Modelling and control of the flame temperature distribution using probability density function shaping

This paper presents three control algorithms for the output probability density function (PDF) control of the 2D and 3D flame distribution systems. For the 2D flame distribution systems, control methods for both static and dynamic flame systems are presented, where at first the temperature distribution of the gas jet flames along the cross-section is approximated. Then the flame energy distribution (FED) is obtained as the output to be controlled by using a B-spline expansion technique. The general static output PDF control algorithm is used in the 2D static flame system, where the dynamic system consists of a static temperature model of gas jet flames and a second-order actuator. This leads to a second-order closed-loop system, where a singular state space model is used to describe the dynamics with the weights of the B-spline functions as the state variables. Finally, a predictive control algorithm is designed for such an output PDF system. For the 3D flame distribution systems, all the temperature values of the flames are firstly mapped into one temperature plane, and the shape of the temperature distribution on this plane can then be controlled by the 3D flame control method proposed in this paper. Three cases are studied for the proposed control methods and desired simulation results have been obtained

Toward precision mass measurements of neutron-rich nuclei relevant to rr-process nucleosynthesis

The open question of where, when, and how the heavy elements beyond iron enrich our Universe has triggered a new era in nuclear physics studies.\ Of all the relevant nuclear physics inputs, the mass of very neutron-rich nuclides is a key quantity for revealing the origin of heavy elements beyond iron.\ Although the precise determination of this property is a great challenge, enormous progress has been made in recent decades, and it has contributed significantly to both nuclear structure and astrophysical nucleosynthesis studies.\ In this review, we first survey our present knowledge of the nuclear mass surface, emphasizing the importance of nuclear mass precision in $r$-process calculations.\ We then discuss recent progress in various methods of nuclear mass measurement with a few selected examples.\ For each method, we focus on recent breakthroughs and discuss possible ways of improving the weighing of $r$-process nuclides.Comment: 10 figures, review articles in Frontiers of Physic

Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at $1$, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an affirmative answer to a conjecture of Melham.Comment: 15page

Binomial coefficients, Catalan numbers and Lucas quotients

Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^2-4m}{p^a}\right)+\left(\frac{m^2-4m}{p^{a-1}}\right)u_{p-(\frac{m^2-4m}{p})}\pmod{p^2},$$ where $(-)$ is the Jacobi symbol, and $\{u_n\}_{n\geqslant0}$ is the Lucas sequence given by $u_0=0$, $u_1=1$ and $u_{n+1}=(m-2)u_n-u_{n-1}$ for $n=1,2,3,\ldots$. As an application, we determine $\sum_{0<k<p^a,\, k\equiv r\pmod{p-1}}C_k$ modulo $p^2$ for any integer $r$, where $C_k$ denotes the Catalan number $\binom{2k}k/(k+1)$. We also pose some related conjectures.Comment: 24 pages. Correct few typo

Freeform Bioprinting of Liver Encapsulated in Alginate Hydrogels Tissue Constructs for Pharmacokinetic Study

An in vitro model that can be realistically and inexpensively used to predict human response to various drug administration and toxic chemical exposure is needed. By fabricating a microscale 3D physiological tissue construct consisting of an array of channels and tissue-embedded chambers, one can selectively develop various biomimicking mammalian tissues for a number of pharmaceutical applications, for example, experimental pharmaceutical screening for drug efficacy and toxicity along with apprehending the disposition and metabolic profile of a candidate drug. This paper addresses issues relating to the development and implementation of a bioprinting process for freeform fabrication of a 3D cell-encapsulated hydrogel-based tissue construct, the direct integration onto a microfluidic device for pharmacokinetic study, and the underlying engineering science for the fabrication of a 3D microscale tissue chamber as well as its application in pharmacokinetic study. To this end, a prototype 3D microfluidic tissue chamber embedded with liver cells encapsulated within a hydrogel matrix construct is bioprinted as a physiological in vitro model for pharmacokinetic study. The developed fabrication processes are further validated and parameters optimized by assessing cell viability and liver cell phenotype, in which metabolic and synthetic liver functions are quantitated.Mechanical Engineerin