Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying the case of a rod confined isotropically into a disk, we show that the emergence of the complexity is associated with a well defined underlying statistical measure that determines the energy distribution of sub-elements,``branches'', of the rod. This result suggests that branches act as the ``microscopic'' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system

Spark ignition internal combustion engine efficiency improvement - a variable compression ratio option

Pressure to reduce energy consumption is increasing. The problem of vehicle fuel consumption and emissions is approached by exploring various vehicle propulsion options, assessing their net eff�ectiveness on a energy conversion basis and on a usability (consumer appeal) basis. Life Cycle Assessment (LCA) of various options indicates that internal combustion engine powered vehicles compare favourably because of low production cost in spite of only achieving modest energy conversion efficiency in operation. Spark ignition (SI) homogeneous charge engines have dominated as passenger vehicle power plants, and are likely to maintain their prevalence for passenger vehicle propulsion into the future, but efficiency improvements are required and achievable. Throttling losses are a signifi�cant contributor to reduced efficiency at low load for SI engines which is the load range most employed in standard driving behaviour. An Induction Air Motor (IAM) was conceived, designed, simulated and prototyped to evaluate the potential to recover some of the work the engine does to reduce its intake air pressure for low load operation. The prototyped IAM produced work which potentially could contribute to the engine output while reducing the intake pressure resulting in improved efficiency. However, further eff�ort is required to reduce the friction in the IAM and optimise the work produced by the IAM. An alternative strategy for efficiency improvement involves high Compression Ratio (CR) in conjunction with a reduced compression stroke volume achieved by Late Valve Closing (LVC). Such an arrangement of the Atkinson cycle is shown by simulation to produce improved brake efficiency in SI engines. In this cofin�guration, the maximum power produced by the engine is considerably lower than the maximum power that is achieved by the same displacement for a full compression stroke. To achieve both the improved efficiency at low load using the Atkinson confi�guration and the power achievable from a full induction stroke, the engine requires Variable Compression Ratio (VCR). Assessment of VCR concepts from literature and patents identifi�ed that the complexity of continuously variable compression ratio designs prevented their development to production-ready con�figurations. A simulation of fuel consumption over a standard driving cycle showed that a two-position VCR arrangement produces the same bene�t as a continuously variable CR for physically achievable piston-rod-crank cofin�gurations. Experiments with supporting simulations were performed for a previously patented two-position VCR device, an eccentric link in the big-end of the connecting rod. This work concludes that the eccentric link is not a viable VCR mechanism. An alternative VCR device involving a hydraulic connecting rod was prompted by further experiments and simulations which identifi�ed the behaviour of oil when compressed at high rates in a hydraulic cylinder impacted by a falling mass. The oil impact work suggested that oil chambers of cross-sectional area that could be arranged in a conventional connecting rod could readily support the loads experienced by the rod in a conventionally con�figured engine, so the design and prototyping of a hydraulic connecting rod proceeded. Experiments and simulation confi�rmed that a relatively easily manufactured hydraulic connection rod can be successfully operated in an engine, achieving controllable two-position VCR. Further development of the hydraulic connecting rod control device and improved production techniques are recommended for this new two-position hydraulic VCR device

Resource-on-demand schemes in 802.11 WLANs with non-zero start-up times

Increasing the density of access points is one of the most effective mechanisms to cope with the growing traffic demand in wireless networks. To prevent energy wastage at low loads, a resource-on-demand (RoD) scheme is required to opportunistically (de)activate access points as network traffic varies. While previous publications have analytically modeled these schemes in the past, they have assumed that resources are immediately available when activated, an assumption that leads to inaccurate results and might result in inappropriate configurations of the RoD scheme. In this paper, we analyze a general RoD scenario with N access points and non-zero start-up times. We first present an exact analytical model that accurately predicts performance but has a high computational complexity, and then derive a simplified analysis that sacrifices some accuracy in exchange for a much lower computational cost. To illustrate the practicality of this model, we present the design of a simple configuration algorithm for RoD. Simulation results confirm the validity of the analyses, and the effectiveness of the configuration algorithm

