Two 3-Branes in Randall-Sundrum Setup and Current Acceleration of the Universe

Five-dimensional spacetimes of two orbifold 3-branes are studied, by assuming that {\em the two 3-branes are spatially homogeneous, isotropic, and independent of time}, following the so-called "bulk-based" approach. The most general form of the metric is obtained, and the corresponding field equations are divided into three groups, one is valid on each of the two 3-branes, and the third is valid in the bulk. The Einstein tensor on the 3-branes is expressed in terms of the discontinuities of the first-order derivatives of the metric coefficients. Thus, once the metric is known in the bulk, the distribution of the Einstein tensor on the two 3-branes is uniquely determined. As applications, we consider two different cases, one is in which the bulk is locally $AdS_{5}$, and the other is where it is vacuum. In some cases, it is shown that the universe is first decelerating and then accelerating. The global structure of the bulk as well as the 3-branes is also studied, and found that in some cases the solutions may represent the collision of two orbifold 3-branes. The applications of the formulas to the studies of the cyclic universe and the cosmological constant problem are also pointed out.Comment: revtex4, 14 figures, published in Nucl. Phys. B797 (2008) 395 - 43

Plateau in Monotonic Linear Interpolation -- A "Biased" View of Loss Landscape for Deep Networks

Monotonic linear interpolation (MLI) - on the line connecting a random initialization with the minimizer it converges to, the loss and accuracy are monotonic - is a phenomenon that is commonly observed in the training of neural networks. Such a phenomenon may seem to suggest that optimization of neural networks is easy. In this paper, we show that the MLI property is not necessarily related to the hardness of optimization problems, and empirical observations on MLI for deep neural networks depend heavily on biases. In particular, we show that interpolating both weights and biases linearly leads to very different influences on the final output, and when different classes have different last-layer biases on a deep network, there will be a long plateau in both the loss and accuracy interpolation (which existing theory of MLI cannot explain). We also show how the last-layer biases for different classes can be different even on a perfectly balanced dataset using a simple model. Empirically we demonstrate that similar intuitions hold on practical networks and realistic datasets.Comment: ICLR 202

Spin Dynamics of a J1-J2-K Model for the Paramagnetic Phase of Iron Pnictides

We study the finite-temperature spin dynamics of the paramagnetic phase of iron pnictides within an antiferromagnetic J_1-J_2 Heisenberg model on a square lattice with a biquadratic coupling $-K (S_i \cdot S_j)^2$ between the nearest-neighbor spins. Our focus is on the paramagnetic phase in the parameter regime of this J_1-J_2-K model where the ground state is a (\pi,0) collinear antiferromagnet. We treat the biquadratic interaction via a Hubbard-Stratonovich decomposition, and study the resulting effective quadratic-coupling model using both modified spin wave and Schwinger boson mean-field theories; the results for the spin dynamics derived from the two methods are very similar. We show that the spectral weight of dynamical structure factor S(q,\omega) is peaked at ellipses in the momentum space at low excitation energies. With increasing energy, the elliptic features expand towards the zone boundary, and gradually split into two parts, forming a pattern around (\pi,\pi). Finally, the spectral weight is anisotropic, being larger along the major axis of the ellipse than along its minor axis. These characteristics of the dynamical structure factor are consistent with the recent measurements of the inelastic neutron scattering spectra on BaFe_2As_2 and SrFe_2As_2.Comment: 13 pages, 11 figures, to be published in Phys. Rev.

Real-Time Manipulation with Magnetically Tunable Structures

Magnetically tunable micropillar arrays with uniform, continuous and extreme tilt angles for real-time manipulation are reported. We experimentally show uniform tilt angles ranging from 0° to 57°, and develop a model to accurately capture the behavior. Furthermore, we demonstrate that the flexible uniform responsive microstructures (μFUR) can dynamically manipulate liquid spreading directionality, control fluid drag, and tune optical transmittance over a large range.United States. Air Force Office of Scientific Research (AFOSR, Grant FA9550-11-1-0059

Absence of dynamical gap generation in suspended graphene

There is an interesting proposal that the long-range Coulomb interaction in suspended graphene can generate a dynamical gap, which leads to a semimetal-insulator phase transition. We revisit this problem by solving the self-consistent Dyson-Schwinger equations of wave function renormalization and fermion gap. In order to satisfy the Ward identity, a suitable vertex function is introduced. The impacts of singular velocity renormalization and dynamical screening on gap generation are both included in this formalism, and prove to be very important. We obtain a critical interaction strength, $3.2 < \alpha_{c} < 3.3$, which is larger than the physical value $\alpha = 2.16$ for suspended graphene. It therefore turns out that suspended graphene is a semimetal, rather than insulator, at zero temperature.Comment: 14 pages, 5 figures, 1 tabl

Non-Abelian Medium Effects in Quark-Gluon Plasma

Based on the kinetic theory, the non-Abelian medium property of hot Quark-Gluon Plasma is investigated. The nonlinearity of the plasma comes from two aspects: The nonlinear wave-wave interaction and self-interaction of color field. The non-Abelian color permittivity is obtained by expanding the kinetic equations to third order. As an application, the nonlinear Landau damping rate and the nonlinear eigenfrequency shift are calculated in the longwave length limit.Comment: 12 pages(Revtex), no figure

China's low-emission pathways toward climate-neutral livestock production for animal-derived foods

Funding Information: This research was supported by the National Natural Science Foundation of China (Grant No. 31922080 and 31872403 ), China Agriculture Research System of MOF and MARA and the Hunan province science and technology plan (Grant No. 2022NK2021 ).Peer reviewedPublisher PD