Universality of slow decorrelation in KPZ growth

There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting fluctuations. In one-dimension, the KPZ class has the dynamical scaling exponent $z=3/2$, that means one should find a universal space-time limiting process under the scaling of time as $t\,T$, space like $t^{2/3} X$ and fluctuations like $t^{1/3}$ as $t\to\infty$. In this paper we provide evidence for this belief. We prove that under certain hypotheses, growth models display temporal slow decorrelation. That is to say that in the scalings above, the limiting spatial process for times $t\, T$ and $t\, T+t^{\nu}$ are identical, for any $\nu<1$. The hypotheses are known to be satisfied for certain last passage percolation models, the polynuclear growth model, and the totally / partially asymmetric simple exclusion process. Using slow decorrelation we may extend known fluctuation limit results to space-time regions where correlation functions are unknown. The approach we develop requires the minimal expected hypotheses for slow decorrelation to hold and provides a simple and intuitive proof which applied to a wide variety of models.Comment: Exposition improved, typos correcte

An electronic system for measuring thermophysical properties of wind tunnel models

An electronic system is described which measures the surface temperature of a small portion of the surface of the model or sample at high speeds using an infrared radiometer. This data is processed along with heating rate data from the reference heat gauge in a small computer and prints out the desired thermophysical properties, time, surface temperature, and reference heat rate. This system allows fast and accurate property measurements over thirty temperature increments. The technique, the details of the apparatus, the procedure for making these measurements, and the results of some preliminary tests are presented

The Establishment of Judicial Review II

In tracing the establishment of judicial review subsequently to the inauguration of the national government it will be important to bear in mind that there are two distinct kinds of judicial review, namely, federal judicial review, or the power of the federal courts to review acts of the State legislatures under the United States Constitution, and Judicial review proper; or the power of the courts to pass upon the constitutionality of acts of the coordinate legislatures. That the Judiciary Act of 1789 contemplated, in the mind of its author, Ellsworth, the exercise of the power of review by the national courts of acts of Congress can be scarcely doubted, but how far others accepted this view of the matter it is impossible even to conjecture, so entirely silent upon this point are the brief records of the debate. Perhaps the first congressional reference to such a power occurs in the House debate of February 21st, 1791, upon the bill to establish a national bank. Jackson of Georgia offered the argument that Congress ought not to adopt a measure which ran the risk being defeated by the judiciary of the United States, who might adjudge it to be contrary to the Constitution and therefore void.\u27 :an objection which however Boudinot of New Jersey and Smith of South Carolina were prompt to convert into an argument for the measure. Said the former, far from converting this right in the judiciary it was his boast and his confidence. It led him to greater decision on all subjects of a constitutional nature when he reflected that if, from inattention, want of precision or any other defect, he should do wrong, that there was a power in the government which could constitutionally prevent the operation of such a measure from affecting his constituents. There can be, I think, not the least doubt that a steadily developing feeling of unworthiness on the part of legislatures and a growing disposition to abdicate all final responsibility to the judiciary has been at once a cause and a consequence of the advancing power of the courts among us. It is therefore rather suggestive to come upon this point of view so early a date

The Establishment of Judicial Review (I)

When Gladstone described the Constitution of the United States as the most wonderful work ever struck off at a given time by the brain and purpose of man, his amiable intention to flatter was forgotten, while what was considered his gross historical error became at once a theme of adverse criticism. Their contemporaries and immediate posterity regarded the work of the Constitutional Fathers as the inspired product of political genius and essentially as a creation out of hand. Subsequently, due partly to the influence of the disciples of Savigny in the field of legal history, partly to the sway of the doctrine of evolution, and partly to a patriotic desire to claim for the Constitution a conformity to the historic spirit and needs of the American people like to that claimed for the English Constitution by English writers, and so inferentially, similar elements of durability, it has become the custom of writers to represent the Constitution as preeminently a deposit of time and event and to accord to the Fathers the substantial but more modest merit of having merely ratified the outcome of habit and usage. Tnis point of view, I am persuaded, has a large admixture of error and the other a correspondingly large element of truth. Because they were not utopists, because they had experienced some disillusionment from their earlier attempts at constitution-making, because they had some conception of the limits set by possibility, all this affords no adequate proof that the Fathers were not of their time and did not participate largely in its way of thinking. The collected wisdom acquired from a long succession of years is laid open for our use in the establishment of our forms of government, wrote Washington in 1783. Here exactly is the attitude of eighteenth century rationalism: its confidence in the reasoned and sifted results of human experience; its belief in the efficacy of ideas for the remedying of institutions, its firm persuasion more particularly of the existence of an available political science and of its mastery of that science,-such was the point of view of the latter quarter of the eighteenth century-the greatest era of reform in government that modern history has seen-such was the point of view of the Constitutional Fathers. They believed that the human reason can of ten intervene successfully to arrest the current of unreflective event and divert it to provided channels. They drew no fallacious line between the organic and the artificial, for their thinking admitted no such categories. Readers of Plutarch, they were confident of their ability to emulate the achievements of Lycurgus and Solon and leave a nation blessed with a polity accordant with its fundamental spirit and abiding necessities, a polity moreover which would be superior to all existing polities in that it would be founded upon nature and reason and not upon force or chance. But this being the point of view of the Fathers, it necessarily results that their indebtedness to the past was for ideas rather than for institutions. Whenever therefore they borrow from the past any of the really distinctive features of our constitutional system, for example Federalism, checks and balances, judicial review, they will be found to have taken them, not in the form of institutions tested and hammered into shape by practice, but as raw ideas

Power of Congress to Declare Peace

In the course of the discussion which has been aroused in Congress by the proposal to declare hostilities with Germany at an end by joint resolution, Senator Thomas of Colorado has brought forward evidence showing that on one occasion the Convention which framed the Constitution voted down unanimously a motion to vest Congress with the power to make peace. This evidence is good so far as it goes, but it does not support all of Senator Thomas\u27s deductions from it, nor indeed has he given an altogether complete account of it. The proposal in question was made and rejected by the Convention on August 17, 1787.1 One ground for its rejection was that the making of peace would naturally fall, not to the Executive, as Senator Thomas would have it, but to the treaty-making body, which was, by the plan at that date before the Convention, the Senate alone.2 And the principal argument which was offered against the proposal Senator Thomas ignores altogether. It was the argument made by Ellsworth and repeated by Madison, that! it should be more easy to get out of war than into it --the obvious deduction being that the, making of peace ought therefore to be lodged with a less cumbersome body than Congress. The Convention were apparently unacquainted with the single-track mind