Well-posedness in the Energy Space for Non-linear System of Wave Equations with Critical Growth

The authors consider the well-posedness in energy space of the critical non-linear system of wave equations with Hamiltonian structure{utt-△u=-F1（｜u｜^2,｜v｜^2）u,utt-△u=-F2（｜u｜^2,｜v｜^2）u where there exists a function F（λ,μ） such that δF（λ,μ）/δλ=F1（λ,μ）.δF（λ,μ）/δμ=F2（λ,μ） By showing that the energy and dilation identities hold for weak solution under some assumptions on the non-linearities, we prove the global well-posedness in energy space by a similar argument to that for global regularity as shown in ＂Shatah and Struwe＇s paper, Ann. of Math. 138, 503-518 （1993）＂.

Conservation laws for energy and momentum in curved spaces

In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, Moeller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.

ALMOST CONSERVATION LAWS AND GLOBAL ROUGH SOLUTIONS OF THE DEFOCUSING NONLINEAR WAVE EQUATION ON R^2

In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].

Laser Properties of Nd_2O_3 Doped Na_2O–CaO–SiO_2 Transparent Glass-Ceramics for Space Solar Energy

A series of Na20-CaO-SiO2 glass ceramics containing different content of Nd3＋ ions were prepared by the method of high temperature melting and subsequent crystallization. The absorption, excitation and emis- sion spectra of these glass ceramics were investigated; effects of Nd3＋ content and crystallization behavior on the laser properties of this material had been studied. The results show that the emission bands origi- nating from the 4F3/2 state of Nd3＋ were firstly enhanced with the increase of the Nd2O3 doping content and the crystallinity degree, and then decreased with more doping content and deepened crystalliza- tion. The possible reasons of this phenomenon were analyzed. Research will be favored to promote the development of glass ceramics laser materials for space solar energy.

Direct measurement of the linear energy transfer of ions in silicon for space application

The single event effect(SEE) is an important consideration in electronic devices used in space environments because it can lead to spacecraft anomalies and failures. The linear energy transfer(LET) of ions is commonly investigated in studies of SEE. The use of a thin detector is an economical way of directly measuring the LET in space. An LET telescope consists of a thin detector as the front detector(D1), along with a back detector that indicates whether D1 was penetrated. The particle radiation effect monitor(PREM) introduced in this paper is designed to categorize the LET into four bins of 0.2–0.4, 0.4–1.0, 1.0–2.0 and 2.0–20 Me V·cm^2/mg, and one integral bin of LET>20 Me V·cm^2/mg. After calibration with heavy ions and Geant4 analysis, the LET boundaries of the first four bins are determined to be 0.236, 0.479, 1.196, 2.254, and 17.551 Me V·cm^2/mg, whereas that of the integral bin is determined to be LET>14.790 Me V·cm^2/mg. The acceptances are calculated by Geant4 analysis as 0.452, 0.451, 0.476, 0.446, and 1.334, respectively. The LET accuracy is shown to depend on the thickness of D1; as D1 is made thinner, the accuracy of the measured values increases.

Friedmann-Like Cosmological Equations for the Accelerated Expansion of the Universe

In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showed in the above references that at t = 0 the radius of the universe need not be zero. And thus, we avoided the problem of singularity. We further showed that the Hubble factor is no longer constant in time and goes on decreasing as confirmed by experiments. We pointed out in the above references that Space is the source of dark energy which is responsible for the accelerated expansion of the universe. With a view to improving the above-mentioned results quantitatively, in this paper, we are discussing the consequences of our axioms using Einstein’s field equations of general theory of relativity. Friedmann-like Cosmological equations with Dark Energy built-in are derived. This derivation is obtained using Robertson-Walker line element and by introducing a suitable expression for Energy-Momentum tensor in terms of matter and Dark energy contents of the universe. The solutions of our cosmological equations obtained here, show that the radius of the universe cannot reach zero but has a minimum value and there is also maximum value for the radius of the universe. The inflationary expansion of the very early universe emerges from our theory.

Assessing cooling energy reduction potentials by retrofitting traditional cavity walls into passively ventilated cavity walls

A major roadblock in achieving substantial building energy reduction is the low performance of old buildings that account for a significant portion of the building energy consumption.Finding low-cost energy retrofit solutions that do not disrupt occupants’daily life during the retrofitting is the key to successful building energy retrofit initiatives.In this paper,a novel and low-cost exterior wall retrofitting solution is introduced,and its performance in reducing space cooling load was quantitatively evaluated to demonstrate its feasibility and effectiveness.The primary goal of this paper is to provide a quantitative assessment of the cooling-energy savings potential by using the proposed new wall system.The intended retrofitting targets are the large amount of existing cavity-wall buildings located in hot climate regions.The quantification of the before-after heat-flux reduction was conducted through a 3-dimensional steady-state low turbulence computational fluid dynamics(CFD)model,which is validated by benchmarking its prediction against the published experimental case results.The outcomes of the investigation suggest that this simple low-cost solution has great potentials in reducing buildings’summer cooling load in hot climate regions.The applicability of this solution is not limited to retrofitting existing buildings.New energy-efficient building designs can also adopt this solution in their envelope systems.