N_pN_n dependence of empirical formula for the lowest excitation energy of the 2^+ states in even-even nuclei

We examine the effects of the additional term of the type $\sim e^{- \lambda' N_pN_n}$ on the recently proposed empirical formula for the lowest excitation energy of the $2^+$ states in even-even nuclei. This study is motivated by the fact that this term carries the favorable dependence of the valence nucleon numbers dictated by the $N_pN_n$ scheme. We show explicitly that there is not any improvement in reproducing $E_x(2_1^+)$ by including the extra $N_pN_n$ term. However, our study also reveals that the excitation energies $E_x(2_1^+)$, when calculated by the $N_pN_n$ term alone (with the mass number $A$ dependent term), are quite comparable to those calculated by the original empirical formula.Comment: 14 pages, 5 figure

Dynamic model for failures in biological systems

A dynamic model for failures in biological organisms is proposed and studied both analytically and numerically. Each cell in the organism becomes dead under sufficiently strong stress, and is then allowed to be healed with some probability. It is found that unlike the case of no healing, the organism in general does not completely break down even in the presence of noise. Revealed is the characteristic time evolution that the system tends to resist the stress longer than the system without healing, followed by sudden breakdown with some fraction of cells surviving. When the noise is weak, the critical stress beyond which the system breaks down increases rapidly as the healing parameter is raised from zero, indicative of the importance of healing in biological systems.Comment: To appear in Europhys. Let

(2,2)-Formalism of General Relativity: An Exact Solution

I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. After presenting the Einstein's field equations in this formalism, I solve them for spherically symmetric case to obtain the Schwarzschild solution. Then I discuss possible applications of this formalism.Comment: 2 figures included, IOP style file neede

Particle-in-cell and weak turbulence simulations of plasma emission

The plasma emission process, which is the mechanism for solar type II and type III radio bursts phenomena, is studied by means of particle-in-cell and weak turbulence simulation methods. By plasma emission, it is meant as a loose description of a series of processes, starting from the solar flare associated electron beam exciting Langmuir and ion-acoustic turbulence, and subsequent partial conversion of beam energy into the radiation energy by nonlinear processes. Particle-in-cell (PIC) simulation is rigorous but the method is computationally intense, and it is difficult to diagnose the results. Numerical solution of equations of weak turbulence (WT) theory, termed WT simulation, on the other hand, is efficient and naturally lends itself to diagnostics since various terms in the equation can be turned on or off. Nevertheless, WT theory is based upon a number of assumptions. It is, therefore, desirable to compare the two methods, which is carried out for the first time in the present paper with numerical solutions of the complete set of equations of the WT theory and with two-dimensional electromagnetic PIC simulation. Upon making quantitative comparisons it is found that WT theory is largely valid, although some discrepancies are also found. The present study also indicates that it requires large computational resources in order to accurately simulate the radiation emission processes, especially for low electron beam speeds. Findings from the present paper thus imply that both methods may be useful for the study of solar radio emissions as they are complementary.Comment: 21 pages, 9 figure

Synthesis and Activity of Six-Membered Cyclic Alkyl Amino Carbene–Ruthenium Olefin Metathesis Catalysts

Ru–cyclic alkyl amino carbene (Ru–CAAC) olefin metathesis catalysts perform extraordinarily in metathesis macrocyclization and ethenolysis, but previous studies have been limited to the use of five-membered CAAC (CAAC-5) ligands. In this work, we synthesized a different group of ruthenium catalysts with more σ-donating and π-accepting six-membered CAAC (CAAC-6) ligands, and their metathesis activity was probed through initiation studies, ring-closing metathesis (RCM), cross-metathesis, and ethenolysis. These catalysts display higher initiation rates than analogous Ru–CAAC-5 complexes but demonstrate lower activity in RCM and ethenolysis

Saturation, labile pools, distribution coefficients for soil phosphorus on Sanborn Field and other Missouri soils

June 1989"Publication authorized December 28, 1988"Includes bibliographical references (pages 4-5)

Crystallography data analysis at LCLS

Serial femtosecond crystallography is the process for which an ultrafast free-electron x-ray laser diffracts a protein crystal into its atomic structural basis. From these atomic structures, scientists can better understand the functions of the diffracted proteins. This is important because the protein structures obtained from this process can also provide valuable information that can help redesign medicinal drugs that will target diseases caused by certain proteins. One of the objectives for this research project is to work with a computational crystallography toolbox (CCBTX) that is still in development towards becoming an automated data analyzing software. We collect data by manually running the built in programs on python and analyzing the outputs given through a variety of parameters for commands such as averaging dark images and masking out bad pixels. This helps determine the efficiency of the built in software of the computational crystallography toolbox. Another objective was to use mathematical theory to calculate the sigma level of an automated peak finding threshold on a given peak value. Further more, we calculated the the probability of obtaining the peak value desired and verified the accuracy of the mathematical derivation through a python simulation on Jupyter Notebook

