The Fourier transform
converts the function's time-domain representation, shown in red, to
the function's frequency-domain representation, shown in blue. The
component frequencies, spread across the frequency spectrum, are
represented as peaks in the frequency domain.
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series. Put simply, a time-domain
graph shows how a signal changes over time, whereas a frequency-domain
graph shows how the signal is distributed within different frequency
bands over a range of frequencies. A complex valued frequency-domain
representation consists of both the magnitude and the phase of a set of sinusoids
(or other basis waveforms) at the frequency components of the signal.
Although it is common to refer to the magnitude portion (the real valued
frequency-domain) as the frequency response of a signal, the phase
portion is required to uniquely define the signal.
A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called transforms. An example is the Fourier transform, which converts a time function into a complex valued sum or integral of sine waves of different frequencies, with amplitudes and phases, each of which represents a frequency component. The "spectrum" of frequency components is the frequency-domain representation of the signal. The inverse Fourier transform converts the frequency-domain function back to the time-domain function. A spectrum analyzer is a tool commonly used to visualize electronic signals in the frequency domain.
A frequency-domain representation may describe either a static
function or a particular time period of a dynamic function (signal or
system). The frequency transform of a dynamic function is performed over
a finite time period of that function and assumes the function repeats
infinitely outside of that time period. Some specialized signal
processing techniques for dynamic functions use transforms that result
in a joint time–frequency domain, with the instantaneous frequency response being a key link between the time domain and the frequency domain.
Advantages
One
of the main reasons for using a frequency-domain representation of a
problem is to simplify the mathematical analysis. For mathematical
systems governed by linear differential equations,
a very important class of systems with many real-world applications,
converting the description of the system from the time domain to a
frequency domain converts the differential equations to algebraic equations, which are much easier to solve.
An example of a field in which frequency-domain analysis gives a better understanding than time domain is music; the theory of operation of musical instruments and the musical notation
used to record and discuss pieces of music is implicitly based on the
breaking down of complex sounds into their separate component
frequencies (musical notes).
Magnitude and phase
In using the Laplace, Z-, or Fourier transforms, a signal is described by a complex function of frequency: the component of the signal at any given frequency is given by a complex number. The modulus of the number is the amplitude of that component, and the argument is the relative phase of the wave. For example, using the Fourier transform, a sound wave,
such as human speech, can be broken down into its component tones of
different frequencies, each represented by a sine wave of a different
amplitude and phase. The response of a system, as a function of
frequency, can also be described by a complex function. In many
applications, phase information is not important. By discarding the
phase information, it is possible to simplify the information in a
frequency-domain representation to generate a frequency spectrum or spectral density. A spectrum analyzer is a device that displays the spectrum, while the time-domain signal can be seen on an oscilloscope.
Types
Although "the"
frequency domain is spoken of in the singular, there is a number of
different mathematical transforms which are used to analyze time-domain
functions and are referred to as "frequency domain" methods. These are
the most common transforms, and the fields in which they are used:
More generally, one can speak of the transform domain
with respect to any transform. The above transforms can be interpreted
as capturing some form of frequency, and hence the transform domain is
referred to as a frequency domain.
A periodic signal has energy only at a base frequency and its harmonics; thus it can be analyzed using a discrete frequency domain. A discrete-time signal
gives rise to a periodic frequency spectrum. In a situation where both
these conditions occur, a signal which is discrete and periodic results
in a frequency spectrum which is also discrete and periodic; this is the
usual context for a discrete Fourier transform.
History of term
The use of the terms "frequency domain" and "time domain" arose in communication engineering in the 1950s and early 1960s, with "frequency domain" appearing in 1953. See time domain: origin of term for details.
The edge of chaos is a transition space between order and disorder
that is hypothesized to exist within a wide variety of systems. This
transition zone is a region of bounded instability that engenders a
constant dynamic interplay between order and disorder.
Even though the idea of the edge of chaos is an abstract one, it has many applications in such fields as ecology, business management, psychology, political science, and other domains of the social sciences. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.
History
The phrase edge of chaos was coined in the late 1980s by chaos theory physicist Norman Packard.In the next decade, Packard and mathematician Doyne Farmer co-authored many papers on understanding how self-organization and order emerges at the edge of chaos. One of the original catalysts that led to the idea of the edge of chaos were the experiments with cellular automata done by computer scientistChristopher Langton where a transition phenomenon was discovered. The phrase refers to an area in the range of a variable, λ (lambda), which was varied while examining the behaviour of a cellular automaton (CA). As λ varied, the behaviour of the CA went through a phase transition of behaviours. Langton found a small area conducive to produce CAs capable of universal computation.At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.
In the sciences in general, the phrase has come to refer to a
metaphor that some physical, biological, economic and social systems
operate in a region between order and either complete randomness or chaos, where the complexity is maximal.
The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others.
The phrase has also been borrowed by the business community and is
sometimes used inappropriately and in contexts that are far from the
original scope of the meaning of the term.
Adaptation
plays a vital role for all living organisms and systems. All of them
are constantly changing their inner properties to better fit in the
current environment. The most important instruments for the adaptation are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".
Adaptation to the edge of chaos refers to the idea that many complex adaptive systems (CASs) seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics has shown that edge of chaos is the optimal settings for control of a system.
