An appropriate cell arrangement plays significant role to design a highly efficient cooling system for the lithium-ion battery pack. This paper performs a comparative analysis of thermal performances ...on different arrangements of cylindrical cells for a LiFePO4 battery pack. A thermal model for the battery pack is developed and is solved in couple with the governing equations of fluid flow in the numerical simulations. The experiments for model validation are conducted on a single cell of the battery pack with forced-air cooling system. The effects of longitudinal and transverse spacing on the cooling performances are analyzed for the battery pack with the aligned and the staggered arrays. Under a specified flow rate of cooling air, the maximum temperature rise is proportional to the longitudinal interval for the staggered arrays, while it is in inverse for the aligned arrangement. Increasing the transverse interval leads to the increase of the battery temperature rise for both aligned and staggered arrangements. By trade-off the design requirements (maximum temperature rise, temperature uniformity, power requirement and cooling index), an appropriate solution in term of the optimal combination of the longitudinal interval, transverse interval, and air inlet width is obtained for the aligned arrangement.
•Forced air-cooling performance for cylindrical lithium-ion battery is evaluated.•Thermal performances for aligned and staggered cell arrangements are compared.•Geometric optimization is investigated for the battery air-cooling system.
In 2006 Sommers and Tymoczko defined so called arrangements of ideal type AI stemming from ideals I in the set of positive roots of a reduced root system. They showed in a case by case argument that ...AI is free if the root system is of classical type or G2 and conjectured that this is also the case for all types. This was established only very recently in a uniform manner by Abe, Barakat, Cuntz, Hoge and Terao. The set of non-zero exponents of the free arrangement AI is given by the dual of the height partition of the roots in the complement of I in the set of positive roots, generalizing the Shapiro–Steinberg–Kostant theorem which asserts that the dual of the height partition of the set of positive roots gives the exponents of the associated Weyl group.
Our first aim in this paper is to investigate a stronger freeness property of the AI. We show that all AI are inductively free, with the possible exception of some cases in type E8.
In the same paper from 2006, Sommers and Tymoczko define a Poincaré polynomial I(t) associated with each ideal I which generalizes the Poincaré polynomial W(t) for the underlying Weyl group W. Solomon showed that W(t) satisfies a product decomposition depending on the exponents of W for any Coxeter group W. Sommers and Tymoczko showed in a case by case analysis in types An, Bn and Cn, and some small rank exceptional types that a similar factorization property holds for the Poincaré polynomials I(t) generalizing the formula of Solomon for W(t). They conjectured that their multiplicative formula for I(t) holds in all types. In our second aim to investigate this conjecture further, the same inductive tools we develop to obtain inductive freeness of the AI are also employed. Here we also show that this conjecture holds inductively in almost all instances with only a small number of possible exceptions.
The freeness of Ish arrangements Abe, Takuro; Suyama, Daisuke; Tsujie, Shuhei
Journal of combinatorial theory. Series A,
February 2017, 2017-02-00, Volume:
146
Journal Article
Peer reviewed
Open access
The Ish arrangement was introduced by Armstrong to give a new interpretation of the q,t-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities ...between the Shi arrangement and the Ish arrangement and posed some problems. One of them is whether the Ish arrangement is a free arrangement or not. In this paper, we verify that the Ish arrangement is supersolvable and hence free. Moreover, we give a necessary and sufficient condition for the deleted Ish arrangement to be free.
A Weyl arrangement is the hyperplane arrangement defined by a root system. Saito proved that every Weyl arrangement is free. The Weyl subarrangements of type Aℓ are represented by simple graphs. ...Stanley gave a characterization of freeness for this type of arrangements in terms of their graph. In addition, the Weyl subarrangements of type Bℓ can be represented by signed graphs. A characterization of freeness for them is not known. However, characterizations of freeness for a few restricted classes are known. For instance, Edelman and Reiner characterized the freeness of the arrangements between type Aℓ−1 and type Bℓ. In this paper, we give a characterization of the freeness and supersolvability of the Weyl subarrangements of type Bℓ under certain assumption.
In this paper, we introduce the region and the faces poset of shi arrangement that J. Y. Shi firstly introduced it. This is an affine arrangement, each of whose hyperplane is parallel to ...some"hyperplane of Coxeter arrangement"(Braid arrangement), the degrees and the exponents of this arrangement were found and we prove the shi arrangement is ahyperfactored arrangement when n=3 and not hyperfactored arrangement when n=4 arrangement.
Let
G
be a simple graph on
ℓ
vertices
{
1
,
⋯
,
ℓ
}
with edge set
E
G
. The graphical arrangement
A
G
consists of hyperplanes
{
x
i
-
x
j
=
0
}
, where
{
i
,
j
}
∈
E
G
. It is well known that three ...properties, chordality of
G
, supersolvability of
A
G
, and freeness of
A
G
are equivalent. Recently, Stanley introduced
ψ
-graphical arrangement
A
G
,
ψ
as a generalization of graphical arrangements. Mu and Stanley characterized the supersolvability of the
ψ
-graphical arrangements and conjectured that the freeness and the supersolvability of
ψ
-graphical arrangements are equivalent. In this paper, we will prove the conjecture.
As the shipbuilding industry is an engineering-to-order industry, different types of products are manufactured according to customer requests, and each product goes through different processes and ...workshops. During the shipbuilding process, if the product is not able to go directly to the subsequent process due to physical constraints of workshop, it temporarily waits in a stockyard. Since the waiting process involves unpredictable circumstances, plans regarding time and space cannot be established in advance. Therefore, unnecessary movement often occurs when ship blocks enter or depart from the stockyard. In this study, a reinforcement learning approach was proposed to minimise rearrangement in such circumstances. For this purpose, an environment in which blocks are arranged and rearranged was defined. Rewards based on the simplified rules were logically defined, and simulation was performed for quantitative evaluation using the proposed reinforcement learning algorithm. This algorithm was verified using an example model derived from actual data from a shipyard. The method proposed in this study can be used not only to the arrangement problem of ship block stockyards but also to the various arrangement and allocation problems or logistics problems in the manufacturing industry.
The extended Shi and Catalan arrangements are well investigated arrangements. In this paper, we prove that the cone of the extended Catalan arrangement of type A is always hereditarily free, while we ...determine the dimension in which the cone of the extended Shi arrangement of type A is hereditarily free. For this purpose, using digraphs, we define a class of arrangements which is closed under restriction, and which contains the extended Shi and Catalan arrangements. We also characterize the freeness for the cone of this arrangement by graphical conditions.
Athanasiadis characterized the freeness of the cones of the arrangements between braid arrangements and Shi arrangements. We are interested in the subarrangements Shi(
G
) of Shi arrangements ...associated with a graph
G
, which may not contain all hyperplanes of braid arrangements. We classify the cones of the arrangements Shi(
G
) which are free. In the meanwhile, we give the graphical interpretation of the exponents of free arrangements
c
(Shi(
G
)).
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