An integrable semi-discretization of the Camassa-Holm equation and its determinant solution

An integrable semi-discretization of the Camassa-Holm equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of $N$-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton-cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented

On the tau-functions of the Degasperis-Procesi equation

The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and pfaffians, and the $\tau$-functions of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and Theoretical, to be publishe

Electric Charge Quantization

Experimentally it has been known for a long time that the electric charges of the observed particles appear to be quantized. An approach to understanding electric charge quantization that can be used for gauge theories with explicit $U(1)$ factors -- such as the standard model and its variants -- is pedagogically reviewed and discussed in this article. This approach uses the allowed invariances of the Lagrangian and their associated anomaly cancellation equations. We demonstrate that charge may be de-quantized in the three-generation standard model with massless neutrinos, because differences in family-lepton--numbers are anomaly-free. We also review the relevant experimental limits. Our approach to charge quantization suggests that the minimal standard model should be extended so that family-lepton--number differences are explicitly broken. We briefly discuss some candidate extensions (e.g. the minimal standard model augmented by Majorana right-handed neutrinos).Comment: 18 pages, LaTeX, UM-P-92/5

Solitary waves of nonlinear nonintegrable equations

Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first class, which includes the well known so-called truncation methods, one \textit{a priori} assumes a given class of expressions (polynomials, etc) for the unknown solution; the involved work can easily be done by hand but all solutions outside the given class are surely missed. In the second class, instead of searching an expression for the solution, one builds an intermediate, equivalent information, namely the \textit{first order} autonomous ODE satisfied by the solitary wave; in principle, no solution can be missed, but the involved work requires computer algebra. We present the application to the cubic and quintic complex one-dimensional Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation.Comment: 28 pages, chapter in book "Dissipative solitons", ed. Akhmediev, to appea

Search for Millicharged Particles at SLAC

Particles with electric charge q < 10^(-3)e and masses in the range 1--100 MeV/c^2 are not excluded by present experiments. An experiment uniquely suited to the production and detection of such "millicharged" particles has been carried out at SLAC. This experiment is sensitive to the infrequent excitation and ionization of matter expected from the passage of such a particle. Analysis of the data rules out a region of mass and charge, establishing, for example, a 95%-confidence upper limit on electric charge of 4.1X10^(-5)e for millicharged particles of mass 1 MeV/c^2 and 5.8X10^(-4)e for mass 100 MeV/c^2.Comment: 4 pages, REVTeX, multicol, 3 figures. Minor typo corrected. Submitted to Physical Review Letter

Stable multicolor periodic-wave arrays

We study the existence and stability of cnoidal periodic wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is the first example in physics of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons.Comment: 12 pages, 3 figure

Impact of COVID-19 on cardiovascular testing in the United States versus the rest of the world

Objectives: This study sought to quantify and compare the decline in volumes of cardiovascular procedures between the United States and non-US institutions during the early phase of the coronavirus disease-2019 (COVID-19) pandemic. Background: The COVID-19 pandemic has disrupted the care of many non-COVID-19 illnesses. Reductions in diagnostic cardiovascular testing around the world have led to concerns over the implications of reduced testing for cardiovascular disease (CVD) morbidity and mortality. Methods: Data were submitted to the INCAPS-COVID (International Atomic Energy Agency Non-Invasive Cardiology Protocols Study of COVID-19), a multinational registry comprising 909 institutions in 108 countries (including 155 facilities in 40 U.S. states), assessing the impact of the COVID-19 pandemic on volumes of diagnostic cardiovascular procedures. Data were obtained for April 2020 and compared with volumes of baseline procedures from March 2019. We compared laboratory characteristics, practices, and procedure volumes between U.S. and non-U.S. facilities and between U.S. geographic regions and identified factors associated with volume reduction in the United States. Results: Reductions in the volumes of procedures in the United States were similar to those in non-U.S. facilities (68% vs. 63%, respectively; p = 0.237), although U.S. facilities reported greater reductions in invasive coronary angiography (69% vs. 53%, respectively; p < 0.001). Significantly more U.S. facilities reported increased use of telehealth and patient screening measures than non-U.S. facilities, such as temperature checks, symptom screenings, and COVID-19 testing. Reductions in volumes of procedures differed between U.S. regions, with larger declines observed in the Northeast (76%) and Midwest (74%) than in the South (62%) and West (44%). Prevalence of COVID-19, staff redeployments, outpatient centers, and urban centers were associated with greater reductions in volume in U.S. facilities in a multivariable analysis. Conclusions: We observed marked reductions in U.S. cardiovascular testing in the early phase of the pandemic and significant variability between U.S. regions. The association between reductions of volumes and COVID-19 prevalence in the United States highlighted the need for proactive efforts to maintain access to cardiovascular testing in areas most affected by outbreaks of COVID-19 infection