Flexoelectric effects in second-order extension of rods

2021 ◽  
Vol 111 ◽  
pp. 103625
Author(s):  
Yilin Qu ◽  
Feng Jin ◽  
Jiashi Yang
Keyword(s):  
Second Order ◽  
Order Extension

Application of the Godunov method and its second-order extension to cascade flow modeling

AIAA Journal ◽  
1984 ◽  
Vol 22 (11) ◽  
pp. 1609-1615 ◽  
Author(s):  
Shmuel Eidelman ◽  
Phillip Colella ◽  
Raymond P. Shreeve
Keyword(s):  
Second Order ◽  
Godunov Method ◽  
Flow Modeling ◽  
Cascade Flow ◽  
Order Extension

scholarly journals Three improvements to the HPSG model theory

2021 ◽  
Author(s):  
Adam Przepiórkowski
Keyword(s):  
Model Theory ◽  
Second Order ◽  
The Third ◽  
Order Extension

The aim of this paper is to propose three improvements to the HPSG model theory. The first is a solution to certain formal problems identified in Richter 2007. These problems are solved if HPSG models are rooted models of utterances and not exhaustive models of languages, as currently assumed. The proposed solution is compatible with all existing views on the nature of objects inhabiting models. The second improvement is a solution to “Höhle’s Problem”, i.e., the problem of massive spurious ambiguities in models of utterances. The third is a formalisation of Yatabe's (2004) analysis of the coordination of unlike categories, one that requires a second-order extension of the language for stating HPSG grammars.

The second order extension of the Gibbs state

1992 ◽  
Vol 1 (2) ◽  
pp. 243-258 ◽  
Author(s):  
Roman S. Ingarden ◽  
Teruaki Nakagomi
Keyword(s):  
Gibbs State ◽  
Second Order ◽  
Order Extension

scholarly journals Simulation of Hydraulic Shock Waves by Hybrid Flux-Splitting Schemes in Finite Volume Method

2005 ◽  
Vol 21 (2) ◽  
pp. 85-101 ◽  
Author(s):  
J.-S. Lai ◽  
G.-F. Lin ◽  
W.-D. Guo
Keyword(s):  
Shock Waves ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Second Order ◽  
Dam Break ◽  
Splitting Scheme ◽  
Hydraulic Shock ◽  
Flux Splitting ◽  
Volume Method ◽  
Order Extension

AbstractIn the framework of the finite volume method, a robust and easily implemented hybrid flux-splitting finite-volume (HFF) scheme is proposed for simulating hydraulic shock waves in shallow water flows. The hybrid flux-splitting algorithm without Jacobian matrix operation is established by applying the advection upstream splitting method to estimate the cell-interface fluxes. The scheme is extended to be second-order accurate in space and time using the predictor-corrector approach with monotonic upstream scheme for conservation laws. The proposed HFF scheme and its second-order extension are verified through simulations of the 1D idealized dam-break problem, the 2D oblique hydraulic shock-wave problem, and the 2D dam-break experiments with channel contraction as well as wet/dry beds. Comparisons of the HFF and several well-known first-order upwind schemes are made to evaluate numerical performances. It is demonstrated that the HFF scheme captures the discontinuities accurately and produces no entropy-violating solutions. The HFF scheme and its second-order extension are proven to achieve the numerical benefits combining the efficiency of flux-vector splitting scheme and the accuracy of flux-difference splitting scheme for the simulation of hydraulic shock waves.

On a theory of weak implications

1988 ◽  
Vol 53 (1) ◽  
pp. 200-211 ◽  
Author(s):  
Mitsuhiro Okada
Keyword(s):  
Intuitionistic Logic ◽  
General Setting ◽  
Second Order ◽  
Inference Rules ◽  
Full Strength ◽  
Circular Argument ◽  
Logical Connectives ◽  
Points Of View ◽  
Weak Implications ◽  
Order Extension

The purpose of this paper is to study logical implications which are much weaker than the implication of intuitionistic logic.In §1 we define the system SI (system of Simple Implication) which is obtained from intuitionistic logic by restricting the inference rules of intuitionistic implication. The implication of the system SI is called the “simple implication” and denoted by ⊃, where the simple implication ⊃ has the following properties:(1) The simple implication ⊃ is much weaker than the usual intuitionistic implication.(2) The simple implication ⊃ can be interpreted by the notion of provability, i.e., we have a very simple semantics for SI so that a sentence A ⊃ B is interpreted as “there exists a proof of B from A”.(3) The full-strength intuitionistic implication ⇒ is definable in a weak second order extension of SI; in other words, it is definable by help of a variant of the weak comprehension schema and the simple implication ⊃. Therefore, though SI is much weaker than the intuitionistic logic, the second order extension of SI is equivalent to the second order extension of the intuitionistic logic.(4) The simple implication is definable in a weak modal logic MI by the use of the modal operator and the intuitionistic implication ⇒ with full strength. More precisely, A ⊃ B is defined as the strict implication of the form ◽(A ⇒ B).In §1, we show (3) and (4). (2) is shown in §2 in a more general setting.Semantics by introduction rules of logical connectives has been studied from various points of view by many authors (e.g. Gentzen [4], Lorentzen [5], Dummett [1], [2], Prawitz [8]. Martin-Löf [7], Maehara [6]). Among them Gentzen (in §§10 and 11 of [4]) introduced such a semantics in order to justify logical inferences and the mathematical induction rule. He observed that all of the inference rules of intuitionistic arithmetic, except for those on implication and negation, are justified by means of his semantics, but justification of the inference rules on implication and negation contains a circular argument for the interpretation by introduction rules, where the natural interpretation of A ⊃ B by ⊃-introduction rule is “there exists a proof of B from A ” (cf. §11 of Gentzen [4]).

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