Scalar field in a minimally coupled brane world: no-hair and other no-go theorems

In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian (\d\phi)^2/2 - V(\phi), confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the usual stress tensor T\mN, the tensor \Pi\mN, quadratic in T\mN, and E\mN describing interaction with the bulk. For models under study, the tensor \Pi\mN has zero divergence, so we can consider a "minimally coupled" brane with E\mN = 0, whose 4D gravity is decoupled from the bulk geometry. Assuming E\mN =0, we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a $Lambda$ term in GR: Minkowski, Schwarzschild, (A)dS and Schwarzschild-(A)dS. A no-hair theorem, saying that, given a potential $V\geq 0$, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region.Comment: 8 pages, Latex2e. Numerical estimates and a few references adde

A Note on the Cosmological Dynamics in Finite-Range Gravity

In this note we consider the homogeneous and isotropic cosmology in the finite-range gravity theory recently proposed by Babak and Grishchuk. In this scenario the universe undergoes late time accelerated expansion if both the massive gravitons present in the model are tachyons. We carry out the phase space analysis of the system and show that the late-time acceleration is an attractor of the model.Comment: RevTex, 4 pages, two figures, New references added, To appear in IJMP

A symplectic realization of the Volterra lattice

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page

OPTIMIZATION OF BURNING PRODUCTION PROCESS OF CERAMSITE WITH SPECIFIED DENSITY

The paper goes into peculiarities of using developed mathematical models of ceramsite burning and computational models created on their basis. The work is done in the light of analysis and synthesis of multivariate control system of kiln angular velocity and kiln charge with volumetric thermal capacity burners. It is shown that computational models of burning as an object of control are problem-oriented on producing ceramsite with specified density. Mathematical model of ceramsite burning process as an object with distributed parameters is synthesized. The transition from model with distributed parameters to the mode with lumped parameters is performed. Then the authors used a model with three bearing cross-sections along Z-axis in Matlab software and created a computational model of multivariate object of control with inter-channel connections. The paper presents experimental computational set up methods and methods of ceramsite burning optimal curve identification on the criterion of minimizing energy consumption for burning. The developed method of staging computational experiments makes it possible to predict the strength of ceramsite if values of control actions are known. The results of modeling help create methodology of choosing optimal modes of ceramsite burning with the required mark of strength and with minimum energy consumption

Settlements of Neighboring Buildings During Piling Works

Two case histories of heavy damaging the neighbouring buildings in Sankt-Petersburg during construction the bored piles are presented. The analysis of causes of the damages has shown that ground inflow into the housing tubes due to low strength properties of water saturated liquid-plastic loams is the main cause of additional settlements of existing houses during construction the bored piles of large diameter close to them

Escaping the complexity-bitrate-quality barriers of video encoders via deep perceptual optimization

We extend the concept of learnable video precoding (rate-aware neural-network processing prior to encoding) to deep perceptual optimization (DPO). Our framework comprises a pixel-to-pixel convolutional neural network that is trained based on the virtualization of core encoding blocks (block transform, quantization, block-based prediction) and multiple loss functions representing rate, distortion and visual quality of the virtual encoder. We evaluate our proposal with AVC/H.264 and AV1 under per-clip rate-quality optimization. The results show that DPO offers, on average, 14.2% bitrate reduction over AVC/H.264 and 12.5% bitrate reduction over AV1. Our framework is shown to improve both distortion- and perception-oriented metrics in a consistent manner, exhibiting only 3% outliers, which correspond to content with peculiar characteristics. Thus, DPO is shown to offer complexity-bitrate-quality tradeoffs that go beyond what conventional video encoders can offe

Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion

It is well known that the long-range nature of the Coulomb interaction makes the definition of asymptotic ``in'' and ``out'' states of charged particles problematic in quantum field theory. In particular, the notion of a simple particle pole in the vacuum charged particle propagator is untenable and should be replaced by a more complicated branch cut structure describing an electron interacting with a possibly infinite number of soft photons. Previous work suggests a Dirac propagator raised to a fractional power dependent upon the fine structure constant, however the exponent has not been calculated in a unique gauge invariant manner. It has even been suggested that the fractal ``anomalous dimension'' can be removed by a gauge transformation. Here, a gauge invariant non-perturbative calculation will be discussed yielding an unambiguous fractional exponent. The closely analogous case of soft graviton exponents is also briefly explored.Comment: Updated with a corrected sign error, longer discussion of fractal dimension, and more reference