through the unique lens of all-optical THz tools provides deeper insights into the origin of magnetic phases in systems with complex interactions between rare-earth and transition metal ions and provides a multitude of a novel combination of closely spaced modes for emerging hybrid spin-wave computation., Comment: The main copy of the manuscript includes 21 pages with 7 figures

In this paper, we discuss the capable and isoclinic properties of the tensor square in the context of multiplicative Lie algebras. We also developed the concept of isoclinic extensions and proved several results for multiplicative Lie algebras. Consequently, we demonstrate that covers of a multiplicative Lie algebra are mutually isoclinic.

The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on the measurable transformation $T$ and the complex-valued measurable function $u$ defined on measure space $(X, \mathcal{A}, \mu)$ that cause the weighted composition operators on Lorentz space $L(p, q)$, $1 < p \leq \infty, 1 \leq q \leq \infty$ to have finite or infinite ascent (descent). We also give a number of examples in support of our findings., Comment: 18 pages and no figure

Conversion of charge to orbital angular momentum through the orbital Hall effect (OHE) holds transformative potential for the development of orbital-based electronics, however, it is challenging to directly observe the electrically generated orbital accumulation. Here, we detect the OHE by directly quantifying the orbital accumulation along the edges of a titanium thin film using a scanning transmission electron microscope. We measure the Ti L-edge using electron energy-loss spectroscopy with nanometer resolution and find a sizable orbital accumulation at the sample's outer perimeters, consistent with all signatures expected for the OHE, and determine an orbital diffusion length $\ell_o \approx 7.3$ nm. Our data points to a surprising dependence of the orbital diffusion length on the nano-structural morphology., Comment: 13 pages, 3 figures

In this paper, we discuss the inducibility problem for automorphisms of multiplicative Lie algebra extensions and show that obstruction to the inducibility of pairs lies in the second cohomology group of multiplicative Lie algebras. We also establish the Wells type exact sequence for multiplicative Lie algebras, which relates automorphism groups with the second cohomology group of multiplicative Lie algebras., Comment: Also lies in category math.KT

In this article, we construct a $16$-dimensional sedenion-like associative algebra, which is an even subalgebra of $2^5$-dimensional Clifford algebra $Cl_{5,0}$. We define the norm on sedenion-like algebra and show that its sixteen-dimensional elements preserves the norm relation $\lVert ST \rVert=\lVert S \rVert \lVert T \rVert$ under the condition $S_rS_d^\dagger + S_r^\dagger S_d=0$, where $S_r,~S_d$ denote the real and dual part of an octonion-like number $S$ respectively and $S^\dagger$ is the transpose of $S$. The elements of this sedenion-like algebra can be written as dual octonion like numbers called split bioctonion-like algebra and $S S^\dagger$ is commutative [i.e. $S S^\dagger=S^\dagger S $ and $(S S^\dagger) T=T(S S^\dagger )$], for any two octonion-like/sedenion-like numbers $S$ and $T$. We define the operations coproduct $\bigtriangleup$, counit $\epsilon $ and antipode $S$ on octonion-like/sedenion-like algebra to construct the Hopf algebra structure on it. We also show that $8$-dimensional octonion-like associative seminormed division algebra is a $\mathbb{Z}_2^4/2$-graded quasialgebra and $16$ dimensional sedenion-like algebra is a $\mathbb{Z}_2^5/2$-graded quasialgebra., Comment: 15 pages

Let $R$ be a commutative ring with identity and $S \subseteq R$ be a multiplicative set. An ideal $Q$ of $R$ (disjoint from $S$) is said to be $S$-primary if there exists an $s\in S$ such that for all $x,y\in R$ with $xy\in Q$, we have $sx\in Q$ or $sy\in rad(Q)$. Also, we say that an ideal of $R$ is $S$-primary decomposable or has an $S$-primary decomposition if it can be written as finite intersection of $S$-primary ideals. In this paper, first we provide an example of $S$-Noetherian ring in which an ideal does not have a primary decomposition. Then our main aim of this paper is to establish the existence and uniqueness of $S$-primary decomposition in $S$-Noetherian rings as an extension of a historical theorem of Lasker-Noether., Comment: 10 pages