One-dimensional reduction of viscous jets. I. Theory

We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model with circular sections. However, when including the first corrections we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model, since it amounts to selectively discard some corrections. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as {\it xAct}, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018)].Comment: 41 pages, 1 figur

On the expressive power of read-once determinants

We introduce and study the notion of read-$k$ projections of the determinant: a polynomial $f \in \mathbb{F}[x_1, \ldots, x_n]$ is called a {\it read-$k$ projection of determinant} if $f=det(M)$, where entries of matrix $M$ are either field elements or variables such that each variable appears at most $k$ times in $M$. A monomial set $S$ is said to be expressible as read-$k$ projection of determinant if there is a read-$k$ projection of determinant $f$ such that the monomial set of $f$ is equal to $S$. We obtain basic results relating read-$k$ determinantal projections to the well-studied notion of determinantal complexity. We show that for sufficiently large $n$, the $n \times n$ permanent polynomial $Perm_n$ and the elementary symmetric polynomials of degree $d$ on $n$ variables $S_n^d$ for $2 \leq d \leq n-2$ are not expressible as read-once projection of determinant, whereas $mon(Perm_n)$ and $mon(S_n^d)$ are expressible as read-once projections of determinant. We also give examples of monomial sets which are not expressible as read-once projections of determinant

On track for solar grade silicon through a Siemens process-type laboratory reactor: operating conditions and energy savings

Polysilicon cost impacts significantly on the photovoltaics (PV) cost and on the energy payback time. Nowadays, the besetting production process is the so called Siemens process, polysilicon deposition by chemical vapor deposition (CVD) from Trichlorosilane. Polysilicon purification level for PV is to a certain extent less demanding that for microelectronics. At the Instituto de Energía Solar (IES) research on this subject is performed through a Siemens process-type laboratory reactor. Through the laboratory CVD prototype at the IES laboratories, valuable information about the phenomena involved in the polysilicon deposition process and the operating conditions is obtained. Polysilicon deposition by CVD is a complex process due to the big number of parameters involved. A study on the influence of temperature and inlet gas mixture composition on the polysilicon deposition growth rate, based on experimental experience, is shown. Moreover, CVD process accounts for the largest contribution to the energy consumption of the polysilicon production. In addition, radiation phenomenon is the major responsible for low energetic efficiency of the whole process. This work presents a model of radiation heat loss, and the theoretical calculations are confirmed experimentally through a prototype reactor at our disposal, yielding a valuable know-how for energy consumption reduction at industrial Siemens reactorsPostprint (published version

On the Cryptographic Hardness of Local Search

We show new hardness results for the class of Polynomial Local Search problems (PLS): - Hardness of PLS based on a falsifiable assumption on bilinear groups introduced by Kalai, Paneth, and Yang (STOC 2019), and the Exponential Time Hypothesis for randomized algorithms. Previous standard model constructions relied on non-falsifiable and non-standard assumptions. - Hardness of PLS relative to random oracles. The construction is essentially different than previous constructions, and in particular is unconditionally secure. The construction also demonstrates the hardness of parallelizing local search. The core observation behind the results is that the unique proofs property of incrementally-verifiable computations previously used to demonstrate hardness in PLS can be traded with a simple incremental completeness property

Topological optimisation of rod-stirring devices

There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly stretch a material such as bread dough or taffy. The goal in these applications is to stretch either material lines (in a fluid) or the material itself (for dough or taffy) as rapidly as possible. The growth rate of material lines is conveniently given by the topological entropy of the rod motion. We discuss the problem of optimising such rod devices from a topological viewpoint. We express rod motions in terms of generators of the braid group, and assign a cost based on the minimum number of generators needed to write the braid. We show that for one cost function -- the topological entropy per generator -- the optimal growth rate is the logarithm of the golden ratio. For a more realistic cost function,involving the topological entropy per operation where rods are allowed to move together, the optimal growth rate is the logarithm of the silver ratio, $1+\sqrt{2}$. We show how to construct devices that realise this optimal growth, which we call silver mixers.Comment: 22 pages, 53 figures. PDFLaTeX with RevTex4 macros