arXiv subjects
Publications and source records attributed to Hyunseok Lee.
In this paper, we introduce the degenerate gamma random variables which are connected with the degenerate gamma functions and the degenerate exponential functions, and deduce the expectation and variance of those random variables.
The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae-Stirling numbers of the first and second kinds. For this purpose, we first introduce Jindalrae-Stirling numbers of the first and second kinds as extensions of the notions of the degenerate Stirling numbers of the first and second kinds, and deduce several relations involving those special numbers. Then we introduce Jindalrae and Gaenari numbers and polynomials and obtain some explicit expressions and identities associated with those numbers and polynomials. In addition, we interpret our results by using umbral calculus.
In this paper, we introduce degenertae generalized hypergeometric functions and study degenerate hypergeometric numbers of order p. These numbers involving of lambda-binomial coefficients and lambda-falling sequence, and can be represented by means of the degenerate generalized hypergeometric functions. we will derive some explicit expressions and combinatorial identities for those numbers. We also consider several related special numbers like lambda-hypergeometric numbers of order p and Apostol type lambda-hypergeometric numbers of order p, of which the latter reduce in a limiting case to the generalized p-th order Franel numbers.
In this paper, we study the degenerate version of the new type Euler polynomials, namely degenerate cosine-Euler polynomials and sime-Euler polynomials and also corresponding ones for Bernoulli polynomials, namely degenerate cosine Bernoulli polynomials and degenerate sine-Bernoulli polynomials by considering the degenerate Euler polynomials of complex variable and the degenerate Bernoulli polynomials of complex variable.
Recent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights into manifestations of many-body chaos. So far the chaotic behavior has been obtained through explicit calculations in specific models. In this paper we propose a unified description of the exponential growth and ballistic butterfly spreading of OTOCs across different systems using a newly formulated "quantum hydrodynamics," which is valid at finite $\hbar$ and to all orders in derivatives. The scrambling of a generic few-body operator in a chaotic system is described as building up a "hydrodynamic cloud," and the exponential growth of the cloud arises from a shift symmetry of the hydrodynamic action. The shift symmetry also shields correlation functions of the energy density and flux, and time ordered correlation functions of generic operators from exponential growth, while leads to chaotic behavior in OTOCs. The theory also predicts an interesting phenomenon of the skipping of a pole at special values of complex frequency and momentum in two-point functions of energy density and flux. This pole-skipping phenomenon may be considered as a "smoking gun" for the hydrodynamic origin of the chaotic mode. We also discuss the possibility that such a hydrodynamic description could be a hallmark of maximally chaotic systems.
We study the dynamics of large, charged dust grains in turbulent giant molecular clouds (GMCs). Massive dust grains behave as aerodynamic particles in primarily neutral dense gas, and thus are able to produce dramatic small-scale fluctuations in the dust-to-gas ratio. Hopkins & Lee (2016) directly simulated the dynamics of neutral dust grains in super-sonic MHD turbulence, typical of GMCs, and showed that the dust-to-gas fluctuations can exceed factor ~1000 on small scales, with important implications for star formation, stellar abundances, and dust behavior and growth. However, even in primarily neutral gas in GMCs, dust grains are negatively charged and Lorentz forces are non-negligible. Therefore, we extend our previous study by including the effects of Lorentz forces on charged grains (in addition to drag). For small charged grains (sizes <0.1 micron), Lorentz forces suppress dust-to-gas ratio fluctuations, while for large grains (sizes >1 micron), Lorentz forces have essentially no effect, trends that are well explained with a simple theory of dust magnetization. In some special intermediate cases, Lorentz forces can enhance dust-gas segregation. Regardless, for the physically expected scaling of dust charge with grain size, we find the most important effects depend on grain size (via the drag equation) with Lorentz forces/charge as a second-order correction. We show that the dynamics we consider are determined by three dimensionless numbers in the limit of weak background magnetic fields: the turbulent Mach number, a dust drag parameter (proportional to grain size) and a dust Lorentz parameter (proportional to grain charge); these allow us to generalize our simulations to a wide range of conditions.
We study the behavior of large dust grains in turbulent molecular clouds (MCs). In primarily neutral regions, dust grains move as aerodynamic particles, not necessarily with the gas. We therefore directly simulate, for the first time, the behavior of aerodynamic grains in highly supersonic, magnetohydrodynamic turbulence typical of MCs. We show that, under these conditions, grains with sizes a >0.01 micron exhibit dramatic (exceeding factor ~1000) fluctuations in the local dust-to-gas ratio (implying large small-scale variations in abundances, dust cooling rates, and dynamics). The dust can form highly filamentary structures (which would be observed in both dust emission and extinction), which can be much thinner than the characteristic width of gas filaments. Sometimes, the dust and gas filaments are not even in the same location. The 'clumping factor' of the dust (critical for dust growth/coagulation/shattering) can reach ~100, for grains in the ideal size range. The dust clustering is maximized around scales ~0.2pc*(a/micron)*(100 cm^-3/n_gas), and is 'averaged out' on larger scales. However, because the density varies widely in supersonic turbulence, the dynamic range of scales (and interesting grain sizes) for these fluctuations is much broader than in the subsonic case. Our results are applicable to MCs of essentially all sizes and densities, but we note how Lorentz forces and other physics (neglected here) may change them in some regimes. We discuss the potentially dramatic consequences for star formation, dust growth and destruction, and dust-based observations of MCs.