The classical Cox-Voinov theory of contact line motion provides a relation between the macroscopically observable contact angle, and the microscopic wetting angle as a function of contact line velocity. Here we investigate how viscoelasticity, specifically the normal stress effect, modifies wetting dynamics. Using the thin film equation for the second-order fluid, it is found that the normal stress effect is dominant at small scales. We show that the effect can be incorporated in the Cox-Voinov theory through an apparent microscopic angle, which differs from the true microscopic angle. The theory is applied to the classical problems of drop spreading and dip-coating, which shows how normal stress facilitates (inhibits) the motion of advancing (receding) contact lines. For rapid advancing motion, the apparent microscopic angle can tend to zero in which case the dynamics is described by a new regime that was already anticipated in Boudaoud (2007).

Let $G$ be the quantum $GL_n$ over a field of characteristic $p\neq 0$. In this paper we define the ring of twisted tilting modules of $G$. We give generators and relations for the ring of twisted tilting modules of quantum $GL_2(k)$. We also show that this is a reduced ring, Comment: 12 pages

Thin-film flows of viscoelastic fluids are encountered in various industrial and biological settings. The understanding of thin viscous film flows in Newtonian fluids is very well developed, which for a large part is due to the so-called thin-film equation. This equation, a single partial differential equation describing the height of the film, is a significant simplification of the Stokes equation effected by the lubrication approximation which exploits the thinness of the film. There is no such established equation for viscoelastic fluid flows. Here we derive the thin-film equation for a second-order fluid, and use it to study the classical Landau-Levich dip-coating problem. We show how viscoelasticity of the fluid affects the thickness of the deposited film, and address the discrepancy on the topic in literature.

The breakup and coalescence of drops are elementary topological transitions in interfacial flows. The breakup of a drop changes dramatically when polymers are added to the fluid. With the strong elongation of the polymers during the process, long threads connecting the two droplets appear prior to their eventual pinch-off. Here, we demonstrate how elasticity affects drop coalescence, the complement of the much studied drop pinch-off. We reveal the emergence of an elastic singularity, characterised by a diverging interface curvature at the point of coalescence. Intriguingly, while the polymers dictate the \emph{spatial} features of coalescence, they hardly affect the \emph{temporal} evolution of the bridge. These results are explained using a novel viscoelastic similarity analysis and are relevant for drops created in biofluids, coating sprays and inkjet printing., Comment: 5 figures

Drop coalescence occurs through the rapid growth of a liquid bridge that connects the two drops. At early times after contact, the bridge dynamics is typically self-similar, with details depending on the geometry and viscosity of the liquid. In this paper we analyse the coalescence of two-dimensional viscous drops that float on a quiescent deep pool; such drops are called liquid lenses. The analysis is based on the thin-sheet equations, which were recently shown to accurately capture experiments of liquid lens coalescence. It is found that the bridge dynamics follows a self-similar solution at leading order, but, depending on the large-scale boundary conditions on the drop, significant corrections may arise to this solution. This dynamics is studied in detail using numerical simulations and through matched asymptotics. We show that the liquid lens coalescence can involve a global translation of the drops, a feature that is confirmed experimentally.

In this article, we consider the tensor product of two simple modules of quanum $GL_2$ over a field of characteristic $p\neq 0$. We show that it can be expressed as a direct sum of indecomposable twisted tilting modules. This problem has been studied by Henke and Doty [1] for $SL_2$ and also later on for $SL_3$ by S R Doty, Chris Bowman and Stuart Martin, ([7, 8])., Comment: 8 Pages

