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J. C. Valenzuela

Publications and source records attributed to J. C. Valenzuela.

2 recordsLinked to original sources

3D Dynamics of a Premagnetized Gas-puff Z-pinch implosion

We present the first simultaneous, spatially-resolved measurement of all three velocity components (radial, azimuthal, and axial) in an annular magnetized argon gas-puff Z-pinch, performed using Collective Thomson Scattering along three orthogonal lines of sight from the same scattering volume at each time step. Measurements were carried out on the Llamp{ü}dke{ñ} pulse-power generator (400 kA peak, 200 ns rise time), for applied axial fields ranging from 0.04 to 0.26 T using two coil configurations: a double coil with negligible initial radial field at the probed plane ($z = 8$ mm), and a single coil that imposes a finite initial radial field. Three principal results are reported. First, the axial velocity component, which had not previously been measured experimentally in this configuration, reaches 60--70~km\,s$^{-1}$ near the axis at low applied fields ($B_{z0} < 0.1$ T) and is suppressed to within $\pm 20$~km\,s$^{-1}$ for stronger applied fields, in correlation with the reduction of the zippering angle, with direct implications for the implosion energy balance. Second, the self-generated rotation extends across the full plasma diameter, not only at the periphery, and the diametrical profile of the azimuthal velocity decreases toward the axis with an exponential-like shape consistent with the underlying current density distribution; this feature was not visible in previous edge-localized measurements. Third, rotation persists in the double-coil case ($B_{r0} \approx 0$) and is enhanced in the single-coil case (finite $B_{r0}$), supporting the interpretation that $B_r$ develops self-consistently during the implosion and drives the rotation through a $J_z \times B_r$ torque. These results constrain the role of each magnetic-field component and motivate direct measurement of $B_r$ and the current density distribution as the next step.

physics.plasm-ph

On the Strong Roman Domination Number of Graphs

Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a "stronger" neighbor place (having two legions), a graph theoretical model called Roman domination in graphs was described. A Roman dominating function for a graph $G=(V,E)$, is a function $f:V\rightarrow \{0,1,2\}$ such that every vertex $v$ with $f(v)=0$ has at least a neighbor $w$ in $G$ for which $f(w)=2$. The Roman domination number of a graph is the minimum weight, $\sum_{v\in V}f(v)$, of a Roman dominating function. In this paper we initiate the study of a new parameter related to Roman domination, which we call strong Roman domination number and denote it by $γ_{StR}(G)$. We approach the problem of a Roman domination-type defensive strategy under multiple simultaneous attacks and begin with the study of several mathematical properties of this invariant. In particular, we first show that the decision problem regarding the computation of the strong Roman domination number is NP-complete, even when restricted to bipartite graphs. We obtain several bounds on such a parameter and give some realizability results for it. Moreover, we prove that for any tree $T$ of order $n\ge 3$, $γ_{StR}(T)\le 6n/7$ and characterize all extremal trees.

math.CO