Analysis of SIF Intrinsic Dynamics

Analysis of SIF Intrinsic Dynamics Abstract. It was recently found that spectral solar incident flux (SIF) as a function of the ultraviolet wavelengths exhibit 1/fà ¯Ã¢â€š ¬Ã‚ ­type power-law correlations. In this study, an attempt was made to explore the SIF intrinsic dynamics versus a wider range of wavelengths, from 115.5nm to 629.5nm. It seemed that the intermittency of SIF data set was very high and the revealed DFA-n exponents were very close to unity. Moreover, the power spectral density was better fitted algebraically than exponentially with exponent very close to unity. Eliminating the fitting of three different types of Planck formula from SIF data set, scaling exponents very close to unity were derived, indicating that the 1/f scaling dynamics concern not the Planck’s law but its variations. 1. Introduction As it is well known, electromagnetic radiation is continuously emitted by every physical body. This emitted radiation is adequately described by Plancks law near thermodynamic equilibrium at a definite temperature. There is a positive correlation between the temperature of an emitting body and the Planck radiation at every wavelength. As the temperature of an emitting surface increases, the maximum wavelength of the emitted radiation increases too. Smith and Gottlieb (1974) re-examined the subject of photon solar flux and its variations versus wavelength and showed that variations in the extreme ultraviolet (UV) spectrum and in the X-ray of solar flux may reach at high orders of magnitude causing significant changes in the Earth’s ionosphere, especially during major solar flares (Kondratyev et al. 1995; Kondratyev and Varotsos 1996; Alexandris et al. 1999; Melnikova 2009; Xue et al. 2011). Simon (1978) examined the solar irradiance fluxes from 120 to 400 nm and suggested that the internal scaling properties of solar radiation during the eleven-year cycle is still unknown, as the cause of the available solar data discrepancies can not be attributed to solar activity. Solanki and Unruh (1998) proposed simple models of the total solar irradiance variations versus wavelength showing that variations on solar flux are mainly caused by magnetic fields at the solar surface. Solar observations may be reproduced by a model of three parameters: the quiet Sun, a facular component and the temperature stratification of sunspots. Tobiska et al. (2000) developed a forecasting solar irradiance model, called SOLAR2000, covering the spectral range of 1–1,000,000 nm. Using this tool, the authors attempted to describe solar variation versus wavelength and through time from X-ray through infrared wavelengths, in order to predict the solar radiation component of the space environment. Very recently, Varotsos et al. (2013a,b) suggested the existence of strong persistent long-range correlations in the solar flux fluctuations versus UV wavelengths. More precisely, by applying the detrending fluctuation analysis (DFA) to the initial SIF versus UV wavelengths data set power-law correlations of the type 1/f, which is omnipresent in nature, was found. In the present study, we examine whether the scaling feature of 1/f noise is apparent in a wider spectrum of SIF, namely for wavelengths (WL) between 115.5 and 629.5nm. 2. Data and analysis As mentioned just above solar incident flux data for WL ranging from 115.5nm to 629.5nm with a step of 1nm were employed. The spectrophotometric data of spectral extraterrestrial solar flux have been taken from the book by Makarova et al. (1991) (see also Makarova et al. 1994; Melnikova and Vasilyev 2005). Fig. 1a depicts SIF values for the wavelength range of 115.5-629.5nm. The principal feature shown in this figure is the existence of non-stationarities into the solar spectral distribution and the strong upward trend. The detrending of this data set was accomplished by applying linear as well as polynomial best fit. To eliminate the non-stationarities of this data set and to detect the intrinsic self-similarity, we applied the well-known DFA method (Peng et al. 1994; Weber and Talkner 2001; Varotsos 2005; Skordas et al. 2010). Furthermore, we calculated the power spectrum for the initial SIF-WL data set, using Fast Fourier Transform (FFT) algorithm as well as the maximum entropy method (MEM) of the TISEAN package (http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.1/index.html). For comparison reasons, we used the Planck formula taking into account the effective temperature obtained from