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Zilong He

Publications and source records attributed to Zilong He.

28 records · Page 2Linked to original sources
arXiv2021

Evaluation of laser diffraction-based particle size measurements using digital inline holography

The measurements of size distribution of small particles (e.g. dusts, droplets, bubbles, etc.) are critical for a broad range of applications in environmental science, public health, industrial manufacturing, etc. Laser diffraction (LD), a widely used method for such applications depends on model-based inversion with underlying assumptions on particle properties. Furthermore, the presence of sampling biases such as velocity differentials are often overlooked by the simple ex-situ calibrations, which introduces as an additional source of error. In contrast, digital inline holography (DIH), a single camera coherent imaging technique, can both measure particle size distributions without the need for a model-based inversion and can directly provide information on the shape characteristics of the particles. In this study, we evaluate the performance of an LD system in characterizing polydisperse droplets produced in a flat fan spray using in-situ DIH based imaging as a reference. The systematic differences in the two techniques are examined. A droplet-trajectory-based correction for the LD-inferred size distributions is proposed to compensate for the observed differences. We validate the correction using NIST standard polydisperse particles undergoing differential settling, and then apply the correction to polydisperse spray droplet measurements. The correction improves agreement between LD and DIH size distributions for droplets over two orders of magnitude, but with LD still underestimating the fraction of droplets at sizes above ~1 mm. This underestimation is possibly linked to the complex oscillatory and rotational motion of droplets which cannot be faithfully captured by measurement or modelled by the correction algorithm without additional information.

physics.flu-dyn↗
arXiv2021

Spatially-Resolved Characterization of Oil-in-Water Emulsion Sprays

This study concerns the effects of pressure, spatial location, and application of oil emulsions on the resulting droplet size, eccentricity, as well as velocity distributions, all of which are crucial information in determining the dispersion dynamics of the droplets during the spray applications. Experiments were conducted with the abovementioned droplets information measured using digital inline holography (DIH). Results show that the volumetric droplet size distributions (VDSD) span widely from sub-200 um to over 2 mm in size. The application of an oil-in-water emulsion results largely in the suppression of smaller droplets, while the VDSD is relatively insensitive to increasing the oil volume fraction beyond a critical level. DIH additionally enables the determination of size-dependent droplet eccentricity and velocity measurements. Interestingly, the application of oil-in-water emulsion generally decreases the eccentricity, more significantly at the center than at the edge of the spray fan. We attribute this decrease to the increase in lamella sheet thickness and thus decrease in characteristic shrinkage rates, consistent with the observation using high-speed shadowgraphs. In all instances, oil-in-water emulsion droplets have higher velocities than equivalent sized water droplets. We attribute this to the earlier action of the spray breakup process in the oil-in-water emulsion, reduced surface energy generation during a breakup (larger droplets), and reduce energy dissipation during breakup with oil-in-water emulsions, leading to increased translational energy after the breakup process. Therefore, it appears that oil-in-water emulsion application simultaneously suppresses small droplet formation and increases droplet velocity, and hence spray penetration in agricultural application.

physics.flu-dyn↗
arXiv2020

Sign changes of Fourier coefficients of cusp forms of half-integral weight over split and inert primes in quadratic number fields

In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class $t\mathbb{Z}^2$, we investigate the sign changes in the $tp^2$-th coefficient as $p$ runs through the split or inert primes over the ring of integers in a quadratic extension of the rationals. We show that sign changes occur in both sets of primes when there exists a prime dividing the discriminant of the field which does not divide the level of the cusp form and find an explicit condition that determines whether sign changes occur when every prime dividing the discriminant also divides the level.

math.NT↗
arXiv2020

Droplet evaporation residue indicating SARS-COV-2 survivability on surfaces

SARS-CoV-2 survives and remains viable on surfaces for several days under different environments as reported in recent studies. However, it is unclear how the viruses survive for such a long time and why their survivability varies across different surfaces. To address these questions, we conduct systematic experiments investigating the evaporation of droplets produced by a nebulizer and human-exhaled gas on surfaces. We found that these droplets do not disappear with evaporation, but instead shrink to a size of a few micrometers (referred to as residues), persist for more than 24 hours, and are highly durable against changes of environmental conditions. The characteristics of these residues change significantly across surface types. Specifically, surfaces with high thermal conductivity like copper do not leave any resolvable residues, while stainless steel, plastic, and glass surfaces form residues from a varying fraction of all deposited droplets at 40% relative humidity. Lowering humidity level suppresses the formation of residues while increasing humidity level enhances it. Our results suggest that these microscale residues can potentially insulate the virus against environmental changes, allowing them to survive inhospitable environments and remain infectious for prolonged durations after deposition. Our findings can also be extended to other viruses transmitted through respiratory droplets (e.g., SARS-CoV, flu viruses, etc.), and can thus lead to practical guidelines for disinfecting surfaces and other prevention measures (e.g., humidity control) for limiting viral transmission.

physics.med-ph↗
arXiv2020

Inequalities for inert primes and their applications

For any given non-square integer $ D\equiv 0,1 \pmod{4} $, we prove Euclid's type inequalities for the sequence $ \{q_{i}\} $ of all primes satisfying the Kronecker symbol $ (D/q_{i})=-1 $, $ i=1,2,\cdots, $ and give a new criterion on a ternary quadratic form to be irregular as an application, which simplifies Dickson and Jones's argument in the classification of regular ternary quadratic forms to some extent.

math.NT↗
arXiv2020

Regular ternary polygonal forms

Inspired by Dickson's classification of regular ternary quadratic forms, we prove that there are no primitive regular $m$-gonal forms when $m$ is sufficiently large. In order to do so, we construct sequences of primes that are inert in a certain quadratic field and show that they satisfy a certain inequality bounding the next prime by the product of the previous primes, a question of independent interest.

math.NT↗
arXiv2014

On the exponent set of nonnegative primitive tensors

In this paper, we present a necessary and sufficient condition for a nonnegative tensor to be a primitive one, show that the exponent set of nonnegative primitive tensors with order $m(\ge n)$ and dimension $n$ is $\{k| 1\le k\le (n-1)^2+1\}. $

math.CO↗
arXiv2013

A conjecture on the primitive degree of Tensors

In this paper, we prove: Let A be a nonnegative primitive tensor with order m and dimension n. Then its primitive degree R(A)\leq (n-1)^2+1, and the upper bound is sharp. This confirms a conjecture of Shao [7].

math.CO↗