It is also an optional setting that can influence the ability of a
physical system to perform primitive functions for computation. In CAS, coevolution
generally occurs near the edge of chaos, and a balance should be
maintained between flexibility and stability to avoid structural
failure. As a response to coping with turbulent environments, CAS bring out flexibility, creativity, agility, anti-fragility, and innovation near the edge of chaos, provided these systems are sufficiently decentralized and non-hierarchical.
Because of the importance of adaptation in many natural systems,
adaptation to the edge of the chaos takes a prominent position in many
scientific researches. Physicists demonstrated that adaptation to state
at the boundary of chaos and order occurs in population of cellular automata rules which optimize the performance evolving with a genetic algorithm. Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.
The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos.
Theoretical analysis allowed prediction of the location of the narrow
parameter regime near the boundary to which the system evolves.
Cerebrovascular disease includes a variety of medical conditions that affect the blood vessels of the brain and the cerebral circulation. Arteries supplying oxygen and nutrients to the brain are often damaged or deformed in these disorders. The most common presentation of cerebrovascular disease is an ischemic stroke or mini-stroke and sometimes a hemorrhagic stroke. Hypertension (high blood pressure) is the most important contributing risk factor for stroke and cerebrovascular diseases as it can change the structure of blood vessels and result in atherosclerosis.
Atherosclerosis narrows blood vessels in the brain, resulting in
decreased cerebral perfusion. Other risk factors that contribute to
stroke include smoking and diabetes. Narrowed cerebral arteries can lead to ischemic stroke, but continually elevated blood pressure can also cause tearing of vessels, leading to a hemorrhagic stroke.
A stroke usually presents with an abrupt onset of a neurologic deficit – such as hemiplegia (one-sided weakness), numbness, aphasia (language impairment), or ataxia (loss of coordination) – attributable to a focal vascular lesion.
The neurologic symptoms manifest within seconds because neurons need a
continual supply of nutrients, including glucose and oxygen, that are
provided by the blood. Therefore, if blood supply to the brain is
impeded, injury and energy failure is rapid.
Besides hypertension, there are also many less common causes of cerebrovascular disease, including those that are congenital or idiopathic and include CADASIL, aneurysms, amyloid angiopathy, arteriovenous malformations, fistulas, and arterial dissections. Many of these diseases can be asymptomatic until an acute event, such as a stroke, occurs. Cerebrovascular diseases can also present less commonly with headache or seizures. Any of these diseases can result in vascular dementia due to ischemic damage to the brain.
Signs and symptoms
Types of brain herniation
The most common presentation of cerebrovascular diseases is an acute
stroke, which occurs when blood supply to the brain is compromised. Symptoms of stroke are usually rapid in onset, and may include weakness of one side of the face or body, numbness on one side of the face or body, inability to produce or understand speech, vision changes, and balance difficulties.
Hemorrhagic strokes can present with a very severe, sudden headache
associated with vomiting, neck stiffness, and decreased consciousness.
Symptoms vary depending on the location and the size of the area of
involvement of the stroke. Edema, or swelling, of the brain may occur
which increases intracranial pressure and may result in brain herniation. A stroke may result in coma or death if it involves key areas of the brain.
Other symptoms of cerebrovascular disease include migraines,
seizures, epilepsy, or cognitive decline. However, cerebrovascular
disease may go undetected for years until an acute stroke occurs. In
addition, patients with some rare congenital cerebrovascular diseases
may begin to have these symptoms in childhood.
Causes
Congenital
Congenital diseases are medical conditions that are present at birth that may be associated with or inherited through genes. Examples of congenital cerebrovascular diseases include arteriovenous malformations, germinal matrix hemorrhage, and CADASIL (cerebral autosomal-dominant arteriopathy with subcortical infarcts and leukoencephalopathy). Arteriovenous malformations are abnormal tangles of blood vessels. Usually, a capillary bed
separates arteries from veins, which protects the veins from the higher
blood pressures that occur in arteries. In arteriovenous malformations,
arteries are directly connected to veins, which increases the risk of
venous rupture and hemorrhage. Cerebral arteriovenous malformations
in the brain have a 2–4% chance of rupture each year. However, many
arteriovenous malformations go unnoticed and are asymptomatic throughout
a person's lifetime.
A germinal matrix hemorrhage
is bleeding into the brain of premature infants caused by the rupture
of fragile blood vessels within the germinal matrix of premature babies.
The germinal matrix is a highly vascularized area within an unborn
infant's brain from which brain cells, including neurons and glial
cells, originate. Infants are at most risk to germinal matrix
hemorrhages when they are born prematurely, before 32 weeks.
The stresses exposed after birth, along with the fragile blood vessels,
increase risk of hemorrhage. Signs and symptoms include flaccid
weakness, seizures, abnormal posturing, or irregular respiration.
CADASIL is an inherited disorder caused by mutations in the NOTCH3 gene located on chromosome 19. NOTCH3 codes for a transmembrane protein
whose function is not well-known. However, the mutation causes
accumulation of this protein within small to medium-sized blood vessels.