NASA (http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html). A brief description of DFA-tool may be given as follows: Consider the SIF data set x(i) of length N which is integrated over WL. In more detail, to integrate the data, we calculate the à ¯Ã‚ ¬Ã¢â‚¬Å¡uctuations of the N observations x(i) from their mean value xave, notably: x(i) xave. Therefore, the integrated data set, y(i), is consisting of the following points: y(1) = [x(1) − xave], y(2) = [x(1) − xave] + [x(2) − xave], . . . , y(i) = (1) We split the integrated data set into non-overlapping boxes of equal length, Ï„. In each box, a best polynomial local trend (of order n) is à ¯Ã‚ ¬Ã‚ tted in order to detrend the integrated profile (by subtracting the locally fitted trend). The root-mean-square fluctuations Fd (Ï„) of this integrated and detrended profile is calculated over all scales (box sizes). The detrended fluctuation function F is defined by: k = 0, 1, 2,†¦, , (2) where z(i) is a linear least-square fit to the Ï„ data contained within a box (Kantelhardt et al. 2002). In case the signals involve scaling, a power-law behavior for the root-mean-square à ¯Ã‚ ¬Ã¢â‚¬Å¡uctuation function Fd (Ï„) is observed: Fd (Ï„) ∠¼ Ï„a (3) where ÃŽ ± is the scaling exponent, a self-afà ¯Ã‚ ¬Ã‚ nity parameter that represents the long-range power-law correlation (Ausloos and Ivanova 2001). It is worthy of note that a is a generalized Hurst exponent (H) being equal between them for the case of a fractional Gaussian noise (FGN) data set, where 0 1. For a fractional Brownian motion (FBM) data set (1 2) the relation between these exponents is H = a − 1 (Ausloos and Ivanova, 2001). For uncorrelated data, the scaling exponent is ÃŽ ± = 0.5. An exponent ÃŽ ± ≠  0.5 in a certain range of Ï„ values implies the existence of long-range correlations in that time interval. If 0ÃŽ ±ÃŽ ± ≠¤1.0 (and if again the data set is nonintermittent), then persistent long-range power-law correlations prevail (the case ÃŽ ± = 1 corresponds to the so-called 1/f noise) (Weber and Talkner 2001). Finally, the scaling properties of SIF-WL data set were also studied using Haar analysis (Lovejoy and Schertzer, 2012a,b). According to Haar analysis the variation of X parameter fluctuations ΔX with scale Δt can be defined using the â€Å"generalized† qth order structure function Sq(Δt) = ÃŽ §(Δt)q >, where the symbol stands for ensemble averaging. In a scaling regime, Sq(Δt) ≈ ΔtÃŽ ¾(q), where the exponent ÃŽ ¾(q)= qH K(q) and K(q) indicates the scaling intermittency (satisfying K(1) = 0). 3. Discussion and results Varotsos et al. (2013a) studying the high-resolution observations of SIF reaching the ground and the top of the atmosphere, suggested that SIF versus ultraviolet WL exhibit 1/fà ¯Ã¢â€š ¬Ã‚ ­type power-law correlations. This result was derived by applying the DFA method on the SIF dataset obtained from the Villard St. Pancrace station of the Lille University of Sciences and Technology and was based on the slope (i.e., 1.02 ±0.02) of the log – log plot of the root mean square fluctuation function of SIF versus the WL segment size Ï„. In order to further establish the power-law scaling mentioned before, Varotsos et al. (2013b) employed the two criteria suggested by Maraun et al. (2004), notably the rejection of the exponential decay of the autocorrelation function and the constancy of â€Å"local slopes† in a certain range towards the low frequencies. The results showed that the power-law fit on the power spectral density (of the detrended SIF-WL versus logÏ„) was much better than exponential one, for scales higher than Ï„ ≈ 1.4 nm, while the method of local slopes exhibited â€Å"constancy† with constant threshold (a ≈ 0.92) at the same range, Ï„ > 1.4 nm. Therefore, the two criteria of Maraum et al. (2004) were satisfied ensuring the 1/fà ¯Ã¢â€š ¬Ã‚ ­type power-law correlations in SIF versus WL suggested by Varotsos et al. (2013a). In the present study, the scaling dynamics of a wider spectrum of SIF-WL data set was studied, for wavelengths between 115.5 and 629.5nm. Firstly, DFA-n seemed to can take care of the trends revealing a DFA-exponent close to unity (after DFA-2), as shown in Fig. 1b. In the following we plotted the power spectral density (using FFT) of the linearly detrended SIF data set. The derived power spectral density showed that the power-law fitting gives coefficient of determination, R2, higher than the exponential one (see Fig. 2a). This was confirmed by F-test, at 95% confidence level. From the other hand, the