The Visible Trial: Judicial Assessment as Adjudication

Only a small fraction of lawsuits ends in trial—a phenomenon termed the “vanishing trial.” Critics of the declining trial rate see a remote, increasingly regressive judicial system. Defenders see a system that allows parties to resolve disputes independently. Analyzing criminal and civil filings in federal district court for the forty-year period from 1980 to 2019, we confirm a steady decline in the absolute and relative number of trials. We find, however, this emphasis on trial rate obscures courts’ vital role and ignores parties’ goals. Judges adjudicate disputes directly by ruling or effectively through other assessments of the parties’ cases. Even as their absolute and relative numbers decrease, trials remain the most visible event in trial courts. The visible trial serves effectively as a guide star. Our findings warrant a fundamental reconceptualization of litigation as primarily about educating parties rather than about trying cases. The assessment theory proposed here views adjudication as a continuous, information-disclosing process that is guided by but not destined for trial. Our evaluation and expectations of the modern justice system should be focused on the effectiveness of judges as teachers

Measuring Justice in State Courts: The Demographics of the State Judiciary

For most individuals and organizations, state courts--especially state trial courts-are the law for all effective purposes. State courts are America\u27s courts. But, we know surprisingly little about state court judges despite their central and powerful role in lawmaking and dispute resolution. This lack of information is especially significant because judges\u27 backgrounds have important implications for the work of courts. The characteristics of those who sit in judgment affect the internal workings of courts as well as the external perception of those courts and judges. The background of judges will influence how they make decisions and can impact the public\u27s acceptance of those decisions. We aim to address this knowledge gap by collecting demographics on state judges in every state. We discovered, however, that the task is extraordinarily difficult due to many factors, including a lack of transparency and an abundant complexity in our state court systems. In this Article, we describe and evaluate the difficulty of studying state courts and the importance of continued efforts to do so. We explain a variety of methods to overcome some of the research challenges. We then lay out our findings on state court demographics. The process and outcome of our project can inform study of the judiciary and its place in our political system. We hope too they will encourage and facilitate future empirical study of state courts

Chief Judges: The Limits of Attitudinal Theory and Possible Paradox of Managerial Judging

Grutter v. Bollinger is familiar to American lawyers, academics, and law students as the Supreme Court decision allowing the consideration of race in law school admissions.1 Grutter\u27s procedural history is nearly as noteworthy as its substantive holding. The University of Michigan Law School, after losing in federal district court, appealed to the U.S. Court of Appeals for the Sixth Circuit. Three Democratic appointees were assigned to the panel: Judges Karen Nelson Moore and Martha Craig Daughtrey, who had heard an earlier interlocutory appeal, and Chief Judge Boyce Martin, who replaced the designated district judge from the earlier panel. The white applicant reqiiested that the entire court, rather than a panel, hear the case. The Sixth Circuit granted the en banc petition. A closely divided en banc court reversed the district court in an opinion authored by Martin. Normally, that is all we would know about the process by which the Sixth Circuit decided the case. But something highly unusual happened. Judge Danny Boggs included with his dissenting opinion a five-page procedural appendix detailing intracourt machinations and accusing the Chief Judge of manipulating procedures to affect the outcome. Boggs alleged that Martin violated circuit rules by assigning himself, rather than a randomly selected judge, to the three-judge panel. This assertion alone does not seem very significant-the case was decided, after all, by the en banc court. Boggs\u27s more pointed accusation was that Martin engineered the en banc voting process to ensure a court balanced in favor of the law school. When the white student petitioned for an en banc hearing, eleven active judges sat on the Sixth Circuit; two of those judges had expressed their intent to take senior status.10 Martin circulated the petition after both judges had taken senior status, making them ineligible to participate. Judge Alice Batchelder responded by writing an internal memo to her colleagues contending that Martin delayed the vote on the white student\u27s request for a hearing en banc until judges opposed to affirmative action took senior status. Boggs\u27s dissent made public those accusations, a fact that one colleague called shameful, and another embarrassing and incomprehensible. Accusations like those made in Grutter are consistent with the attitudinal theory of judicial decisionmaking. Attitudinal theory proffers that judges are political actors who make decisions that will maximize their policy preferences. Developed primarily by political scientists, this approach has gained increasing currency in legal scholarship. If the theory is an accurate account of any judicial action on the courts of appeals, we would expect, at a minimum, to see evidence in the behavior of chief judges, who have more opportunities than other circuit judges to achieve policy goals. Chief judges may behave attitudinally in exercising their formal powers as well as their informal authority and influence