Semi-linear wave equations with effective damping

We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical case.Comment: 28 page

From p0(n)p_0(n) to p0(n+2)p_0(n+2)

In this note we study the global existence of small data solutions to the Cauchy problem for the semi-linear wave equation with a not effective scale-invariant damping term, namely $$v_{tt}-\triangle v + \frac2{1+t}\,v_t = |v|^p, \qquad v(0,x)=v_0(x),\quad v_t(0,x)=v_1(x),$$ where $p>1$, $n\ge 2$. We prove blow-up in finite time in the subcritical range $p\in(1,p_2(n)]$ and an existence result for $p>p_2(n)$, $n=2,3$. In this way we find the critical exponent for small data solutions to this problem. All these considerations lead to the conjecture $p_2(n)=p_0(n+2)$ for $n\ge2$, where $p_0(n)$ is the Strauss exponent for the classical wave equation

Operand Folding Hardware Multipliers

This paper describes a new accumulate-and-add multiplication algorithm. The method partitions one of the operands and re-combines the results of computations done with each of the partitions. The resulting design turns-out to be both compact and fast. When the operands' bit-length $m$ is 1024, the new algorithm requires only $0.194m+56$ additions (on average), this is about half the number of additions required by the classical accumulate-and-add multiplication algorithm ($\frac{m}2$)

Performance comparison between signal digitizers and low-cost digital oscilloscopes: spectroscopic, pulse shape discrimination and timing capabilities for nuclear detectors

Signal digitizers revolutionized the approach to the electronics readout of radiation detectors in Nuclear Physics. These highly specialized pieces of equipment are designed to acquire the signals that are characteristic of the detectors in nuclear physics experiments. The functions of the several modules that were once needed for signal acquisition, can now be substituted by a single digitizer. As suggested by the name, with such readout modules, signals are first digitized (i.e. the signal waveform is sampled and converted to a digital representation) and then either stored or analyzed on-the-fly. The performances can be comparable or better than the traditional analog counterparts, in terms of energy, time resolution, and acquisition rate. In this work, we investigate the use of general-purpose digital oscilloscopes as signal digitizers for nuclear detectors. In order to have a proper comparison, we employ a distributed data acquisition system (DAQ), that standardizes the interface between the hardware and the on-line data analysis. The signals, from a set of typical radiation detectors, are digitized and analyzed with the very same algorithms in order to avoid biases due to different software analysis. We compare two traditional signal digitizers (CAEN DT5725 and CAEN DT5751) to two low-cost digital oscilloscopes (Digilent Analog Discovery 2, and Red Pitaya STEMLab 125-14), in terms of their capabilities for spectroscopy (energy resolution), time resolution, pulse shape discrimination, and maximum acquisition rate.Comment: 17 pages, 8 figures, 4 tables, Prepared for submission to JINS

Material recognition with a 252Cf source

Material recognition is studied by measuring simultaneously the transmission of neutron and gamma rays produced by a time-tagged 252Cf source. Light elements (C,N,O) are identified by using the measured transmission versus neutron time of flight. The yield of the transmitted gamma ray as a function of energy provides high precision identification of the atomic number of the sample up to Z=83 . A tomography system, currently under construction, is described