This disease often presents in early adulthood with migraines, stroke,
mood disturbances, and cognitive deterioration. MRI shows white matter changes in the brain and also signs of repeated strokes. The diagnosis can be confirmed by gene testing.
Acquired
Acquired
cerebrovascular diseases are those that are obtained throughout a
person's life that may be preventable by controlling risk factors. The
incidence of cerebrovascular disease increases as an individual ages. Causes of acquired cerebrovascular disease include atherosclerosis, embolism, aneurysms, and arterial dissections.
Atherosclerosis leads to narrowing of blood vessels and less perfusion
to the brain, and it also increases the risk of thrombosis, or a
blockage of an artery, within the brain. Major modifiable risk factors
for atherosclerosis include:
Illustration of a cerebral aneurysm, demonstrating the bulge in an artery in the brain
Controlling these risk factors can reduce the incidence of atherosclerosis and stroke. Atrial fibrillation
is also a major risk factor for strokes. Atrial fibrillation causes
blood clots to form within the heart, which may travel to the arteries
within the brain and cause an embolism. The embolism prevents blood flow
to the brain, which leads to a stroke.
An aneurysm
is an abnormal bulging of small sections of arteries, which increases
the risk of artery rupture. Intracranial aneurysms are a leading cause
of subarachnoid hemorrhage,
or bleeding around the brain within the subarachnoid space. There are
various hereditary disorders associated with intracranial aneurysms,
such as Ehlers-Danlos syndrome, autosomal dominant polycystic kidney disease, and familial hyperaldosteronism type I.
However, individuals without these disorders may also obtain aneurysms.
The American Heart Association and American Stroke Association
recommend controlling modifiable risk factors including smoking and
hypertension.
Arterial dissections are tears of the internal lining of arteries, often associated with trauma. Dissections within the carotid arteries or vertebral arteries may compromise blood flow to the brain due to thrombosis, and dissections increase the risk of vessel rupture.
Idiopathic
Idiopathic diseases are those that occur spontaneously without a known cause. Moyamoya is an example of an idiopathic cerebrovascular disorder that results in narrowing and occlusion of intracranial blood vessels.
The most common presentation is stroke or transient ischemic attack,
but cognitive decline within children may also be a presenting symptom. The disease may begin to show symptoms beginning in adolescence, but some may not have symptoms until adulthood.
Pathophysiology
Mechanism of brain cell death
When a reduction in blood flow lasting seconds occurs, the brain tissue suffers ischemia, or inadequate blood supply. If the interruption of blood flow is not restored in minutes, the tissue suffers infarction followed by tissue death.
When the low cerebral blood flow persists for a longer duration, this
may develop into an infarction in the border zones (areas of poor blood
flow between the major cerebral artery distributions). In more severe
instances, global hypoxia-ischemia causes widespread brain injury
leading to a severe cognitive sequelae called hypoxic-ischemic encephalopathy.
An ischemic cascade
occurs where an energetic molecular problem arises due to lack of
oxygen and nutrients. The cascade results in decreased production of adenosine triphosphate (ATP), which is a high-energy molecule needed for cells in the brain to function.
Consumption of ATP continues in spite of insufficient production, this
causes total levels of ATP to decrease and lactate acidosis to become
established (ionic homeostasis in neurons is lost). The downstream
mechanisms of the ischemic cascade thus begins. Ion pumps no longer
transport Ca2+ out of cell, this triggers release of
glutamate, which in turn allows calcium into cell walls. In the end the
apoptosis pathway is initiated and cell death occurs.
There are several arteries that supply oxygen to different areas
of the brain, and damage or occlusion of any of them can result in
stroke. The carotid arteries cover the majority of the cerebrum.
The common carotid artery divides into the internal and the external
carotid arteries. The internal carotid artery becomes the anterior
cerebral artery and the middle central artery. The ACA transmits blood
to the frontal parietal. From the basilar artery
are two posterior cerebral arteries. Branches of the basilar and PCA
supply the occipital lobe, brain stem, and the cerebellum.
Ischemia is the loss of blood flow to the focal region of the brain.
This produces heterogeneous areas of ischemia at the affected vascular
region, furthermore, blood flow is limited to a residual flow. Regions
with blood flow of less than 10 mL/100 g of tissue/min are core regions
(cells here die within minutes of a stroke). The ischemic penumbra with a blood flow of <25 ml/100g tissue/min, remain usable for more time (hours).
Types of stroke
There
are two main divisions of strokes: ischemic and hemorrhagic. Ischemic
stroke involves decreased blood supply to regions of the brain, while
hemorrhagic stroke is bleeding into or around the brain.
Transient ischemic attack (TIA) also called a mini-stroke.
This is a condition in which the blood flow to a region of the brain is
blocked, but blood flow is quickly restored and the brain tissue can
fully recover. The symptoms are only transient, leaving no sequelae, or long-term deficits. In order to diagnose this entity, all neurologic signs and symptoms must have been resolved within 24 hrs without evidence of brain infarction on brain imaging.
Hemorrhagic
Subarachnoid haemorrhage occurs when blood leaks out of damaged vessels into the cerebrospinal fluid in the subarachnoid space around the brain.
The most common cause of a subarachnoid hemorrhage is an aneurysm
rupture due to the weakened blood vessel walls and increased wall
stress.
