Related papers: Fundamental Limits to Moore's Law
The validity of the orbital motion limited (OML) theory is reviewed with reference to the floating potential acquired by a spherical object immersed in a plasma. A new and perhaps more realistic approach for obtaining the floating potential…
We establish a central limit theorem and prove a moderate deviation principle for stochastic scalar conservation laws. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and…
The largely open problem of scaling laws in fully developed turbulence is discussed, with the stress put on similarities and differences with scaling in field theory. A soluble model of the passive advection is examined in more detail in…
We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.
We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar…
In mechanical engineering W\"ohler plots serve to measure the average number of load cycles before materials break, as a function of the maximal stress in each cycle. Although such plots are prevalent in engineering for more than 150 years,…
The biggest question in beyond the standard model physics is what are the scales of new physics. Ideas about scales, as well as experimental evidence and constraints, are surveyed for a variety of possible forms of new physics:…
In this talk, I will concentrate on $Q^2$-dependence of deep inelastic sum rules. I will first give a modern definition of deep-inelastic sum rules and then discuss physical origins of their scaling violation at finite $Q^2$. Following…
In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and independent increments. For convenience we refer to them as…
We give some detailed numerical information about extremal metrics on four different toric surfaces. These are sample of many other cases which can be treated using a computer programme outlined in the paper.
Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific…
A succinct statement and justification of all the principles necessary to understand and evaluate interpretations of quantum mechanics is given. These principles provide strong constraints on interpretations. They imply the particle-like…
The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild…
Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related…
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…
The generalized allocation scheme is studied. Its extension for coloured balls is defined. Some analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers are obtained for the number of boxes containing fixed numbers…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer…
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…
The fundamental action is dependent on momentum. Some consequences are presented for matter waves and scalar quantum field theory.