DFA-1 exponent was 1.24, while by applying the multiple DFA on the linearly detrended SIF data, the derived exponents ranged from 0.94 to 1. Similar results were derived when we repeated the above mentioned analysis for the polynomially (of 6th degree) detrended SIF data set. The derived power spectral density was, once more, better fitted algebraically than exponentially (a result which was confirmed by F-test, at 95% confidence level), while the linearly DFA-exponent was 1.01 (see Fig.2b). In other words, it seemed that no detrending is needed for the studied data set. Next, to resume our results we analysed the initial SIF-WL data set by using Haar analysis (Lovejoy and Schertzer, 2012a,b). According to Haar analysis, as also mentioned in the Section 2, the variation of SIF fluctuations versus wavelength Ï„ can be defined using the â€Å"generalized† qth order structure function Sq(Ï„) = RF(Ï„)q >, for which it holds that in a scaling regime Sq(Ï„) ≈ Ï„Î ¾(q), where the exponent ÃŽ ¾(q)= qH K(q) and K(q) illustrates the scaling intermittency (satisfying K(1) = 0 and ÃŽ ¾(1) = H). Fig. 3b shows that the intermittency of SIF data set is very high (C1=0.20), hence the RMS exponent = ÃŽ ¾(2)/2=0.60 is quite different from the q=1 exponent (H) and the data are far from Gaussian. In the classical quasi-Gaussian case, K(q) = 0 so that ÃŽ ¾(q) is linear. More generally, if the field is intermittent – for example if it is the result of a multifractal process – then the exponent K(q) is generally non linear and co nvex and characterizes the intermittency. The physical significance of H is thus that it determines the rate at which mean fluctuations grow (H > 0) or decrease (H Ï„. According to Fig. 3a,b, the exponent ÃŽ ¾(2) of the structure function equals to zero (at scales below 10 nm), a fact which means that the power spectrum exponent ÃŽ ²=1+ÃŽ ¾(2) equals to 1 (1/f structure). On the other hand, at larger scales, the exponents ÃŽ ¾(2) and ÃŽ ² seem to equal to 1.2 and 2.2, respectively. To clarify this aspect, we calculated the power spectrum for the initial SIF-WL data set, using the MEM. Then, we plotted in Fig. 4a the power spectral density versus frequency and we compared these results with 1/f and 1/f2.2 structure, following the exponent ÃŽ ¾(2)= 1.2 shown in Fig. 3. Interestingly, the results lied in between these two lines. Furthermore, we calculated the power spectrum for the initial as well as for the polynomially (of 6th and 7th degree) detrended SIF data set, using again the MEM. We plotted in Fig. 4b the power spectral density versus WL and the corresponding algebraically fitting in the range from 10 to 100 nm. In the latter fitting we found exponent very close to unity. However, Varotsos et al. (2013a) tried to formulate the above-shown finding, i.e., that the solar spectral irradiance obeys 1/f power-law as a function of UV wavelength, using the well-known Plancks law: which, in the limit of small wavelengths tends to the Wien approximation: , where I(Ï„,ÃŽ ¤) is the amount of energy emitted at a wavelength Ï„ per unit surface area per unit time per unit solid angle per unit wavelength, T is the temperature of the black body, h is Plancks constant, c is the speed of light, and k is Boltzmanns constant. By applying the DFA method on the various values of I(Ï„,ÃŽ ¤) Varotsos et al. (2013a) showed that the calculated I(Ï„,ÃŽ ¤) values do not obey the 1/fà ¯Ã¢â€š ¬Ã‚ ­type scaling. In an effort to clarify this aspect, we firstly applied on the initial SIF data set a fitting that was based on the Planck formula: Planck(Ï„)= and the derived exponents were a1 = 6799.86 ± 45.39(0.6674%) and b1= 2754.38  ± 15.85 (0.5755%) (see Fig. 5). Next, we applied the formula: p(Ï„)= which releases the exponent in front of the Bose-Einstein distribution giving a possible explanation for the different distribution of photons. The derived exponents were a= 3250.17  ± 90.65 (2.79%), b= 4456.26  ± 121.3 (2.72%) and c= 8.81914  ± 0.2589 (2.94%). Our last step was to use the Planck formula taking into account the effective temperature obtained from NASA. However, since hc = 1.986à ¯Ã†â€™-10-25 Jm and k = 1.38à ¯Ã†â€™-10-23 J/K, the Planck formula gives ÃŽ ¤sun = 5224.3 K while the p(Ï„) formula gives ÃŽ ¤sun = 3229.5 K. Furthermore, the Wien displacement law: Ï„max à ¯Ã†â€™-T = b, where Ï„max = 450 nm is the peak wavelength and b = 2.898à ¯Ã†â€™-10−3mK is a constant of proportionality called Wiens displacement constant, gives ÃŽ ¤sun = 6440K. The analysis based on Planck and Wien laws gives ÃŽ ¤sun = (5224 + 6440) / 2 K = 5832 K which is less than 1% from the effective temperature obtained from NASA. Finally, the application of DFA method on the detrended SIF data, eliminating the fitting of Planck, p(Ï„) and Plank(Ï„, Tef) formula, gave again DFA-exponents very close to 1 (ranging from 1.01 to 1.08) as shown in Fig. 6. All the previous discussion indicates that the 1/f scaling dynamics observed in solar flux concerns not the Planck’s law but its variations. 