The neurologic symptoms are produced by the blood mass effect on neural
structures, from the toxic effects of blood on the brain tissue, or by
the increasing of intracranial pressure.
Intracerebral haemorrhage is bleeding directly into the brain rather than around the brain. Causes and risk factors include hypertension, blood thinning medications, trauma, and arteriovenous malformations.
Diagnosis
MRI demonstrating white matter changes in the brain of patients with CADASIL
acute stroke imaging is generally performed in significant symptoms of new onset.
It is important to differentiate the symptoms caused by a stroke from those caused by syncope
(fainting) which is also a reduction in cerebral blood flow, almost
always generalized, but they are usually caused by systemic hypotension
of various origins: cardiac arrhythmias, myocardial infarction, hemorrhagic shock, among others.
calcium channel blockers - in particular Nimodipine reduces the incidence and severity of ischemic deficits in patients with subarachnoid hemorrhage (SAH)
Prognostics factors:
Lower Glasgow Coma Scale
score, higher pulse rate, higher respiratory rate and lower arterial
oxygen saturation level is prognostic features of in-hospital mortality
rate in acute ischemic stroke.
Worldwide, it is estimated there are 31 million stroke survivors,
though about 6 million deaths were due to cerebrovascular disease (2nd
most common cause of death in the world and 6th most common cause of
disability).
Cerebrovascular disease primarily occurs with advanced age; the
risk for developing it goes up significantly after 65 years of age. CVD
tends to occur earlier than Alzheimer's Disease (which is rare before
the age of 80). In some countries such as Japan, CVD is more common than AD.
In 2012, 6.4 million adults from the US had a stroke, which
corresponds to 2.7% of the US. This is approximately 129,000 deaths in
2013.
Geographically, a "stroke belt"
in the US has long been known, similar to the "diabetes belt" which
includes all of Mississippi and parts of Alabama, Arkansas, Florida,
Georgia, Kentucky, Louisiana, North Carolina, Ohio, Pennsylvania, South
Carolina, Tennessee, Texas, Virginia, and West Virginia.
Balance of trade is the difference between the monetary value of a nation's exports and imports over a certain time period. Sometimes a distinction is made between a balance of trade for goods versus one for services. The balance of trade measures a flow variable
of exports and imports over a given period of time. The notion of the
balance of trade does not mean that exports and imports are "in balance"
with each other.
If a country exports a greater value than it imports, it has a trade surplus or positive trade balance, and conversely, if a country imports a greater value than it exports, it has a trade deficit or negative trade balance. As of 2016, about 60 out of 200 countries have a trade surplus.
The notion that bilateral trade deficits are per se detrimental to the
respective national economies is overwhelmingly rejected by trade
experts and economists.
Explanation
Balance of trade in goods and services (Eurozone countries)US trade balance from 1960U.S. trade balance and trade policy (1895–2015)U.K. balance of trade in goods (since 1870)
The balance of trade forms part of the current account, which includes other transactions such as income from the net international investment position
as well as international aid. If the current account is in surplus, the
country's net international asset position increases correspondingly.
Equally, a deficit decreases the net international asset position.
The trade balance is identical to the difference between a
country's output and its domestic demand (the difference between what
goods a country produces and how many goods it buys from abroad; this
does not include money re-spent on foreign stock, nor does it factor in
the concept of importing goods to produce for the domestic market).
Measuring the balance of trade can be problematic because of
problems with recording and collecting data. As an illustration of this
problem, when official data for all the world's countries are added up,
exports exceed imports by almost 1%; it appears the world is running a
positive balance of trade with itself. This cannot be true, because all
transactions involve an equal credit or debit
in the account of each nation. The discrepancy is widely believed to be
explained by transactions intended to launder money or evade taxes,
smuggling and other visibility problems. While the accuracy of
developing countries' statistics would be suspicious, most of the
discrepancy actually occurs between developed countries of trusted
statistics.
Factors that can affect the balance of trade include:
The cost of production (land, labor, capital, taxes, incentives, etc.) in the exporting economy vis-à-vis those in the importing economy;
The cost and availability of raw materials, intermediate goods and other inputs;
Currency exchange rate movements;
Multilateral, bilateral and unilateral taxes or restrictions on trade;
Non-tariff barriers such as environmental, health or safety standards;
The availability of adequate foreign exchange with which to pay for imports; and
Prices of goods manufactured at home (influenced by the responsiveness of supply)
In addition, the trade balance is likely to differ across the business cycle.
In export-led growth (such as oil and early industrial goods), the
balance of trade will shift towards exports during an economic
expansion.
However, with domestic demand-led growth (as in the United States and
Australia) the trade balance will shift towards imports at the same
stage in the business cycle.
The monetary balance of trade is different from the physical balance of trade
(which is expressed in amount of raw materials, known also as Total
Material Consumption). Developed countries usually import a substantial
amount of raw materials from developing countries. Typically, these
imported materials are transformed into finished products and might be
exported after adding value. Financial trade balance statistics conceal
material flow. Most developed countries have a large physical trade
deficit because they consume more raw materials than they produce.
Many countries in early modern Europe adopted a policy of mercantilism,
which theorized that a trade surplus was beneficial to a country.