Long and slender liquid filaments are produced during inkjet printing, which can subsequently either retract to form a single droplet, or break up to form a primary droplet and one or more satellite droplets. These satellite droplets are undesirable since they degrade the quality and reproducibility of the print. Existing strategies for the suppression of satellite droplet formation include, among others, adding viscoelasticity to the ink. In the present work, we aim to improve the understanding of the role of viscoelasticity in suppressing satellite droplets in inkjet printing. We demonstrate that very dilute viscoelastic aqueous solutions (concentrations $\sim$ 0.003\% wt. polyethylene oxide (PEO), corresponding to nozzle Deborah number $De_{n}$ $\sim$ 3) can suppress satellite droplet formation. Furthermore, we show that, for a given driving condition, upper and lower bounds of polymer concentration exist, within which satellite droplets are suppressed. Satellite droplets are formed at concentrations below the lower bound, while jetting ceases for concentrations above the upper bound (for fixed driving conditions). Moreover, we observe that, with concentrations in between the two bounds, the filaments retract at velocities larger than the corresponding Taylor-Culick velocity for the Newtonian case. We show that this enhanced retraction velocity can be attributed to the elastic tension due to polymer stretching, which builds up during the initial jetting phase. These results shed some light on the complex interplay between inertia, capillarity, and viscoelasticity for retracting liquid filaments, which is important for the stability and quality of inkjet printing of polymer solutions., Comment: 22 pages, 7 figures

In this paper, we establish various sufficient conditions for a family of holomorphic mappings on a domain $D\subseteq\mathbb{C}$ into $\mathbb{P}^n$ to be normal. Our results are improvements to the Montel-Carath\'eodory Theorem for a family of $\mathbb{P}^n$-valued holomorphic curves.

A basic feature of liquid drops is that they can merge upon contact to form a larger drop. In spite of its importance to various applications, drop coalescence on pre-wetted substrates has received little attention. Here, we experimentally and theoretically reveal the dynamics of drop coalescence on a thick layer of a low-viscosity liquid. It is shown that these so-called "liquid lenses" merge by the self-similar vertical growth of a bridge connecting the two lenses. Using a slender analysis, we derive similarity solutions corresponding to the viscous and inertial limits. Excellent agreement is found with the experiments without any adjustable parameters, capturing both the spatial and temporal structure of the flow during coalescence. Finally, we consider the crossover between the two regimes and show that all data of different lens viscosities collapse on a single curve capturing the full range of the coalescence dynamics.

In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's normality test in a certain sense.

Schwick, in [6], states that let $\mathcal{F}$ be a family of meromorphic functions on a domain $D$ and if for each $f\in\mathcal{F}$, $(f^n)^{(k)}\neq 1$, for $z\in D$, where $n, k$ are positive integers such that $n\geq k+3$, then $\mathcal{F}$ is a normal family in $D$. In this paper, we investigate the opposite view that if for each $f\in\mathcal{F}$, $(f^n)^{(k)}(z)-\psi(z)$ has zeros in $D$, where $\psi(z)$ is a holomorphic function in $D$, then what can be said about the normality of the family $\mathcal{F}$?

Microswimmers in nature often experience spatial gradients of viscosity. In this work we develop theoretical results for the dynamics of active particles, biological or otherwise, swimming through viscosity gradients. We model the active particles using the squirmer model, and show how viscosity gradients lead to viscotaxis for squirmers, and how the effects of viscosity gradients depend on the swimming gait of the microswimmers. We also show how such gradients in viscosity can be used to control active particles and suggest a mechanism to sort them based on their swimming style., Comment: 5 pages, 2 figures

Many microorganisms swim in fluids with complex rheological properties. Although much is now understood about motion of these swimmers in Newtonian fluids, the understanding is still developing in non-Newtonian fluids --- this understanding is crucial for various biomimetic and biomedical applications. Here we study a common model for microswimmers, the squirmer model, in two common viscoelastic fluid models, the Giesekus fluid model and fluids of differential type (grade three), at zero Reynolds number. Through this article we address a recent commentary that discussed suitable values of parameters in these model and pointed at higher order viscoelastic effects on the squirming motion.