4. Conclusions The main conclusions of the present survey were: DFA-n applied on the initial SIF data set revealed DFA-exponents very close to unity (after DFA-2). Power spectral density for the linearly detrended SIF data set showed that the power-law fitting gives coefficient of determination, R2, higher than the exponential one, while DFA-1 exponent was 1.24 and DFA-n exponents ranged from 0.94 to 1. Similar results were extracted when we repeated the above mentioned analysis for the polynomially (of 6th degree) detrended SIF data set and it seemed that no detrending is needed for the studied data set. To resume our results we analysed the initial SIF-WL data set by using Haar analysis. As ÃŽ ¹t was derived, the intermittency of SIF data set was very high and the data were far from Gaussian. At scales below 10 nm, the power spectrum exponent ÃŽ ² was almost 1 (1/f structure), while at larger scales, the exponents ÃŽ ¾(2) and ÃŽ ² seemed to equal to 1.2 and 2.2, respectively. The results of the power spectral density for the initial SIF-WL data set (using the MEM) versus frequency seemed to lie in between 1/f and 1/f2.2 structure. The power spectral density versus WL for the initial as well as for the polynomially (of 6th and 7th degree) detrended SIF data set (using again the MEM) revealed also exponent very close to unity. Eliminating the fitting of three different types of Planck formula from SIF data set, scaling exponents very close to unity were derived Finally, the 1/f scaling dynamics observed in solar flux concerns not the Planck’s law but its variations.

Macbeth :: essays research papers

The play is about a man called Macbeth who on his journey home meets three witches who for tell his future as first becoming thane of Cawdor and, later king. Macbeth instantly sercomes to the witches and believes what the witches say. When Duncan announces is successor as his son Malcolm is dream of becoming king through honesty are dashed. Lady Macbeth quickly comes up with a plan to make Macbeth king, by killing king Duncan and making his son Malcolm flee in hope to save his own life. The plan is followed through Duncan dies and Malcolm flees for his life leaving Macbeth as king. But the guilt is too much and he soon starts to see the goast of King Duncan, meanwhile his wife goes insane with guilt and kills herself. Malcolm army soon attacks on Macbeth and Macduff kills Macbeth. Malcolm was made king.Shakespeare use of witches in act 1 scene 3 and act 4 scene 1 is highly significant, I also believe that they say a lot about Shakespeare and how he would of thought. The main reasons though that I feel the witches roles were so significant is because Shakespeare wanted to please the king who was interested in demonology, to expose Macbeths mind the witches sort of showed his conscious escaping. Also to show human weakness or temptation, which gives the audience, a lot to listen for.The witches appearing in Act 1 had a huge affect on the story line. Even before we meet the witches we know the next few minuets will be very important, because of the significant weather change. You notice it has become very dark and tense this instantly makes the audience aware of their surroundings. When you do meet the witches you notice a good use of pathetic fallacy because the sky is dark and gray and so is the mood of the characters.When he meets the witches they tell him of his future as King Macbeths response is the expected yer right its more of a great! He doesn’t seem to need to know how? Or why? Or even how do you know? Which suggests that he may already have had these ambitions he doesn’t seem to question the witches as if he already thought it out minuet by minuet and he doesn’t need any more answers.I also believe that Lady Macbeth shared the same ambitions as her husband because when Macbeth tells her of the witches prophesies she also doesn’t questions whatthe witches say which can suggest she is a witch or that she also has an ambitions of her husband becoming king.