Mercantilist ideas also influenced how European nations regulated trade
policies with their colonies, promoting the idea that natural resources
and cash crops should be exported to Europe, with processed goods being exported back to the colonies in return. Ideas such as bullionism spurred the popularity of mercantilism in European governments.
Merchandise exports (1870–1992)Trade policy, exports and growth in selected European countries
An early statement concerning the balance of trade appeared in Discourse of the Common Wealth of this Realm of England,
1549: "We must always take heed that we buy no more from strangers than
we sell them, for so should we impoverish ourselves and enrich them." Similarly, a systematic and coherent explanation of balance of trade was made public through Thomas Mun's 1630 "England's treasure by foreign trade, or, The balance of our foreign trade is the rule of our treasure".
Since the mid-1980s, the United States has had a growing deficit in tradeable goods,
especially with Asian nations (China and Japan) which now hold large
sums of U.S. debt that has in part funded the consumption.
The U.S. has a trade surplus with nations such as Australia. The issue
of trade deficits can be complex. Trade deficits generated in tradeable
goods such as manufactured goods or software may impact domestic
employment to different degrees than do trade deficits in raw materials.
Economies that have savings surpluses, such as Japan and Germany,
typically run trade surpluses. China, a high-growth economy, has tended
to run trade surpluses. A higher savings rate generally corresponds to a
trade surplus. Correspondingly, the U.S. with its lower savings rate
has tended to run high trade deficits, especially with Asian nations.
Some have said that China pursues a mercantilist economic policy.
Russia pursues a policy based on protectionism, according to which
international trade is not a "win-win" game but a zero-sum game: surplus
countries get richer at the expense of deficit countries.
Views on economic impact
The
notion that bilateral trade deficits are bad in and of themselves is
overwhelmingly rejected by trade experts and economists. According to the IMF trade deficits can cause a balance of payments problem, which can affect foreign exchange shortages and hurt countries. On the other hand, Joseph Stiglitz
points out that countries running surpluses exert a "negative
externality" on trading partners, and pose a threat to global
prosperity, far more than those in deficit. Ben Bernanke
argues that "persistent imbalances within the euro zone are...
unhealthy, as they lead to financial imbalances as well as to unbalanced
growth. The fact that Germany is selling so much more than it is buying
redirects demand from its neighbors (as well as from other countries
around the world), reducing output and employment outside Germany." According to Carla Norrlöf, there are three main benefits to trade deficits for the United States:
Greater consumption than production: the US enjoys the better side of the bargain by being able to consume more than it produces
Usage of efficiently produced foreign-made intermediate goods is
productivity-enhancing for US firms: the US makes the most effective use
of the global division of labor
A large market that other countries are reliant on for exports enhances American bargaining power in trade negotiations
A 2018 National Bureau of Economic Research paper by economists at
the International Monetary Fund and University of California, Berkeley,
found in a study of 151 countries over 1963-2014 that the imposition of
tariffs had little effect on the trade balance.
In the foregoing part of this
chapter I have endeavoured to show, even upon the principles of the
commercial system, how unnecessary it is to lay extraordinary restraints
upon the importation of goods from those countries with which the
balance of trade is supposed to be disadvantageous.
Nothing, however, can be more absurd than this whole doctrine of the
balance of trade, upon which, not only these restraints, but almost all
the other regulations of commerce are founded. When two places trade
with one another, this [absurd] doctrine supposes that, if the balance
be even, neither of them either loses or gains; but if it leans in any
degree to one side, that one of them loses and the other gains in
proportion to its declension from the exact equilibrium.
— Smith, 1776, book IV, ch. iii, part ii
Keynesian theory
In the last few years of his life, John Maynard Keynes was much preoccupied with the question of balance in international trade. He was the leader of the British delegation to the United Nations Monetary and Financial Conference in 1944 that established the Bretton Woods system of international currency management.
He was the principal author of a proposal – the so-called Keynes Plan – for an International Clearing Union.
The two governing principles of the plan were that the problem of
settling outstanding balances should be solved by 'creating' additional
'international money', and that debtor and creditor should be treated
almost alike as disturbers of equilibrium. In the event, though, the
plans were rejected, in part because "American opinion was naturally
reluctant to accept the principle of equality of treatment so novel in
debtor-creditor relationships".
The new system is not founded on free-trade (liberalisation of foreign trade)
but rather on the regulation of international trade, in order to
eliminate trade imbalances: the nations with a surplus would have a
powerful incentive to get rid of it, and in doing so they would
automatically clear other nations' deficits.
He proposed a global bank that would issue its own currency – the
bancor – which was exchangeable with national currencies at fixed rates
of exchange and would become the unit of account between nations, which
means it would be used to measure a country's trade deficit or trade
surplus. Every country would have an overdraft facility in its bancor
account at the International Clearing Union. He pointed out that
surpluses lead to weak global aggregate demand – countries running
surpluses exert a "negative externality" on trading partners, and posed
far more than those in deficit, a threat to global prosperity.
In "National Self-Sufficiency" The Yale Review, Vol. 22, no. 4 (June 1933), he already highlighted the problems created by free trade.
