Variable Space Dimension Research Articles

A physics‐based spectral matching (PBSM) method for generating fully site‐related ground motions

AbstractThe response spectrum is generally adopted in the seismic design to represent the seismic fortification level, but the structural dynamic analysis requires the ground motions as an input. However, ground motions generated by the traditional spectral matching methods do not have site‐related physical backgrounds for the target site. In this study, a physics‐based spectral matching (PBSM) method is developed to generate fully site‐related broadband ground motions (i.e., the generated ground motions have real physical backgrounds for the target site, including the source process, propagation path, and local site conditions) that are compatible to the target spectrum. In this method, the three‐dimensional (3D) numerical model around the target site is constructed to calculate the strain Green's tensors of all potential source locations using adjoint simulations. The variable space dimension of the seismic source is significantly reduced by applying the self‐similar feature of the multidimension source model, so that the optimization algorithm can be used to search for the rupture process that generates the physics‐based and spectrum‐matched ground motions (abbreviated to PBSM ground motions). The proposed method is applied to the Xiluodu dam in China. Compared with the traditional techniques, the generated ground motions have fully site‐related physical backgrounds and are compatible to the target spectrum. Additionally, as this method generates broadband ground motions based on the deterministic rupture process, any features of ground motions, such as large velocity pulses, can be taken into account throughout the optimization process. This study introduces the deterministic physical backgrounds of earthquakes to performance‐based seismic design and analysis. The proposed method may have a significant application potential in earthquake engineering.

Quantum Magnetism and Topological Ordering via Rydberg Dressing near Förster Resonances.

We devise a cold-atom approach to realizing a broad range of bilinear quantum magnets. Our scheme is based on off-resonant single-photon excitation of Rydberg P states (Rydberg dressing), whose strong interactions are shown to yield controllable XYZ interactions between effective spins, represented by different atomic ground states. The distinctive features of Förster-resonant Rydberg atom interactions are exploited to enhance the effectiveness of Rydberg dressing and, thereby, yield large spin interactions that greatly exceed the corresponding decoherence rates. We illustrate the concept on a spin-1 chain implemented with cold rubidium atoms, and demonstrate that this permits the dynamical preparation of topological magnetic phases. Generally, the described approach provides a viable route to exploring quantum magnetism with dynamically tunable (an)isotropic interactions as well as variable space and spin dimensions in cold-atom experiments.

TIME VARIATION OF THE FINE STRUCTURE CONSTANT IN DECRUMPLING OR TVSD MODEL

Within the framework of a model universe with time variable space dimension (TVSD), known as decrumpling or TVSD model, we study the time variation of the fine structure constant. Using observational bounds on the present time variation of the fine structure constant, we are able to obtain an upper limit for the absolute value of the present time variation of spatial dimensions.

DYNAMICS OF INFLATIONARY COSMOLOGY IN TVSD MODEL

Within the framework of a model Universe with time variable space dimensions (TVSD), known as decrumpling or TVSD model, we study TVSD chaotic inflation and obtain dynamics of the inflaton, scale factor and spatial dimension. We also study the quantum fluctuations of the inflaton field and obtain the spectral index and its running in this model. Two classes of examples have been studied and comparisons made with the standard slow-roll formulas. We compare our results with the recent Wilkinson Microwave Anisotropy Probe (WMAP) data.

Dynamics of chaotic inflation with variable space dimension

Within the framework of a model Universe with variable space dimension, we study chaotic inflation with the potential m 2 φ 2/2, and calculate the dynamical solutions of the inflaton field, variable space dimension, scale factor, and their interdependence during the inflationary epoch. We show that the characteristic of the variability of the space dimension causes the inflationary epoch in the variable space dimension to last longer than the inflationary epoch in the constant space dimension.

CHAOTIC INFLATION WITH TIME-VARIABLE SPACE DIMENSIONS

Assuming the space dimension is not constant but decreases during the expansion of the Universe, we study chaotic inflation with the potential m2ϕ2/2. Our investigations are based on a model Universe with variable space dimensions. We write down field equations in the slow-roll approximation, and define slow-roll parameters by assuming the number of space dimensions decreases continuously as the Universe expands. The dynamical character of the space dimension shifts the initial and final value of the inflaton field to larger values. We obtain an upper limit for the space dimension at the Planck length. This result is in agreement with previous works for the effective time variation of the Newtonian gravitational constant in a model Universe with variable space dimensions.

Model universe with variable space dimension: Its dynamics and wave function

Assuming the space dimension is not constant, but varies with the expansion of the Universe, a Lagrangian formulation for a toy model Universe is given. There is a free paremeter in the theory, $C$, with which we can fix the dimension of space at the Planck time. The standard FRW model corresponds to the limiting case $C \to +\infty$. We study the Wheeler-De Witt equation and the wave function of the Universe and the probability density in our model Universe. In the limit of constant space dimension, our wave function approaches to the Hartle-Hawking wave function or to a modified Linde wave function.

Effective time variation of G in a model universe with variable space dimension

Time variation of the Newtonian gravitational constant, G, is studied in model universes with a variable space dimension proposed recently. Using the Lagrangian formulation of these models, we find the effective gravitational constant as a function of time. To compare it with observational data, a test theory for the time variation of G is formulated. We have assumed a power law behavior of the time variation of G where the exponent β is itself time dependent. Within this test theory we are able to restrict the free parameter of the theories under consideration and give upper bounds for the space dimension at the Planck era. The time variation of G at earlier times, such as the time of nucleosynthesis is also predicted which express the needs to look for related observational data.