The Red Cross

Kevin Smith The Red Cross is an International organization that thrives on donations and the kindness of others to succeed. This Red Cross supports military families, disaster relief, health and safety training along with education, and blood drives that save thousands of lives yearly. The Red Cross started In the year 1881 and was mainly used to help wounded soldiers from the battlefield. â€Å"The global Red Cross has evolved into the world's largest humanitarian network- the only non-governmental organization with specific irresponsibleness outlined In the Geneva conventions†(RedCross, 2013). The Red Cross has established itself in the cyber community to succeed. With online donations exceeding 36 million dollars the Red Cross has been able to far exceed anything It did In the years prior to the Internet. The Red cross relies on its volunteers as its strength to work donation sites for all actions the organization participates in. The challenges the Red Cross faces today is the ability to keep enough volunteers on hand to run the organization. While the Red cross has full time members like any business this organizations success comes from those willing to help. The challenges the Red Cross faces In the media environment include many things. System hacking can be seen as hackers will set up take websites that look like the Red Cross web page. This in turn turns out to be a scam and people will give donations to a hacker Instead of the Red Cross. There can be other challenges out there for this organization that would include government policy. Foreign policy. ND legislative issues that can be strain the mission of the Red Cross. The Instant access the Red Cross has to the world has helped this organization in ways that are unimaginable. The Instant media environment has created an unlimited amount of people it can reach throughout the world. The money raised on dally donations Is lox the amount today ads It was In the uses. This is due to the instant access the world has to the Red Cross. The Red Cross uses the social media during disasters because this is the fastest and most effective way to reach a large number of Individuals.The Instant media environment has done nothing but help the Red Cross succeed. I mentioned earlier that volunteer are a challenge for the Red Cross, but with social media and instant media the Red Cross as been able alleviate some of the stress as they can collect for volunteers over the internet The Red Cross will use multiple tactics to get its message out to the community. The Red Cross will gain its target audience by associating someone within the organization to speak or Interact with the community that Is In question.This tactic is used by military recruiters and it tends to work well with inner city communities as well as communities with language barriers. The Red Cross has volunteers trot all walks tot elite so it would only be natural to use those people trot that community to spread the Red C ross message too particular group of immunity. The internal messaging of the employees Is that of care for the community and to give security to those in need The mission stays the same in the Red Cross and that is to provide care to all walks of life that may need it.The message stays the same internally throughout the world for the Red Cross as well. The Red Cross is not the largest humanitarian organization by doing things the wrong way. The internal structure is sound and solid and provides excellent support to all communities throughout the world. This is done with compassion, time, and hard work on behalf of the employees and the thousands of volunteers within the organization. I researched the Red Cross for numerous hours and found that it takes compassion and dedication too cause to make this organization successful.The Red Cross can be unified with many different events and by anybody willing to put in the time and energy to do so. I recently was a part of the Golf for Life rally which was to raise money and blood donations for the Red Cross. There are other events that happen all over the United States on a daily basis in which blood and money is raised for this organization. This is not only going on in the United States, but all over the world. If a person was to look up how to do an event on the Red Cross website it would show them exactly not only to go about doing it, but also show them ways it can be successful.

African Americans Played a Key Role in Vietnam War Essay

Thesis: African Americans played a key role in Vietnam War and, in the process, changed the complexion of the U.S. Armed Forces I. African Americans involves in the army a. Irregular percentage of African Americans drafted in the military b. The role of blacks in the Army c. The Vietnam War as a genocide II. Discrimination Issues a. Armed Forces dominated by whites b. Personal racism c. Racist practices against blacks d. African Americans in combat III. Black Women in the Armed Forces a. Segregation in working areas b. Black women and their assignments IV. The Black Power a. Response to racism b. The new black culture c. Black’s own terminology V. Consequences of Black response a. Banned†¦show more content†¦During American involvement in the war, African Americans were listed and reenlisted on the military draft at higher rates than any other nationalities including whites and Latin-Americans (Westheider 9). As a result, more African Americans than any othe r minority fought and died in combat. In addition, they constantly faced racism. One militant protested forcefully against the unfair conditions: â€Å"You should see for yourself how the black man is being treated over here and the ay we are dying. When it comes to rank, we are left out. When it comes to special privileges, we are left out. When it comes to patrols, perataions and so forth, we are first† (Gallagher). According to Dr. Martin Luther King Jr., black youths represented an unequal share of early draftees and faced a significantly higher chance of seeing combat. â€Å"Rumors abounded that the U.S. government were using the Vietnam War as a form of genocide. Money was being pumped into Vietnam instead of poor black communities in America† (Gallegher). Blacks had to deal with many discrimination issues throughout their experiences in Vietnam. â€Å"The armed forces were dominated and controlled by whites, and more often than not the cultural needs of African American were ignored† (Young 339). Dr. King described the Vietnam War as racist stating: â€Å" a white man’s war, a black man’s fight†. However, personal racism was the most noticeable, as stated by James E. Westheider.Show MoreRelatedEssay on The Civil Rights Movement1708 Words   |  7 Pagesof grassroots activists and national leaders to obtain for African Americans the basic rights guaranteed to American citizens in the Constitution. The key players in succeeding with the civil rights movement were the soldiers returning from the war, Martin Luther King Jr, Malcolm X, The Student Nonviolent Coordinating Committee (SNCC), and the anti-Vietnam War activists . During the civil rights movement, nearly every African American had experienced segregation at lunch stands. 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