His view, supported by many economists and commentators at the
time, was that creditor nations may be just as responsible as debtor
nations for disequilibrium in exchanges and that both should be under an
obligation to bring trade back into a state of balance. Failure for
them to do so could have serious consequences. In the words of Geoffrey Crowther, then editor of The Economist,
"If the economic relationships between nations are not, by one means or
another, brought fairly close to balance, then there is no set of
financial arrangements that can rescue the world from the impoverishing
results of chaos."
These ideas were informed by events prior to the Great Depression
when – in the opinion of Keynes and others – international lending,
primarily by the U.S., exceeded the capacity of sound investment and so
got diverted into non-productive and speculative uses, which in turn
invited default and a sudden stop to the process of lending.
Influenced by Keynes, economics texts in the immediate post-war
period put a significant emphasis on balance in trade. For example, the
second edition of the popular introductory textbook, An Outline of Money,
devoted the last three of its ten chapters to questions of foreign
exchange management and in particular the 'problem of balance'. However,
in more recent years, since the end of the Bretton Woods system in 1971, with the increasing influence of monetarist
schools of thought in the 1980s, and particularly in the face of large
sustained trade imbalances, these concerns – and particularly concerns
about the destabilising effects of large trade surpluses – have largely
disappeared from mainstream economics discourse and Keynes' insights have slipped from view.
Monetarist theory
Prior to 20th-century monetarist theory, the 19th-century economist and philosopher Frédéric Bastiat
expressed the idea that trade deficits actually were a manifestation of
profit, rather than a loss. He proposed as an example to suppose that
he, a Frenchman, exported French wine and imported British coal, turning
a profit. He supposed he was in France and sent a cask of wine which
was worth 50 francs to England. The customhouse would record an export
of 50 francs. If in England, the wine sold for 70 francs (or the pound
equivalent), which he then used to buy coal, which he imported into
France (the customhouse would record an import of 70 francs), and was
found to be worth 90 francs in France, he would have made a profit of 40
francs. But the customhouse would say that the value of imports
exceeded that of exports and was trade deficit of 20 against the ledger
of France.This is not true for the current account that would be in
surplus.
By reductio ad absurdum,
Bastiat argued that the national trade deficit was an indicator of a
successful economy, rather than a failing one. Bastiat predicted that a
successful, growing economy would result in greater trade deficits, and
an unsuccessful, shrinking economy would result in lower trade deficits.
This was later, in the 20th century, echoed by economist Milton Friedman.
In the 1980s, Friedman, a Nobel Memorial Prize-winning economist and a proponent of monetarism,
contended that some of the concerns of trade deficits are unfair
criticisms in an attempt to push macroeconomic policies favorable to
exporting industries.
Friedman argued that trade deficits are not necessarily
important, as high exports raise the value of the currency, reducing
aforementioned exports, and vice versa for imports, thus naturally
removing trade deficits not due to investment. Since 1971, when
the Nixon administration decided to abolish fixed exchange rates,
America's Current Account accumulated trade deficits have totaled $7.75
trillion as of 2010. This deficit exists as it is matched by investment
coming into the United States – purely by the definition of the balance
of payments, any current account deficit that exists is matched by an
inflow of foreign investment.
In the late 1970s and early 1980s, the U.S. had experienced high
inflation and Friedman's policy positions tended to defend the stronger
dollar at that time. He stated his belief that these trade deficits were
not necessarily harmful to the economy at the time since the currency
comes back to the country (country A sells to country B, country B sells
to country C who buys from country A, but the trade deficit only
includes A and B). However, it may be in one form or another including
the possible tradeoff of foreign control of assets. In his view, the
"worst-case scenario" of the currency never returning to the country of
origin was actually the best possible outcome: the country actually
purchased its goods by exchanging them for pieces of cheaply made paper.
As Friedman put it, this would be the same result as if the exporting
country burned the dollars it earned, never returning it to market
circulation.
This position is a more refined version of the theorem first discovered by David Hume.
Hume argued that England could not permanently gain from exports,
because hoarding gold (i.e., currency) would make gold more plentiful in
England; therefore, the prices of English goods would rise, making them
less attractive exports and making foreign goods more attractive
imports. In this way, countries' trade balances would balance out.
Friedman presented his analysis of the balance of trade in Free to Choose, widely considered his most significant popular work.
Trade balance’s effects upon a nation's GDP
Exports
directly increase and imports directly reduce a nation's balance of
trade (i.e. net exports). A trade surplus is a positive net balance of
trade, and a trade deficit is a negative net balance of trade. Due to
the balance of trade being explicitly added to the calculation of the
nation's gross domestic product using the expenditure method of
calculating gross domestic product (i.e. GDP), trade surpluses are
contributions and trade deficits are "drags" upon their nation's GDP;
however, foreign made goods sold (e.g., retail) contribute to total GDP.
Includes only visible imports and exports, i.e. imports and exports
of merchandise. The difference between exports and imports is called the
balance of trade. If imports are greater than exports, it is sometimes
called an unfavourable balance of trade. If exports exceed imports, it
is sometimes called a favourable balance of trade.
Includes all those visible and invisible items exported from and
imported into the country in addition to exports and imports of
merchandise.
Includes revenues received or paid on account of imports and exports of merchandise. It shows only revenue items.
