•The endwall heat transfer characteristics of typical lattice arrays are obtained through experiments.•A comparison on the thermos-fluid behaviors between staggered pin fins and staggered lattices is ...presented.•Compared with the pin fins, lattices exhibit 17–41% higher endwall-averaged heat transfer.•The asymmetry of Kagome geometry results in a heat transfer difference of 46–54% between the bottom wall and the top wall.
Truss-type lattices present good mechanical and thermal properties and are regarded as promising structures for internal cooling. This study presents a systematic comparison of thermo-fluid behaviors among staggered pin fin array, Kagome lattice array and Body Centered Cubic (BCC) lattice array in a rectangular channel under an identical porosity. Transient liquid crystals (TLC) and numerical methods were utilized to explore the flow and endwall heat transfer characteristics in structures. The results reveal that, due to stronger flow mixing and more irregular vortices, the endwall-averaged Nusselt number of the Kagome array and the BCC array is 17–24% and 26–41% higher than that of the pin fin array, respectively. The similar topology results in similar heat transfer characteristics between the Kagome array and the BCC array, and an arc-shaped high heat transfer wake region outside the vertex is induced by the horseshoe vortex and the secondary flow washing the endwall. Meanwhile, for the Kagome array, a strong counter rotating vortex is formed near the bottom endwall, while in contrast, there is no obvious similar flow behavior near the top endwall. This leads to a 46–54% difference in the Nusselt number between the bottom endwall and the top endwall of the Kagome. In addition, the relationship between the element-averaged Nusselt number and Reynolds number of each array is obtained to guide practical applications. This research indicates that BCC or Kagome lattices may become a potential alternative to conventional pin fins due to their higher thermal efficiency.
Here, we find a simple spin Hamiltonian to describe physical states of $(2+1)$-dimensional SU(2) lattice gauge theory on a honeycomb lattice with a truncation of the electric field representation at ...$j_{max}=\frac{1}{2}$. The simple spin Hamiltonian contains only local products of Pauli matrices, even though Gauss’s law has been completely integrated out.
Additively manufactured lattice structures enable the realisation of light-weight, multi-functional, structures. For example, lattices can be used for high stiffness and buckling resistance in ...sandwich structures or as support material for additive manufacturing. Topology optimisation and additive manufacturing are two technologies that allow the design, optimisation and manufacture of complex lattice designs. In this work, a new lattice optimisation methodology is presented that tailors the size, shape and orientation of individual lattice trusses in three-dimensional space by using principal strain fields obtained from topology optimisation. This new method of generating functionally graded lattices is shown both numerically and experimentally to be capable of generating lattice structures with greatly improved stiffness and strength when compared to lattice structures with a uniform lattice infill. Upper and lower relative density thresholds and minimum truss member sizes are included in the optimisation workflow to ensure that the optimised lattice designs are compatible with additive manufacturing process constraints. The functional grading method is also shown to be capable of generating conformal lattice structures in three dimensions, even for complex loading conditions and arbitrary volume boundaries.
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•A novel lattice infill methodology creates optimally aligned lattice structures.•Lattice structures are automatically generated using principal strain trajectories.•The lattices conform to arbitrary 3D design space volumes.•Optimally aligned lattice structures have higher stiffness and strength.•Additively manufactured lattices validate the optimisation predictions.
We elaborate, strengthen, and generalize known representation theorems by different authors for regular operators on vector and Banach lattices. Our main result asserts, in particular, that every ...regular linear operator T acting from a vector lattice E with the principal projection property to a Dedekind complete vector lattice F, which is an ideal of some order continuous Banach lattice G, admits a unique representation T=Ta+Tc$T = T_a + T_c$, where Ta$T_a$ is the sum of an absolutely order summable family of disjointness preserving operators and Tc$T_c$ is an order narrow (= diffuse) operator. Our main contribution is waiver of the order continuity assumption on T. In proofs, we use new techniques that allow obtaining more general results for a wider class of orthogonally additive operators, which has somewhat different order structure than the linear subspace of linear operators.