In this paper, we present various sufficient conditions for a family of meromorphic mappings on a domain $D\subset \mathbb{C}^m$ into $\mathbb{P}^n$ to be meromorphically normal. Meromorphic normality is a notion of sequential compactness in the meromorphic category introduced by Fujimoto. We give a general condition for meromorphic normality that is influenced by Fujimoto's work. The approach to proving this result allows us to establish meromorphic analogues of several recent results on normal families of $\mathbb{P}^n$-valued holomorphic mappings. We also establish a meromorphic version of the Montel-Carath\'eodory theorem., Comment: 13 pages

We examine swimmers comprising of two rigid spheres which oscillate periodically along their axis of symmetry, considering both when the oscillation is in phase and anti-phase, and study the effects of fluid viscoelasticity on their net motion. These swimmers both display reciprocal motion in a Newtonian fluid and hence no net swimming is achieved over one cycle. Conversely, we find that when the two spheres are of different sizes, the effect of viscoelasticity acts to propel the swimmers forward in the direction of the smaller sphere. Finally, we compare the motion of rigid spheres oscillating in viscoelastic fluids with elastic spheres in Newtonian fluids where we find similar results., Comment: 3 figures

Semantic similarity based retrieval is playing an increasingly important role in many IR systems such as modern web search, question-answering, similar document retrieval etc. Improvements in retrieval of semantically similar content are very significant to applications like Quora, Stack Overflow, Siri etc. We propose a novel unsupervised model for semantic similarity based content retrieval, where we construct semantic flow graphs for each query, and introduce the concept of "soft seeding" in graph based semi-supervised learning (SSL) to convert this into an unsupervised model. We demonstrate the effectiveness of our model on an equivalent question retrieval problem on the Stack Exchange QA dataset, where our unsupervised approach significantly outperforms the state-of-the-art unsupervised models, and produces comparable results to the best supervised models. Our research provides a method to tackle semantic similarity based retrieval without any training data, and allows seamless extension to different domain QA communities, as well as to other semantic equivalence tasks., Comment: Published in Proceedings of the 2017 ACM Conference on Information and Knowledge Management (CIKM '17)

Particle motion in non-Newtonian fluids can be markedly different than in Newtonian fluids. Here we look at the change in dynamics for a few problems involving rigid spherical particles in shear-thinning fluids in the absence of inertia. We give analytical formulas for sedimenting spheres, obtained by means of the reciprocal theorem, and demonstrate quantitively differences in comparison to a Newtonian fluid. We also calculate the first correction to the suspension viscosity, the Einstein viscosity, for a dilute suspension of spheres in a weakly shear-thinning fluid., Comment: 12 pages, 1 figure

In this work, we numerically investigate the dynamics of a self-propelling autophoretic Janus particle in a weakly viscoelastic fluid. The self-propulsion is achieved by an asymmetry in the properties of the surface of the Janus particle that drives a surface slip velocity and bulk flow. Here we investigate the effect of viscoelasticity on this advection-diffusion problem over a range of P\'eclet and Damk\"ohler numbers. Particles are found to swim faster, or slower, in viscoelastic fluids, and we show how reaction and diffusion rates affect the viscoelastic stresses that lead to changes in propulsion., Comment: 10 pages, 9 figures

Corporations spend millions of dollars on developing creative image-based promotional content to advertise to their user-base on platforms like Twitter. Our paper is an initial study, where we propose a novel method to evaluate and improve outreach of promotional images from corporations on Twitter, based purely on their describable aesthetic attributes. Existing works in aesthetic based image analysis exclusively focus on the attributes of digital photographs, and are not applicable to advertisements due to the influences of inherent content and context based biases on outreach. Our paper identifies broad categories of biases affecting such images, describes a method for normalization to eliminate effects of those biases and score images based on their outreach, and examines the effects of certain handcrafted describable aesthetic features on image outreach. Optimizing on the describable aesthetic features resulting from this research is a simple method for corporations to complement their existing marketing strategy to gain significant improvement in user engagement on social media for promotional images., Comment: Accepted to SIGIR 2017

In this work, we study active particles with prescribed surface velocities in non-Newtonian fluids. We employ the reciprocal theorem to obtain the velocity of an active spherical particle with an arbitrary axisymmetric slip-velocity in an otherwise quiescent second-order fluid. We then determine how the motion of a diffusiophoretic Janus particle is affected by complex fluid rheology, namely viscoelasticity and shear-thinning viscosity, compared to a Newtonian fluid, assuming a fixed slip-velocity. We find that a Janus particle may go faster or slower in a viscoelastic fluid, but is always slower in a shear-thinning fluid as compared to a Newtonian fluid., Comment: 9 pages, 3 figures