Includes all revenue and capital items whether visible or
non-visible. The balance of trade thus forms a part of the balance of
payments.
Surface temperatures
in the western North Atlantic: Most of the North American landmass is
black and dark blue (cold), while the Gulf Stream is red (warm). Source:
NASA
The Gulf Stream is a warm and swift Atlanticocean current that originates in the Gulf of Mexico and flows through the Straits of Florida
and up the eastern coastline of the United States, then veers east near
36°N latitude (North Carolina) and moves toward Northwest Europe as
the North Atlantic Current. The process of western intensification causes the Gulf Stream to be a northward-accelerating current off the east coast of North America. Around 40°0′N30°0′W,
it splits in two, with the northern stream, the North Atlantic Drift,
crossing to Northern Europe and the southern stream, the Canary Current, recirculating off West Africa.
The Gulf Stream influences the climate of the coastal areas of
the East Coast of the United States from Florida to southeast Virginia
(near 36°N latitude), and to a greater degree, the climate of Northwest
Europe. A consensus exists that the climate of Northwest Europe is
warmer than other areas of similar latitude at least partially because
of the strong North Atlantic Current. It is part of the North Atlantic Gyre. Its presence has led to the development of strong cyclones of all types, both within the atmosphere and within the ocean.
History
Benjamin Franklin's chart of the Gulf Stream printed in London in 1769
European discovery of the Gulf Stream dates to the 1512 expedition of Juan Ponce de León, after which it became widely used by Spanish ships sailing from the Caribbean to Spain.
A summary of Ponce de León's voyage log on April 22, 1513, noted, "A
current such that, although they had great wind, they could not proceed
forwards, but backwards and it seems that they were proceeding well; at
the end, it was known that the current was more powerful than the wind."
Benjamin Franklin became interested in the North Atlantic Ocean circulation patterns. In 1768, while in England, Franklin heard a curious complaint from the Colonial Board of Customs:
"Why did it take British packets several weeks longer to reach New York
from England than it took an average American merchant ship to reach Newport, Rhode Island, despite the merchant ships leaving from London and having to sail down the River Thames and then the length of the English Channel before they sailed across the Atlantic, while the packets left from Falmouth in Cornwall?"
Franklin asked his cousin Timothy Folger, a Nantucket Island
whaling captain, for an answer. Folger explained that merchant ships
routinely crossed the current—which was identified by whale behaviour,
measurement of the water's temperature, and changes in the water's
colour—while the mail packet captains ran against it.
Franklin had Folger sketch the path of the current on a chart of the
Atlantic and add notes on how to avoid the current when sailing from
England to America. Franklin then forwarded the chart to Anthony Todd,
secretary of the British Post Office. Franklin's Gulf Stream chart was printed in 1769 in London, but it was mostly ignored by British sea captains.
A copy of the chart was printed in Paris circa 1770–1773, and a third
version was published by Franklin in Philadelphia in 1786.
Properties
The Gulf Stream proper is a western-intensified current, driven largely by wind stress. In 1958, oceanographer Henry Stommel noted, "very little water from the Gulf of Mexico is actually in the stream". The North Atlantic Current, in contrast, is largely driven by thermohaline circulation.
Its carrying warm water northeast across the Atlantic makes Western
Europe and especially Northern Europe warmer and milder than it
otherwise would be.
Formation and behaviour
Evolution of the Gulf Stream to the west of Ireland continuing as the North Atlantic Current
A river of sea water, called the Atlantic North Equatorial Current,
flows westwards off the coast of Central Africa. When this current
interacts with the northeastern coast of South America, the current
forks into two branches. One passes into the Caribbean Sea, while a second, the Antilles Current, flows north and east of the West Indies. These two branches rejoin north of the Straits of Florida.
The trade winds blow westwards in the tropics, and the westerlies blow eastwards at mid-latitudes. This wind pattern applies a stress to the subtropical ocean surface with negative curl across the north Atlantic Ocean. The resulting Sverdrup transport is equatorward.
Because of the conservation of potential vorticity caused by the northward-moving winds on the subtropical ridge's
western periphery and the increased relative vorticity of
northward-moving water, transport is balanced by a narrow, accelerating
poleward current. This flows along the western boundary of the ocean
basin, outweighing the effects of friction with the western boundary
current, and is known as the Labrador Current.
The conservation of potential vorticity also causes bends along the
Gulf Stream, which occasionally break off as the Gulf Stream's position
shifts, forming separate warm and cold eddies.
This overall process, known as western intensification, causes
currents on the western boundary of an ocean basin, such as the Gulf
Stream, to be stronger than those on the eastern boundary.
As a consequence, the resulting Gulf Stream is a strong ocean
current. It transports water at a rate of 30 million cubic metres per
second (30 sverdrups) through the Florida Straits. As it passes south of Newfoundland, this rate increases to 150 sverdrups.
The volume of the Gulf Stream dwarfs all rivers that empty into the
Atlantic combined, which total 0.6 sverdrups. It is weaker, however,
than the Antarctic Circumpolar Current.
Given the strength and proximity of the Gulf Stream, beaches along the
East Coast of the United States may be more vulnerable to large
sea-level anomalies, which significantly impact rates of coastal erosion.