Coupling a qubit coherently to an ensemble is the basis for collective quantum memories. A single driven electron in a quantum dot can deterministically excite low-energy collective modes of a ...nuclear spin ensemble in the presence of lattice strain. We propose to gate a quantum state transfer between this central electron and these low-energy excitations-spin waves-in the presence of a strong magnetic field, where the nuclear coherence time is long. We develop a microscopic theory capable of calculating the exact time evolution of the strained electron-nuclear system. With this, we evaluate the operation of quantum state storage and show that fidelities up to 90% can be reached with a modest nuclear polarization of only 50%. These findings demonstrate that strain-enabled nuclear spin waves are a highly suitable candidate for quantum memory.
A Schreier decoration is a combinatorial coding of an action of the free group Fd on the vertex set of a 2d-regular graph. We investigate whether a Schreier decoration exists on various countably ...infinite transitive graphs as a factor of iid. We show that Zd,d≥3, the square lattice and also the three other Archimedean lattices of even degree have finitary-factor-of-iid Schreier decorations, and, answering a question of Thornton, exhibit examples of transitive graphs of arbitrary even degree in which obtaining such a decoration as a factor of iid is impossible.
We also prove that symmetrical planar lattices with all degrees even have a factor-of-iid balanced orientation, meaning the indegree of every vertex is equal to its outdegree, and demonstrate the existence of transitive graphs G whose classical chromatic number χ(G) is equal to their factor-of-iid chromatic number.
Cesàro vector lattices and their ideals of finite elements Gönüllü, Uğur; Polat, Faruk; Weber, Martin R.
Positivity : an international journal devoted to the theory and applications of positivity in analysis,
04/2023, Letnik:
27, Številka:
2
Journal Article
Recenzirano
For the Cesàro matrix
C
=
(
c
nm
)
n
,
m
∈
N
, where
c
nm
=
1
n
, if
n
≥
m
and
c
nm
=
0
otherwise, the Cesàro sequence spaces
c
e
s
0
,
c
e
s
p
(for
1
<
p
<
∞
) and
c
e
s
∞
are defined. These spaces ...turn out to be real vector lattices and with respect to a corresponding (naturally introduced) norm they are all Banach lattices, and so possess (or not possess) some interesting properties. In particular, the relations to their generating ideals
c
0
,
ℓ
p
and
ℓ
∞
are investigated. Finally the ideals of all finite, totally finite and selfmajorizing elements in
c
e
s
0
,
c
e
s
p
(for
1
<
p
<
∞
) and
c
e
s
∞
are described in detail.
Mesoscale modelling of soft flowing crystals Montessori, A; Lauricella, M; Succi, S
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
04/2019, Letnik:
377, Številka:
2142
Journal Article
Recenzirano
Odprti dostop
We outline the main ideas behind the numerical modelling of soft flowing crystals, paying special attention to their application to microfluidic devices for the design of novel mesoscale porous ...materials. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.
Prussian blue and its analogues have received particular attention as superior cathodes for Na-ion batteries due to their potential 2-Na storage capacity (∼170 mAh g–1) and low cost. However, most of ...the Prussian blue compounds obtained from the conventional synthetic routes contain large amounts of Fe(CN)6 vacancies and coordinated water molecules, which leads to the collapse of cyano-bridged framework and serious deterioration of their Na-storage ability. Herein, we propose a facile citrate-assisted controlled crystallization method to obtain low-defect Prussian blue lattice with greatly improved Na-storage capacity and cycling stability. As an example, the as-prepared Na2CoFe(CN)6 nanocrystals demonstrate a reversible 2-Na storage reaction with a high specific capacity of 150 mAh g–1 and a ∼ 90% capacity retention over 200 cycles, possibly serving as a low cost and high performance cathode for Na-ion batteries. In particular, the synthetic strategy described in this work may be extended to other coordination-framework materials for a wide range of energy conversion and storage applications.
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