The Gulf Stream is typically 100 km (62 mi) wide and 800 to
1,200 m (2,600 to 3,900 ft) deep. The current velocity is fastest near
the surface, with the maximum speed typically about 2.5 m/s (5.6 mph).
As it travels north, the warm water transported by the Gulf Stream
undergoes evaporative cooling. The cooling is wind-driven; wind moving
over the water causes evaporation, cooling the water and increasing its salinity and density. When sea ice forms, salts are left out of the ice, a process known as brine exclusion.
These two processes produce water that is denser and colder (or more
precisely, water that is still liquid at a lower temperature). In the
North Atlantic Ocean, the water becomes so dense that it begins to sink
down through less salty and less dense water. (The convective action is similar to a lava lamp.) This downdraft of cold, dense water becomes a part of the North Atlantic Deep Water, a southgoing stream. Very little seaweed lies within the current, although seaweed lies in clusters to its east.
In April 2018, two studies published in the British scientific journal Nature found the Gulf Stream to be at its weakest for at least 1,600 years.
Localized effects
The Gulf Stream is influential on the climate of the Florida peninsula. The portion off the Florida coast, referred to as the Florida Current,
maintains an average water temperature of at least 24 °C (75 °F) during
the winter, and often 29 °C (84 °F) in summer and fall. East winds moving over this warm water move warm air from over the Gulf Stream inland, helping to keep temperatures milder across the state than elsewhere across the Southeastern United States during the winter.
The Gulf Stream carries a wide variety of tropical fish and organisms northward along the East Coast from Florida to extreme southeast Massachusetts
in spring and summer. Following the warm waters of the Gulf Stream,
tropical fish are often encountered off the East Coast as they search
for food, including several species of Batoidea, Dolphin, Barracuda, and Triggerfish. The Gulf Stream's proximity to Nantucket, Massachusetts, adds to its biodiversity,
because it is the northern limit for southern varieties of plant life,
and the southern limit for northern plant species, Nantucket being
warmer during winter than the mainland in winter just 30 miles to the north. North of Nantucket Island along the New England coast northward to the eastern Canadian coast the cold Labrador Current is found.
The North Atlantic Current of the Gulf Stream, along with similar warm air currents, helps keep Ireland and the western coast of Great Britain a few degrees warmer than the east. However, the difference is most dramatic in the western coastal islands of Scotland. A noticeable effect of the Gulf Stream and the strong westerly winds on Europe occurs along the Norwegian coast. Northern parts of Norway lie close to the Arctic
zone, most of which is covered with ice and snow in winter. However,
almost all of Norway's coast remains free of ice and snow throughout the
year.
The warming effect provided by the Gulf Stream has allowed fairly large
settlements to be developed and maintained on the coast of Northern Norway, including Tromsø,
the third-largest city north of the Arctic Circle. Weather systems
warmed by the Gulf Stream drift into Northern Europe, also warming the
climate behind the Scandinavian Mountains.
The possibility of a Gulf Stream collapse has been covered by some news publications. The IPCC Sixth Assessment Report
addressed this issue specifically, and found that based on model
projections and theoretical understanding, the Gulf Stream will not shut
down in a warming climate. While the Gulf Stream is expected to slow down as the Atlantic Meridional Overturning Circulation (AMOC) weakens, it will not collapse, even if the AMOC were to collapse.
Nevertheless, this slowing down will have significant effects,
including a rise in sea level along the North American coast, reduced
precipitation in the midlatitudes, changing patterns of strong
precipitation around Europe and the tropics, and stronger storms in the
North Atlantic.
Effect on cyclone formation
Hurricane Sandy intensified as it tracked northward along the axis of the Gulf Stream in 2012
The warm water and temperature contrast along the edge of the Gulf Stream often increase the intensity of cyclones, tropical or otherwise. Tropical cyclone generation normally requires water temperatures in excess of 26.5 °C (79.7 °F).
Tropical cyclone formation is common over the Gulf Stream, especially
in July. Storms travel westward through the Caribbean and then either
move in a northward direction and curve towards the eastern coast of the
United States or stay on a north-westward track and enter the Gulf of Mexico. Such storms have the potential to create strong winds and extensive damage to the United States' Southeast coastal areas. Hurricane Sandy in 2012 was a recent example of a hurricane tracking along the Gulf Stream and gaining strength.
Strong extratropical cyclones have been shown to deepen significantly along a shallow frontal zone, forced by the Gulf Stream, during the cold season. Subtropical cyclones
also tend to be generated near the Gulf Stream. About 75% of such
systems documented between 1951 and 2000 formed near this warm-water
current, with two annual peaks of activity occurring during May and
October.
Cyclones within the ocean itself form under the Gulf Stream, extending
as deep as 3,500 m (11,500 ft) beneath the ocean's surface.
The Gulf Stream periodically forms rings resulting from a meander of
the Gulf Stream being closed off from an alternate route distinctive
from that meander, creating an independent eddy. These eddies have two
types - cold-core rings, which rotate cyclonically
(counterclockwise in the Northern Hemisphere and clockwise in the
Southern Hemisphere), and warm-core rings, which rotate
anticyclonically. These rings have the capacity to transport the
distinct biological, chemical, and physical properties of their
originating waters to the new waters into which they travel.
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